1
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Šimkovic F, Rossi R, Georges A, Ferrero M. Origin and fate of the pseudogap in the doped Hubbard model. Science 2024; 385:eade9194. [PMID: 39298591 DOI: 10.1126/science.ade9194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 07/09/2024] [Indexed: 09/22/2024]
Abstract
The relationship between the pseudogap and underlying ground-state phases has not yet been rigorously established. We investigated the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations, allowing for the computation of spectral properties in the infinite-size limit and with arbitrary momentum resolution. We found three distinct regimes as a function of doping and interaction strength: a weakly correlated metal, a correlated metal with strong interaction effects, and a pseudogap regime at low doping. We show that the pseudogap forms both at weak coupling, when the magnetic correlation length is large, and at strong coupling, when it is shorter. As the temperature goes to zero, the pseudogap regime extrapolates precisely to the ordered stripe phase found by ground-state methods.
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Affiliation(s)
- Fedor Šimkovic
- CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
| | - Riccardo Rossi
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- LPTMC, CNRS, Sorbonne Université, 4 place Jussieu, F-75005 Paris, France
| | - Antoine Georges
- CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
- DQMP, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève, Suisse
| | - Michel Ferrero
- CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
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2
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Lechiara A, Marino V, Tocchio LF. Variational Monte Carlo study of stripes as a function of doping in thet-t'Hubbard model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:395602. [PMID: 38914109 DOI: 10.1088/1361-648x/ad5b43] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 06/24/2024] [Indexed: 06/26/2024]
Abstract
We perform variational Monte Carlo simulations of the single-band Hubbard model on the square lattice with both nearest (t) and next-nearest (t') neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair-pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.
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Affiliation(s)
- Antonio Lechiara
- Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, I-10129 Torino, Italy
| | - Vito Marino
- Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, I-10129 Torino, Italy
| | - Luca F Tocchio
- Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, I-10129 Torino, Italy
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3
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Bluschke M, Gupta NK, Jang H, Husain AA, Lee B, Kim M, Na M, Dos Remedios B, Smit S, Moen P, Park SY, Kim M, Jang D, Choi H, Sutarto R, Reid AH, Dakovski GL, Coslovich G, Nguyen QL, Burdet NG, Lin MF, Revcolevschi A, Park JH, Geck J, Turner JJ, Damascelli A, Hawthorn DG. Orbital-selective time-domain signature of nematicity dynamics in the charge-density-wave phase of La 1.65Eu 0.2Sr 0.15CuO 4. Proc Natl Acad Sci U S A 2024; 121:e2400727121. [PMID: 38819998 PMCID: PMC11161785 DOI: 10.1073/pnas.2400727121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Accepted: 04/25/2024] [Indexed: 06/02/2024] Open
Abstract
Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump-probe time-resolved resonant X-ray scattering on the (0 0 1) Bragg peak at the Cu [Formula: see text] and O [Formula: see text] resonances, we investigate nonequilibrium dynamics of [Formula: see text] nematic order and its association with both charge density wave (CDW) order and lattice dynamics in La[Formula: see text]Eu[Formula: see text]Sr[Formula: see text]CuO[Formula: see text]. The orbital selectivity of the resonant X-ray scattering cross-section allows nematicity dynamics associated with the planar O 2[Formula: see text] and Cu 3[Formula: see text] states to be distinguished from the response of anisotropic lattice distortions. A direct time-domain comparison of CDW translational-symmetry breaking and nematic rotational-symmetry breaking reveals that these broken symmetries remain closely linked in the photoexcited state, consistent with the stability of CDW topological defects in the investigated pump fluence regime.
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Affiliation(s)
- Martin Bluschke
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - Naman K. Gupta
- Department of Physics and Astronomy, University of Waterloo, Waterloo, ONN2L 3G1, Canada
| | - Hoyoung Jang
- X-ray Free Electron Laser Beamline Division, Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang37673, Gyeongbuk, Republic of Korea
- Photon Science Center, Pohang University of Science and Technology, Pohang37673, Gyeongbuk, Republic of Korea
| | - Ali. A. Husain
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - Byungjune Lee
- Max Planck - Pohang University of Science and Technology/Korea Research Initiative, Center for Complex Phase Materials, Pohang37673, Republic of Korea
- Department of Physics, Pohang University of Science and Technology, Pohang37673, Republic of Korea
| | - Minjune Kim
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - MengXing Na
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - Brandon Dos Remedios
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - Steef Smit
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - Peter Moen
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - Sang-Youn Park
- X-ray Free Electron Laser Beamline Division, Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang37673, Gyeongbuk, Republic of Korea
| | - Minseok Kim
- X-ray Free Electron Laser Beamline Division, Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang37673, Gyeongbuk, Republic of Korea
| | - Dogeun Jang
- X-ray Free Electron Laser Beamline Division, Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang37673, Gyeongbuk, Republic of Korea
| | - Hyeongi Choi
- X-ray Free Electron Laser Beamline Division, Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang37673, Gyeongbuk, Republic of Korea
| | | | - Alexander H. Reid
- Linac Coherent Light Source, Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
| | - Georgi L. Dakovski
- Linac Coherent Light Source, Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
| | - Giacomo Coslovich
- Linac Coherent Light Source, Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
| | - Quynh L. Nguyen
- Linac Coherent Light Source, Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
- Stanford PULSE Institute, Stanford University and Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
| | - Nicolas G. Burdet
- Linac Coherent Light Source, Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
- Stanford Institute for Materials and Energy Sciences, Stanford Linear Accelerator Center National Accelerator Laboratory and Stanford University, Menlo Park, CA94025
| | - Ming-Fu Lin
- Linac Coherent Light Source, Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
| | - Alexandre Revcolevschi
- Institut de Chimie Moléculaire et des Matériaux d’Orsay, Université Paris-Saclay, Centre National de la Recherche Scientifique, UMR 8182, 91405Orsay, France
| | - Jae-Hoon Park
- Max Planck - Pohang University of Science and Technology/Korea Research Initiative, Center for Complex Phase Materials, Pohang37673, Republic of Korea
- Department of Physics, Pohang University of Science and Technology, Pohang37673, Republic of Korea
| | - Jochen Geck
- Institute of Solid State and Materials Physics, Technische Universität Dresden, 01069Dresden, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062Dresden, Germany
| | - Joshua J. Turner
- Linac Coherent Light Source, Stanford Linear Accelerator Center National Accelerator Laboratory, Menlo Park, CA94025
- Stanford Institute for Materials and Energy Sciences, Stanford Linear Accelerator Center National Accelerator Laboratory and Stanford University, Menlo Park, CA94025
| | - Andrea Damascelli
- Quantum Matter Institute, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BCV6T 1Z1, Canada
| | - David G. Hawthorn
- Department of Physics and Astronomy, University of Waterloo, Waterloo, ONN2L 3G1, Canada
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4
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Vinograd I, Souliou SM, Haghighirad AA, Lacmann T, Caplan Y, Frachet M, Merz M, Garbarino G, Liu Y, Nakata S, Ishida K, Noad HML, Minola M, Keimer B, Orgad D, Hicks CW, Le Tacon M. Using strain to uncover the interplay between two- and three-dimensional charge density waves in high-temperature superconducting YBa 2Cu 3O y. Nat Commun 2024; 15:3277. [PMID: 38627407 PMCID: PMC11021565 DOI: 10.1038/s41467-024-47540-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2023] [Accepted: 04/05/2024] [Indexed: 04/19/2024] Open
Abstract
Uniaxial pressure provides an efficient approach to control charge density waves in YBa2Cu3Oy. It can enhance the correlation volume of ubiquitous short-range two-dimensional charge-density-wave correlations, and induces a long-range three-dimensional charge density wave, otherwise only accessible at large magnetic fields. Here, we use x-ray diffraction to study the strain dependence of these charge density waves and uncover direct evidence for a form of competition between them. We show that this interplay is qualitatively described by including strain effects in a nonlinear sigma model of competing superconducting and charge-density-wave orders. Our analysis suggests that strain stabilizes the 3D charge density wave in the regions between disorder-pinned domains of 2D charge density waves, and that the two orders compete at the boundaries of these domains. No signatures of discommensurations nor of pair density waves are observed. From a broader perspective, our results underscore the potential of strain tuning as a powerful tool for probing competing orders in quantum materials.
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Affiliation(s)
- I Vinograd
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077, Göttingen, Germany
| | - S M Souliou
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany
| | - A-A Haghighirad
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany
| | - T Lacmann
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany
| | - Y Caplan
- Racah Institute of Physics, The Hebrew University, Jerusalem, 91904, Israel
| | - M Frachet
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany
| | - M Merz
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany
- Karlsruhe Nano Micro Facility (KNMFi), Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany
| | - G Garbarino
- ESRF, The European Synchrotron, 71, avenue des Martyrs, CS 40220, F-38043, Grenoble Cedex 9, France
| | - Y Liu
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569, Stuttgart, Germany
| | - S Nakata
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569, Stuttgart, Germany
| | - K Ishida
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, D-01187, Dresden, Germany
- Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan
| | - H M L Noad
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, D-01187, Dresden, Germany
| | - M Minola
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569, Stuttgart, Germany
| | - B Keimer
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569, Stuttgart, Germany
| | - D Orgad
- Racah Institute of Physics, The Hebrew University, Jerusalem, 91904, Israel
| | - C W Hicks
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, D-01187, Dresden, Germany
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
| | - M Le Tacon
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Kaiserstr. 12, D-76131, Karlsruhe, Germany.
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5
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Gauquelin N, Forte F, Jannis D, Fittipaldi R, Autieri C, Cuono G, Granata V, Lettieri M, Noce C, Miletto-Granozio F, Vecchione A, Verbeeck J, Cuoco M. Pattern Formation by Electric-Field Quench in a Mott Crystal. NANO LETTERS 2023; 23:7782-7789. [PMID: 37200109 DOI: 10.1021/acs.nanolett.3c00574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The control of the Mott phase is intertwined with the spatial reorganization of the electronic states. Out-of-equilibrium driving forces typically lead to electronic patterns that are absent at equilibrium, whose nature is however often elusive. Here, we unveil a nanoscale pattern formation in the Ca2RuO4 Mott insulator. We demonstrate how an applied electric field spatially reconstructs the insulating phase that, uniquely after switching off the electric field, exhibits nanoscale stripe domains. The stripe pattern has regions with inequivalent octahedral distortions that we directly observe through high-resolution scanning transmission electron microscopy. The nanotexture depends on the orientation of the electric field; it is nonvolatile and rewritable. We theoretically simulate the charge and orbital reconstruction induced by a quench dynamics of the applied electric field providing clear-cut mechanisms for the stripe phase formation. Our results open the path for the design of nonvolatile electronics based on voltage-controlled nanometric phases.
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Affiliation(s)
- Nicolas Gauquelin
- Electron Microscopy for Materials Research (EMAT), Department of Physics, University of Antwerp, BE-2020 Antwerpen, Belgium
- NANOlab Center of Excellence, University of Antwerp, BE-2020 Antwerpen, Belgium
| | - Filomena Forte
- CNR-SPIN, I-84084 Fisciano, Salerno, Italy
- Dipartimento di Fisica "E.R. Caianiello", Università di Salerno, I-84084 Fisciano, Salerno, Italy
| | - Daen Jannis
- Electron Microscopy for Materials Research (EMAT), Department of Physics, University of Antwerp, BE-2020 Antwerpen, Belgium
- NANOlab Center of Excellence, University of Antwerp, BE-2020 Antwerpen, Belgium
| | - Rosalba Fittipaldi
- CNR-SPIN, I-84084 Fisciano, Salerno, Italy
- Dipartimento di Fisica "E.R. Caianiello", Università di Salerno, I-84084 Fisciano, Salerno, Italy
| | - Carmine Autieri
- International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland
| | - Giuseppe Cuono
- International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland
| | - Veronica Granata
- Dipartimento di Fisica "E.R. Caianiello", Università di Salerno, I-84084 Fisciano, Salerno, Italy
| | | | - Canio Noce
- CNR-SPIN, I-84084 Fisciano, Salerno, Italy
- Dipartimento di Fisica "E.R. Caianiello", Università di Salerno, I-84084 Fisciano, Salerno, Italy
| | - Fabio Miletto-Granozio
- CNR-SPIN, I-80126 Napoli, Italy
- Dipartimento di Fisica, Università di Napoli, I-80126 Napoli, Italy
| | - Antonio Vecchione
- CNR-SPIN, I-84084 Fisciano, Salerno, Italy
- Dipartimento di Fisica "E.R. Caianiello", Università di Salerno, I-84084 Fisciano, Salerno, Italy
| | - Johan Verbeeck
- Electron Microscopy for Materials Research (EMAT), Department of Physics, University of Antwerp, BE-2020 Antwerpen, Belgium
- NANOlab Center of Excellence, University of Antwerp, BE-2020 Antwerpen, Belgium
| | - Mario Cuoco
- CNR-SPIN, I-84084 Fisciano, Salerno, Italy
- Dipartimento di Fisica "E.R. Caianiello", Università di Salerno, I-84084 Fisciano, Salerno, Italy
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6
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Wietek A. Fragmented Cooper Pair Condensation in Striped Superconductors. PHYSICAL REVIEW LETTERS 2022; 129:177001. [PMID: 36332257 DOI: 10.1103/physrevlett.129.177001] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
Condensation of bosons in Bose-Einstein condensates or Cooper pairs in superconductors refers to a macroscopic occupation of a few single- or two-particle states. A condensate is called "fragmented" if not a single, but multiple states are macroscopically occupied. While fragmentation is known to occur in particular Bose-Einstein condensates, we propose that fragmentation naturally takes place in striped superconductors. To this end, we investigate the nature of the superconducting ground state realized in the two-dimensional t-t^{'}-J model. In the presence of charge density modulations, the condensate is shown to be fragmented and composed of partial condensates located on the stripes. The fragments of the condensates hybridize to form an extended macroscopic wave function across the system. The results are obtained from evaluating the singlet-pairing two-particle density matrix of the ground state on finite cylinders computed via the density matrix renormalization group method. Our results shed light on the intricate relation between stripe order and superconductivity in systems of strongly correlated electrons.
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Affiliation(s)
- Alexander Wietek
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA and Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, Dresden 01187, Germany
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7
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Zhang S, Zhang P, Chern GW. Anomalous phase separation in a correlated electron system: Machine-learning-enabled large-scale kinetic Monte Carlo simulations. Proc Natl Acad Sci U S A 2022; 119:e2119957119. [PMID: 35486688 PMCID: PMC9170136 DOI: 10.1073/pnas.2119957119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Accepted: 03/25/2022] [Indexed: 11/18/2022] Open
Abstract
SignificancePhase separation is crucial to the functionalities of many correlated electron materials with notable examples including colossal magnetoresistance in manganites and high-Tc superconductivity in cuprates. However, the nonequilibrium phase-separation dynamics in such systems are poorly understood theoretically, partly because the required multiscale modeling is computationally very demanding. With the aid of machine-learning methods, we have achieved large-scale dynamical simulations in a representative correlated electron system. We observe an unusual relaxation process that is beyond the framework of classical phase-ordering theories. We also uncover a correlation-induced freezing behavior, which could be a generic feature of phase separation in correlated electron systems.
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Affiliation(s)
- Sheng Zhang
- Department of Physics, University of Virginia, Charlottesville, VA 22904
| | - Puhan Zhang
- Department of Physics, University of Virginia, Charlottesville, VA 22904
| | - Gia-Wei Chern
- Department of Physics, University of Virginia, Charlottesville, VA 22904
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8
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Qin M. Effect of hole doping on the 120 degree order in the triangular lattice Hubbard model: a Hartree-Fock revisit. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:235603. [PMID: 35294934 DOI: 10.1088/1361-648x/ac5e79] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2021] [Accepted: 03/16/2022] [Indexed: 06/14/2023]
Abstract
We revisit the unrestricted Hartree Fock study on the evolution of the ground state of the Hubbard model on the triangular lattice with hole doping. At half-filling, it is known that the ground state of the Hubbard model on triangular lattice develops a 120 degree coplanar order at half-filling in the strong interaction limit, i.e., in the spin 1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. The ground state property in the doped case is still in controversy even though extensive studies were performed in the past. Within Hartree Fock theory, we find that the 120 degree order persists from zero doping to about 0.3 hole doping. At 1/3 hole doping, a three-sublattice collinear order emerges in which the doped hole is concentrated on one of the three sublattices with antiferromagnetic Neel order on the remaining two sublattices, which forms a honeycomb lattice. Between the 120 degree order and 1/3 doping region, a phase separation occurs in which the 120 degree order coexists with the collinear anti-ferromagnetic order in different regions of the system. The collinear phase extends from 1/3 doping to about 0.41 doping, beyond which the ground state is paramagnetic with uniform electron density. The phase diagram from Hartree Fock could provide guidance for the future study of the doped Hubbard model on triangular lattice with more sophisticated many-body approaches.
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Affiliation(s)
- Mingpu Qin
- Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
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9
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Uniaxial pressure induced stripe order rotation in La1.88Sr0.12CuO4. Nat Commun 2022; 13:1795. [PMID: 35379813 PMCID: PMC8979978 DOI: 10.1038/s41467-022-29465-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 03/16/2022] [Indexed: 11/08/2022] Open
Abstract
AbstractStatic stripe order is detrimental to superconductivity. Yet, it has been proposed that transverse stripe fluctuations may enhance the inter-stripe Josephson coupling and thus promote superconductivity. Direct experimental studies of stripe dynamics, however, remain difficult. From a strong-coupling perspective, transverse stripe fluctuations are realized in the form of dynamic “kinks”—sideways shifting stripe sections. Here, we show how modest uniaxial pressure tuning reorganizes directional kink alignment. Our starting point is La1.88Sr0.12CuO4 where transverse kink ordering results in a rotation of stripe order away from the crystal axis. Application of mild uniaxial pressure changes the ordering pattern and pins the stripe order to the crystal axis. This reordering occurs at a much weaker pressure than that to detwin the stripe domains and suggests a rather weak transverse stripe stiffness. Weak spatial stiffness and transverse quantum fluctuations are likely key prerequisites for stripes to coexist with superconductivity.
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10
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Intertwined spin, charge, and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit. Proc Natl Acad Sci U S A 2022; 119:2112806119. [PMID: 35140180 PMCID: PMC8851552 DOI: 10.1073/pnas.2112806119] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/17/2021] [Indexed: 11/18/2022] Open
Abstract
The high-temperature superconducting cuprates are governed by intertwined striped magnetic and charge orders, in addition to superconductivity. Remarkably similar behavior has also been seen in numerical calculations for the Hubbard model describing the copper–oxygen layers in these materials. Finite-cluster methods typically find that spin- and charge-stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit, often conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in an embedded cluster calculation for the Hubbard model. This discovery demonstrates that striped states survive in the thermodynamic limit and allows us to study their influence on the model’s superconducting properties, where we find evidence for pair-density-wave correlations intertwined with the stripe correlations. The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite-cluster methods typically indicate that stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides an opportunity to study the influence of fluctuating stripe correlations on the model’s pairing correlations within a unified numerical framework. Using this approach, we also find evidence for pair-density-wave correlations whose strength is correlated with that of the stripes.
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11
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Stripe order enhanced superconductivity in the Hubbard model. Proc Natl Acad Sci U S A 2022; 119:2109406119. [PMID: 34930822 PMCID: PMC8740580 DOI: 10.1073/pnas.2109406119] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/05/2021] [Indexed: 11/22/2022] Open
Abstract
The Hubbard model plays a central role in the theory of highly correlated systems. Its simplicity allows conceptual issues—which are generally complicated in the context of experiments on interesting materials—to be sharply posed and definitively answered. Recently, a variety of numerical studies have led to the conclusion that the “pure” Hubbard model on the square lattice at intermediate coupling, U, is not superconducting in the range of electron densities in which many previous approximate treatments had inferred high-temperature superconductivity. Here, using controlled density matrix renormalization group methods, we show that superconductivity is spectacularly enhanced if the hopping matrix elements are periodically modulated in a stripe-like pattern, with important (if suggestive) implications concerning the mechanism of unconventional superconductivity. Unidirectional (“stripe”) charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of “optimal” inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated—mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi–long-range order with a Luttinger exponent, Ksc∼1.
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12
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Topological Doping and Superconductivity in Cuprates: An Experimental Perspective. Symmetry (Basel) 2021. [DOI: 10.3390/sym13122365] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.
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13
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Ground-state phase diagram of the t-t' -J model. Proc Natl Acad Sci U S A 2021; 118:2109978118. [PMID: 34706937 DOI: 10.1073/pnas.2109978118] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/05/2021] [Indexed: 11/18/2022] Open
Abstract
We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.
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14
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Gong S, Zhu W, Sheng DN. Robust d-Wave Superconductivity in the Square-Lattice t-J Model. PHYSICAL REVIEW LETTERS 2021; 127:097003. [PMID: 34506200 DOI: 10.1103/physrevlett.127.097003] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 07/16/2021] [Indexed: 06/13/2023]
Abstract
Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.
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Affiliation(s)
- Shoushu Gong
- Department of Physics, Beihang University, Beijing 100191, China
| | - W Zhu
- School of Science, Westlake University, Hangzhou 310024, China; Institute of Natural Sciences, Westlake Institute of Advanced Study, Hangzhou 310024, China; and Key Laboratory for Quantum Materials of Zhejiang Province, Westlake University, Hangzhou 310024, China
| | - D N Sheng
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA
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15
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Jiang HC, Kivelson SA. High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid. PHYSICAL REVIEW LETTERS 2021; 127:097002. [PMID: 34506188 DOI: 10.1103/physrevlett.127.097002] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
We have performed density-matrix renormalization group studies of a square lattice t-J model with small hole doping, δ≪1, on long four and six-leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, J_{2}=J_{1}/2, such that the undoped (δ=0) "parent" state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the six-leg cylinder in the absence of frustration, we find power-law SC correlations with a Luttinger exponent, K_{SC}≈1, consistent with a strongly diverging SC susceptibility, χ∼T^{-(2-K_{SC})} as the temperature T→0. The spin-spin correlations-as in the undoped state-fall exponentially suggesting that the SC "pairing" correlations evolve smoothly from the insulating parent state.
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Affiliation(s)
- Hong-Chen Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
| | - Steven A Kivelson
- Department of Physics, Stanford University, Stanford, California 94305, USA
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16
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Ricci A, Poccia N, Campi G, Mishra S, Müller L, Joseph B, Shi B, Zozulya A, Buchholz M, Trabant C, Lee JCT, Viefhaus J, Goedkoop JB, Nugroho AA, Braden M, Roy S, Sprung M, Schüßler-Langeheine C. Measurement of Spin Dynamics in a Layered Nickelate Using X-Ray Photon Correlation Spectroscopy: Evidence for Intrinsic Destabilization of Incommensurate Stripes at Low Temperatures. PHYSICAL REVIEW LETTERS 2021; 127:057001. [PMID: 34397237 DOI: 10.1103/physrevlett.127.057001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 05/10/2021] [Indexed: 06/13/2023]
Abstract
We study the temporal stability of stripe-type spin order in a layered nickelate with x-ray photon correlation spectroscopy and observe fluctuations on timescales of tens of minutes over a wide temperature range. These fluctuations show an anomalous temperature dependence: they slow down at intermediate temperatures and speed up on both heating and cooling. This behavior appears to be directly connected with spatial correlations: stripes fluctuate slowly when stripe correlation lengths are large and become faster when spatial correlations decrease. A low-temperature decay of nickelate stripe correlations, reminiscent of what occurs in cuprates as a result of a competition between stripes and superconductivity, hence occurs via loss of both spatial and temporal correlations.
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Affiliation(s)
- Alessandro Ricci
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Nicola Poccia
- Institute for Metallic Materials, Leibniz Institute for Solid State and Materials Research IFW Dresden, 01069 Dresden, Germany
| | - Gaetano Campi
- Institute of Crystallography, CNR, Via Salaria km. 29,3 - 00015 Monterotondo, Roma, Italy
| | - Shrawan Mishra
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- School of Materials Science and Technology, Indian Institute of Technology, Banaras Hindu University, Varanasi 221005, India
| | - Leonard Müller
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Boby Joseph
- Elettra Sincrotrone Trieste, Strada Statale 14 - km 163,5, AREA Science Park, I-34149 Basovizza, Trieste, Italy
| | - Bo Shi
- Van der Waals-Zeeman Institute, University of Amsterdam, 1098 XH Amsterdam, Netherlands
| | - Alexey Zozulya
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Marcel Buchholz
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
| | - Christoph Trabant
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Albert-Einstein-Straße 15, 12489 Berlin, Germany
| | - James C T Lee
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics and Astronomy, Sonoma State University, 1801 East Cotati Avenue, Rohnert Park, California 94928-3609, USA
- Department of Physics, Concordia College, 901 8th Street South, Moorhead, Minnesota 56562 USA
| | - Jens Viefhaus
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Albert-Einstein-Straße 15, 12489 Berlin, Germany
| | - Jeroen B Goedkoop
- Van der Waals-Zeeman Institute, University of Amsterdam, 1098 XH Amsterdam, Netherlands
| | - Agustinus Agung Nugroho
- Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung, Jalan Ganesha 10 Bandung, 40132, Indonesia
| | - Markus Braden
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
| | - Sujoy Roy
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Michael Sprung
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
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17
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Wang Q, von Arx K, Horio M, Mukkattukavil DJ, Küspert J, Sassa Y, Schmitt T, Nag A, Pyon S, Takayama T, Takagi H, Garcia-Fernandez M, Zhou KJ, Chang J. Charge order lock-in by electron-phonon coupling in La 1.675Eu 0.2Sr 0.125CuO 4. SCIENCE ADVANCES 2021; 7:eabg7394. [PMID: 34193430 PMCID: PMC8245032 DOI: 10.1126/sciadv.abg7394] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Accepted: 05/17/2021] [Indexed: 06/13/2023]
Abstract
Charge order is universal to all hole-doped cuprates. Yet, the driving interactions remain an unsolved problem. Electron-electron interaction is widely believed to be essential, whereas the role of electron-phonon interaction is unclear. We report an ultrahigh-resolution resonant inelastic x-ray scattering (RIXS) study of the in-plane bond-stretching phonon mode in stripe-ordered cuprate La1.675Eu0.2Sr0.125CuO4 Phonon softening and lifetime shortening are found around the charge ordering wave vector. In addition to these self-energy effects, the electron-phonon coupling is probed by its proportionality to the RIXS cross section. We find an enhancement of the electron-phonon coupling around the charge-stripe ordering wave vector upon cooling into the low-temperature tetragonal structure phase. These results suggest that, in addition to electronic correlations, electron-phonon coupling contributes substantially to the emergence of long-range charge-stripe order in cuprates.
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Affiliation(s)
- Qisi Wang
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.
| | - Karin von Arx
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Masafumi Horio
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | | | - Julia Küspert
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Yasmine Sassa
- Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Thorsten Schmitt
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Abhishek Nag
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, UK
| | - Sunseng Pyon
- Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
| | - Tomohiro Takayama
- Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Hidenori Takagi
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
| | | | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, UK
| | - Johan Chang
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.
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18
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Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane. Nat Commun 2021; 12:597. [PMID: 33500415 PMCID: PMC7838423 DOI: 10.1038/s41467-020-20824-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 12/21/2020] [Indexed: 11/08/2022] Open
Abstract
In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi2Sr2CaCu2O8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern. Knowledge of effective Coulomb interactions is central to understand emergent quantum phases in strongly correlated systems. Here, Boschini et al. report a dynamic quasi-circular spectrum of charge density wave fluctuations in the CuO2 plane of Bi2Sr2CaCu2O8+δ, shedding a light on understanding how Coulomb interactions can lead to rotational and translational symmetry breaking in the cuprates.
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19
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Julià-Farré S, Müller M, Lewenstein M, Dauphin A. Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator. PHYSICAL REVIEW LETTERS 2020; 125:240601. [PMID: 33412044 DOI: 10.1103/physrevlett.125.240601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 11/05/2020] [Indexed: 06/12/2023]
Abstract
Many-body interactions in topological quantum systems can give rise to new phases of matter, which simultaneously exhibit both rich spatial features and topological properties. In this work, we consider spinless fermions on a checkerboard lattice with nearest and next-to-nearest neighbor interactions. We calculate the phase diagram at half filling, which presents, in particular, an interaction-induced quantum anomalous Hall phase. We study the system at incommensurate fillings using an unrestricted Hartree-Fock ansatz and report a rich zoo of solutions such as self-trapped polarons and domain walls above an interaction-induced topological insulator. We find that, as a consequence of the interplay between the interaction-induced topology and topological defects, these domain walls separate two phases with opposite topological invariants and host topologically protected chiral edge states. Finally, we discuss experimental prospects to observe these novel phenomena in a quantum simulator based on laser-dressed Rydberg atoms in an optical lattice.
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Affiliation(s)
- Sergi Julià-Farré
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - Markus Müller
- Institute for Quantum Information, RWTH Aachen University, D-52074 Aachen, Germany
- Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52428 Jülich, Germany
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
- ICREA, Passeig Lluís Companys 23, 08010 Barcelona, Spain
| | - Alexandre Dauphin
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
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20
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Peng YY, Husain AA, Mitrano M, Sun SXL, Johnson TA, Zakrzewski AV, MacDougall GJ, Barbour A, Jarrige I, Bisogni V, Abbamonte P. Enhanced Electron-Phonon Coupling for Charge-Density-Wave Formation in La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}. PHYSICAL REVIEW LETTERS 2020; 125:097002. [PMID: 32915627 DOI: 10.1103/physrevlett.125.097002] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Revised: 03/04/2020] [Accepted: 07/30/2020] [Indexed: 06/11/2023]
Abstract
Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu L_{3} edge resonant inelastic x-ray scattering, we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}. We investigate the interplay between charge order and EPC as a function of doping and temperature and find that the EPC is enhanced in a narrow momentum region around the CDW ordering vector. By detuning the incident photon energy from the absorption resonance, we extract an EPC matrix element at the CDW ordering vector of M≃0.36 eV, which decreases to M≃0.30 eV at high temperature in the absence of the CDW. Our results suggest a feedback mechanism in which the CDW enhances the EPC which, in turn, further stabilizes the CDW.
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Affiliation(s)
- Y Y Peng
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - A A Husain
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - M Mitrano
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S X-L Sun
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - T A Johnson
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - A V Zakrzewski
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - G J MacDougall
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - A Barbour
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - I Jarrige
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - V Bisogni
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - P Abbamonte
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
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21
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Frano A, Blanco-Canosa S, Keimer B, Birgeneau RJ. Charge ordering in superconducting copper oxides. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:374005. [PMID: 31829986 DOI: 10.1088/1361-648x/ab6140] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2019] [Accepted: 12/12/2019] [Indexed: 06/10/2023]
Abstract
Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.
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Affiliation(s)
- Alex Frano
- Department of Physics, University of California, San Diego, CA 92093, United States of America
| | - Santiago Blanco-Canosa
- Donostia International Physics Center, DIPC, 20018 Donostia-San Sebastian, Basque Country, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
| | - Bernhard Keimer
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Robert J Birgeneau
- Department of Physics, University of California, Berkeley, CA 94720, United States of America
- Department of Materials Science and Engineering, University of California Berkeley, Berkeley, CA 94720, United States of America
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22
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Lin JQ, Miao H, Mazzone DG, Gu GD, Nag A, Walters AC, García-Fernández M, Barbour A, Pelliciari J, Jarrige I, Oda M, Kurosawa K, Momono N, Zhou KJ, Bisogni V, Liu X, Dean MPM. Strongly Correlated Charge Density Wave in La_{2-x}Sr_{x}CuO_{4} Evidenced by Doping-Dependent Phonon Anomaly. PHYSICAL REVIEW LETTERS 2020; 124:207005. [PMID: 32501068 DOI: 10.1103/physrevlett.124.207005] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
The discovery of charge-density-wave-related effects in the resonant inelastic x-ray scattering spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. Here, we report a comprehensive resonant inelastic x-ray scattering study of La_{2-x}Sr_{x}CuO_{4} finding that charge-density wave effects persist up to a remarkably high doping level of x=0.21 before disappearing at x=0.25. The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross section for phonons and charge-density-wave-induced phonon softening. We interpret our results in terms of a charge-density wave that is generated by strong correlations and a phonon response that is driven by the charge-density-wave-induced modification of the lattice.
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Affiliation(s)
- J Q Lin
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - H Miao
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - D G Mazzone
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - G D Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - A Nag
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - A C Walters
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - M García-Fernández
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - A Barbour
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - J Pelliciari
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - I Jarrige
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - M Oda
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - K Kurosawa
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - N Momono
- Department of Sciences and Informatics, Muroran Institute of Technology, Muroran 050-8585, Japan
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - V Bisogni
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - X Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - M P M Dean
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
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23
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Spatially inhomogeneous competition between superconductivity and the charge density wave in YBa 2Cu 3O 6.67. Nat Commun 2020; 11:990. [PMID: 32080170 PMCID: PMC7033133 DOI: 10.1038/s41467-020-14536-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 01/13/2020] [Indexed: 11/08/2022] Open
Abstract
The charge density wave in the high-temperature superconductor YBa2Cu3O7-x (YBCO) has two different ordering tendencies differentiated by their c-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDWs in neighbouring CuO2 bilayers. This discovery has prompted several fundamental questions: how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use x-ray diffraction to study YBa2Cu3O6.67 as a function of magnetic field and temperature. We show that regions with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations impact both the superconducting and normal state properties of YBCO.
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Wang X, Yuan Y, Xue QK, Li W. Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:013002. [PMID: 31487703 DOI: 10.1088/1361-648x/ab41c5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Since the discovery of stripe order in La1.6-x Nd0.4Sr x CuO4 superconductors in 1995, charge ordering in cuprate superconductors has been intensively studied by various experimental techniques. Among these studies, scanning tunneling microscope (STM) plays an irreplaceable role in determining the real space structures of charge ordering. STM imaging of different families of cuprates over a wide range of doping levels reveal similar checkerboard-like patterns, indicating that such a charge ordered state is likely a ubiquitous and intrinsic characteristic of cuprate superconductors, which may shed light on understanding the mechanism of high-temperature superconductivity. In another class of high-temperature superconductors, iron-based superconductors, STM studies reveal several charge ordered states as well, but their real-space patterns and the interplay with superconductivity are markedly different among different materials. In this paper, we present a brief review on STM studies of charge ordering in these two classes of high-temperature superconductors. Possible origins of charge ordering and its interplay with superconductivity will be discussed.
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Affiliation(s)
- Xintong Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China. Collaborative Innovation Center of Quantum Matter, Beijing 100084, People's Republic of China
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25
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Amoretti A, Areán D, Goutéraux B, Musso D. Universal Relaxation in a Holographic Metallic Density Wave Phase. PHYSICAL REVIEW LETTERS 2019; 123:211602. [PMID: 31809185 DOI: 10.1103/physrevlett.123.211602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Revised: 09/04/2019] [Indexed: 06/10/2023]
Abstract
In this Letter, we uncover a universal relaxation mechanism of pinned density waves, combining gauge-gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (e.g., by disorder or lattice effects), these phonons are pinned with a mass m and damped at a rate Ω, which we explicitly compute. This contribution to Ω is distinct from that of topological defects. We show that Ω≃Gm^{2}Ξ, where G is the shear modulus and Ξ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high T_{c} superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.
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Affiliation(s)
- Andrea Amoretti
- Dipartimento di Fisica, Università di Genova, via Dodecaneso 33, I-16146 Genova, Italy and I.N.F.N.-Sezione di Genova and Physique Théorique et Mathématique and International Solvay Institutes Université Libre de Bruxelles, C.P. 231, 1050 Brussels, Belgium
| | - Daniel Areán
- Instituto de Física Teórica UAM/CSIC, Calle Nicolás Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain
| | - Blaise Goutéraux
- CPHT, CNRS, Ecole polytechnique, IP Paris, F-91128 Palaiseau, France and Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
| | - Daniele Musso
- Departamento de Física de Partículas, Universidade de Santiago de Compostela and Instituto Galego de Física de Altas Enerxías (IGFAE), Santiago de Compostela, 15705, Spain
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26
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Jiang HC, Devereaux TP. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping
t
′. Science 2019; 365:1424-1428. [DOI: 10.1126/science.aal5304] [Citation(s) in RCA: 78] [Impact Index Per Article: 15.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2018] [Accepted: 08/20/2019] [Indexed: 11/02/2022]
Affiliation(s)
- Hong-Chen Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, CA 94025, USA
| | - Thomas P. Devereaux
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, CA 94025, USA
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
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27
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Mitrano M, Lee S, Husain AA, Delacretaz L, Zhu M, de la Peña Munoz G, Sun SXL, Joe YI, Reid AH, Wandel SF, Coslovich G, Schlotter W, van Driel T, Schneeloch J, Gu GD, Hartnoll S, Goldenfeld N, Abbamonte P. Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La 2-x Ba x CuO 4. SCIENCE ADVANCES 2019; 5:eaax3346. [PMID: 31453340 PMCID: PMC6697434 DOI: 10.1126/sciadv.aax3346] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2019] [Accepted: 07/03/2019] [Indexed: 05/23/2023]
Abstract
Charge order is universal among high-T c cuprates, but its relation to superconductivity is unclear. While static order competes with superconductivity, dynamic order may be favorable and even contribute to Cooper pairing. Using time-resolved resonant soft x-ray scattering at a free-electron laser, we show that the charge order in prototypical La2-x Ba x CuO4 exhibits transverse fluctuations at picosecond time scales. These sub-millielectron volt excitations propagate by Brownian-like diffusion and have an energy scale remarkably close to the superconducting T c. At sub-millielectron volt energy scales, the dynamics are governed by universal scaling laws defined by the propagation of topological defects. Our results show that charge order in La2-x Ba x CuO4 exhibits dynamics favorable to the in-plane superconducting tunneling and establish time-resolved x-rays as a means to study excitations at energy scales inaccessible to conventional scattering techniques.
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Affiliation(s)
- Matteo Mitrano
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
- Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Sangjun Lee
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
- Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Ali A. Husain
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
- Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Luca Delacretaz
- Department of Physics, Stanford University, Stanford, CA 94305-4060, USA
| | - Minhui Zhu
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | | | - Stella X.-L. Sun
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
- Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Young Il Joe
- National Institute of Standards and Technology, Boulder, CO 80305, USA
| | - Alexander H. Reid
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - Scott F. Wandel
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - Giacomo Coslovich
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - William Schlotter
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - Tim van Driel
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
| | - John Schneeloch
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - G. D. Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Sean Hartnoll
- Department of Physics, Stanford University, Stanford, CA 94305-4060, USA
| | - Nigel Goldenfeld
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Peter Abbamonte
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
- Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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28
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Zhao H, Ren Z, Rachmilowitz B, Schneeloch J, Zhong R, Gu G, Wang Z, Zeljkovic I. Charge-stripe crystal phase in an insulating cuprate. NATURE MATERIALS 2019; 18:103-107. [PMID: 30559411 DOI: 10.1038/s41563-018-0243-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 11/06/2018] [Indexed: 06/09/2023]
Abstract
High-temperature (high-Tc) superconductivity in cuprates arises from carrier doping of an antiferromagnetic Mott insulator. This carrier doping leads to the formation of electronic liquid-crystal phases1. The insulating charge-stripe crystal phase is predicted to form when a small density of holes is doped into the charge-transfer insulator state1-3, but this phase is yet to be observed experimentally. Here, we use surface annealing to extend the accessible doping range in Bi-based cuprates and realize the lightly doped charge-transfer insulating state of the cuprate Bi2Sr2CaCu2O8+x. In this insulating state with a charge transfer gap on the order of ~1 eV, our spectroscopic imaging scanning tunnelling microscopy measurements provide strong evidence for a unidirectional charge-stripe order with a commensurate 4a0 period along the Cu-O-Cu bond. Notably, this insulating charge-stripe crystal phase develops before the onset of the pseudogap and formation of the Fermi surface. Our work provides fresh insight into the microscopic origin of electronic inhomogeneity in high-Tc cuprates.
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Affiliation(s)
- He Zhao
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | - Zheng Ren
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | | | | | | | - Genda Gu
- Brookhaven National Laboratory, Upton, NY, USA
| | - Ziqiang Wang
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | - Ilija Zeljkovic
- Department of Physics, Boston College, Chestnut Hill, MA, USA.
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29
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Zheng BX, Chung CM, Corboz P, Ehlers G, Qin MP, Noack RM, Shi H, White SR, Zhang S, Chan GKL. Stripe order in the underdoped region of the two-dimensional Hubbard model. Science 2018; 358:1155-1160. [PMID: 29191901 DOI: 10.1126/science.aam7127] [Citation(s) in RCA: 107] [Impact Index Per Article: 17.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2017] [Accepted: 10/17/2017] [Indexed: 11/02/2022]
Abstract
Competing inhomogeneous orders are a central feature of correlated electron materials, including the high-temperature superconductors. The two-dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models, even in challenging settings.
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Affiliation(s)
- Bo-Xiao Zheng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA. .,Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
| | - Chia-Min Chung
- Department of Physics and Astronomy, University of California-Irvine, Irvine, CA 92697, USA
| | - Philippe Corboz
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands.,Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Georg Ehlers
- Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Ming-Pu Qin
- Department of Physics, The College of William and Mary, Williamsburg, VA 23187, USA
| | - Reinhard M Noack
- Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Hao Shi
- Department of Physics, The College of William and Mary, Williamsburg, VA 23187, USA
| | - Steven R White
- Department of Physics and Astronomy, University of California-Irvine, Irvine, CA 92697, USA
| | - Shiwei Zhang
- Department of Physics, The College of William and Mary, Williamsburg, VA 23187, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
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30
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Huang EW, Mendl CB, Liu S, Johnston S, Jiang HC, Moritz B, Devereaux TP. Numerical evidence of fluctuating stripes in the normal state of high-Tccuprate superconductors. Science 2017; 358:1161-1164. [DOI: 10.1126/science.aak9546] [Citation(s) in RCA: 94] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Revised: 01/30/2017] [Accepted: 10/02/2017] [Indexed: 11/02/2022]
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31
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High-temperature charge density wave correlations in La 1.875Ba 0.125CuO 4 without spin-charge locking. Proc Natl Acad Sci U S A 2017; 114:12430-12435. [PMID: 29114049 DOI: 10.1073/pnas.1708549114] [Citation(s) in RCA: 67] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic X-ray scattering to follow the evolution of charge correlations in the canonical stripe-ordered cuprate La1.875Ba0.125CuO4 across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates.
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32
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Cai RG, Li L, Wang YQ, Zaanen J. Intertwined Order and Holography: The Case of Parity Breaking Pair Density Waves. PHYSICAL REVIEW LETTERS 2017; 119:181601. [PMID: 29219557 DOI: 10.1103/physrevlett.119.181601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Indexed: 06/07/2023]
Abstract
We present a minimal bottom-up extension of the Chern-Simons bulk action for holographic translational symmetry breaking that naturally gives rise to pair density waves. We construct stationary inhomogeneous black hole solutions in which both the U(1) symmetry and spatially translational symmetry are spontaneously broken at a finite temperature and charge density. This novel solution provides a dual description of a superconducting phase intertwined with charge, current, and parity orders.
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Affiliation(s)
- Rong-Gen Cai
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Li Li
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18018, USA
| | - Yong-Qiang Wang
- Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China
| | - Jan Zaanen
- Institute Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
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33
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Chainani A, Sicot M, Fagot-Revurat Y, Vasseur G, Granet J, Kierren B, Moreau L, Oura M, Yamamoto A, Tokura Y, Malterre D. Evidence for Weakly Correlated Oxygen Holes in the Highest-T_{c} Cuprate Superconductor HgBa_{2}Ca_{2}Cu_{3}O_{8+δ}. PHYSICAL REVIEW LETTERS 2017; 119:057001. [PMID: 28949729 DOI: 10.1103/physrevlett.119.057001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Indexed: 06/07/2023]
Abstract
We study the electronic structure of HgBa_{2}Ca_{2}Cu_{3}O_{8+δ} (Hg1223; T_{c}=134 K) using photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). Resonant valence band PES across the O K edge and Cu L edge identifies correlation satellites originating in O 2p and Cu 3d two-hole final states, respectively. Analyses using the experimental O 2p and Cu 3d partial density of states show quantitatively different on-site Coulomb energy for the Cu site (U_{dd}=6.5±0.5 eV) and O site (U_{pp}=1.0±0.5 eV). Cu_{2}O_{7}-cluster calculations with nonlocal screening explain the Cu 2p core level PES and Cu L-edge XAS spectra, confirm the U_{dd} and U_{pp} values, and provide evidence for the Zhang-Rice singlet state in Hg1223. In contrast to other hole-doped cuprates and 3d-transition metal oxides, the present results indicate weakly correlated oxygen holes in Hg1223.
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Affiliation(s)
- A Chainani
- RIKEN SPring-8 Centre, 1-1-1 Sayo-cho, Hyogo 679-5148, Japan
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
| | - M Sicot
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
| | - Y Fagot-Revurat
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
| | - G Vasseur
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
| | - J Granet
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
| | - B Kierren
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
| | - L Moreau
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
| | - M Oura
- RIKEN SPring-8 Centre, 1-1-1 Sayo-cho, Hyogo 679-5148, Japan
| | - A Yamamoto
- Strong Correlation Physics Division, RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - Y Tokura
- Strong Correlation Physics Division, RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - D Malterre
- Institut Jean Lamour, Université de Lorraine, UMR 7198 CNRS, BP70239, 54506 Vandoeuvre lés Nancy, France
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34
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Schäfer T, Katanin AA, Held K, Toschi A. Interplay of Correlations and Kohn Anomalies in Three Dimensions: Quantum Criticality with a Twist. PHYSICAL REVIEW LETTERS 2017; 119:046402. [PMID: 29341780 DOI: 10.1103/physrevlett.119.046402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2016] [Indexed: 06/07/2023]
Abstract
A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that-in contradiction to the conventional Hertz-Millis-Moriya theory-its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electronic correlations become strong.
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Affiliation(s)
- T Schäfer
- Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna, Austria
| | - A A Katanin
- Institute of Metal Physics, 620990, Kovalevskaya str. 18, Ekaterinburg, Russia and Ural Federal University, Mira str. 19, 620002 Ekaterinburg, Russia
| | - K Held
- Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna, Austria
| | - A Toschi
- Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna, Austria
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35
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Wu J, Bollinger AT, He X, Božović I. Spontaneous breaking of rotational symmetry in copper oxide superconductors. Nature 2017; 547:432-435. [DOI: 10.1038/nature23290] [Citation(s) in RCA: 90] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2016] [Accepted: 06/08/2017] [Indexed: 11/09/2022]
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36
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Abstract
Nuclear magnetic resonance (NMR) shifts, if stripped of their uncertainties, must hold key information about the electronic fluid in the cuprates. The early shift interpretation that favored a single-fluid scenario will be reviewed, as well as recent experiments that reported its failure. Thereafter, based on literature shift data for planar Cu, a contrasting shift phenomenology for cuprate superconductors is developed, which is very different from the early view while being in agreement with all published data. For example, it will be shown that the hyperfine scenario used up to now is inadequate as a large isotropic shift component is discovered. Furthermore, the changes of the temperature dependences of the shifts above and below the superconducting transitions temperature proceed according to a few rules that were not discussed before. It appears that there can be substantial spin shift at the lowest temperature if the magnetic field is perpendicular to the CuO 2 plane, which points to a localization of spin in the 3 d ( x 2 − y 2 ) orbital. A simple model is presented based on the most fundamental findings. The analysis must have new consequences for theory of the cuprates.
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37
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Commensurate 4 a0-period charge density modulations throughout the Bi 2Sr 2CaCu 2O 8+x pseudogap regime. Proc Natl Acad Sci U S A 2016; 113:12661-12666. [PMID: 27791157 DOI: 10.1073/pnas.1614247113] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Theories based upon strong real space (r-space) electron-electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4a0) periodicity should occur in the hole-doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector QA of the CDM to evolve continuously as if driven primarily by momentum-space (k-space) effects. Here we introduce phase-resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this technique reveals a virtually doping-independent locking of the local CDM wavevector at [Formula: see text] throughout the underdoped phase diagram of the canonical cuprate Bi2Sr2CaCu2O8 These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi-surface)-based picture of the cuprate CDMs but are consistent with strong-coupling r-space-based theories. Our findings imply that it is the latter that provides the intrinsic organizational principle for the cuprate CDM state.
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38
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Mankowsky R, Först M, Cavalleri A. Non-equilibrium control of complex solids by nonlinear phononics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:064503. [PMID: 27223639 DOI: 10.1088/0034-4885/79/6/064503] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We review some recent advances in the use of optical fields at terahertz frequencies to drive the lattice of complex materials. We will focus on the control of low energy collective properties of solids, which emerge on average when a high frequency vibration is driven and a new crystal structure induced. We first discuss the fundamentals of these lattice rearrangements, based on how anharmonic mode coupling transforms an oscillatory motion into a quasi-static deformation of the crystal structure. We then discuss experiments, in which selectively changing a bond angle turns an insulator into a metal, accompanied by changes in charge, orbital and magnetic order. We then address the case of light induced non-equilibrium superconductivity, a mysterious phenomenon observed in some cuprates and molecular materials when certain lattice vibrations are driven. Finally, we show that the dynamics of electronic and magnetic phase transitions in complex-oxide heterostructures follow distinctly new physical pathways in case of the resonant excitation of a substrate vibrational mode.
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Affiliation(s)
- Roman Mankowsky
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
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39
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Yamase H, Eberlein A, Metzner W. Coexistence of Incommensurate Magnetism and Superconductivity in the Two-Dimensional Hubbard Model. PHYSICAL REVIEW LETTERS 2016; 116:096402. [PMID: 26991188 DOI: 10.1103/physrevlett.116.096402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2015] [Indexed: 06/05/2023]
Abstract
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Néel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order.
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Affiliation(s)
- Hiroyuki Yamase
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
- National Institute for Materials Science, Tsukuba 305-0047, Japan
| | - Andreas Eberlein
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Walter Metzner
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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40
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Markiewicz RS, Lorenzana J, Seibold G, Bansil A. Short range smectic order driving long range nematic order: example of cuprates. Sci Rep 2016; 6:19678. [PMID: 26813579 PMCID: PMC4728556 DOI: 10.1038/srep19678] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2015] [Accepted: 11/19/2015] [Indexed: 12/03/2022] Open
Abstract
We present a model for describing the combined presence of nematic and 'smectic' or stripe-like orders seen in recent scanning tunneling microscopy (STM) experiments on cuprates. The smectic order is treated as an electronic charge density wave with an associated Peierls distortion or a 'Pomeranchuk wave'. This primary order is restricted to nanoscale domains by disorder effects, while the secondary coupling to strain generates the nematic order with a considerably longer range. A variety of experimental results are shown to be consistent with our theoretical predictions.
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Affiliation(s)
- R. S. Markiewicz
- Physics Department, Northeastern University, Boston MA 02115, USA
| | - J. Lorenzana
- ISC-CNR and Dipartimento di Fisica, Università di Roma “La Sapienza”, P. Aldo Moro 2, 00185 Roma, Italy
- ISC-CNR, Via dei Taurini 19, I-00185 Roma, Italy
| | - G. Seibold
- Institut Für Physik, BTU Cottbus-Senftenberg, PBox 101344, 03013 Cottbus, Germany
| | - A. Bansil
- Physics Department, Northeastern University, Boston MA 02115, USA
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41
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Comin R, Sutarto R, He F, da Silva Neto EH, Chauviere L, Fraño A, Liang R, Hardy WN, Bonn DA, Yoshida Y, Eisaki H, Achkar AJ, Hawthorn DG, Keimer B, Sawatzky GA, Damascelli A. Symmetry of charge order in cuprates. NATURE MATERIALS 2015; 14:796-800. [PMID: 26006005 DOI: 10.1038/nmat4295] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2014] [Accepted: 04/16/2015] [Indexed: 05/23/2023]
Abstract
Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.
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Affiliation(s)
- R Comin
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - R Sutarto
- Canadian Light Source, Saskatoon, Saskatchewan S7N 2V3, Canada
| | - F He
- Canadian Light Source, Saskatoon, Saskatchewan S7N 2V3, Canada
| | - E H da Silva Neto
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada [3] Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany [4] Quantum Materials Program, Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - L Chauviere
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada [3] Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - A Fraño
- 1] Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany [2] Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein Straße 15, 12489 Berlin, Germany
| | - R Liang
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - W N Hardy
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - D A Bonn
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - Y Yoshida
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan
| | - H Eisaki
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan
| | - A J Achkar
- Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
| | - D G Hawthorn
- Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
| | - B Keimer
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - G A Sawatzky
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - A Damascelli
- 1] Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada [2] Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
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42
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Electronic polymers and soft-matter-like broken symmetries in underdoped cuprates. Nat Commun 2015; 6:7691. [PMID: 26144868 PMCID: PMC4506492 DOI: 10.1038/ncomms8691] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2014] [Accepted: 05/29/2015] [Indexed: 11/12/2022] Open
Abstract
Empirical evidence in heavy fermion, pnictide and other systems suggests that unconventional superconductivity appears associated to some form of real-space electronic order. For the cuprates, despite several proposals, the emergence of order in the phase diagram between the commensurate antiferromagnetic state and the superconducting state is not well understood. Here we show that in this regime doped holes assemble in ‘electronic polymers'. Within a Monte Carlo study, we find that in clean systems by lowering the temperature the polymer melt condenses first in a smectic state and then in a Wigner crystal both with the addition of inversion symmetry breaking. Disorder blurs the positional order leaving a robust inversion symmetry breaking and a nematic order, accompanied by vector chiral spin order and with the persistence of a thermodynamic transition. Such electronic phases, whose properties are reminiscent of soft-matter physics, produce charge and spin responses in good accord with experiments. High-Tc superconductivity is thought to be associated with spatial electronic ordering, which for cuprates is not well understood yet. Here the authors use Monte Carlo simulations to show the emergence of a soft-matter-like electronic phase between the antiferromagnetic and the superconducting states.
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43
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From quantum matter to high-temperature superconductivity in copper oxides. Nature 2015; 518:179-86. [PMID: 25673411 DOI: 10.1038/nature14165] [Citation(s) in RCA: 486] [Impact Index Per Article: 54.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2014] [Accepted: 12/22/2014] [Indexed: 11/09/2022]
Abstract
The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.
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44
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McDermott D, Olson Reichhardt CJ, Reichhardt C. Stripe systems with competing interactions on quasi-one dimensional periodic substrates. SOFT MATTER 2014; 10:6332-6338. [PMID: 25030212 DOI: 10.1039/c4sm01341g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of increasing substrate strength or period we show that a remarkable variety of distinct orderings can be realized, including modulated stripes, prolate clump phases, two dimensional ordered kink structures, crystalline void phases, and smectic phases. Additionally in some cases the stripes align perpendicular to the substrate troughs. Our results suggest that a new route to self assembly for systems with competing interactions can be achieved through the addition of a simple periodic modulated substrate.
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Affiliation(s)
- Danielle McDermott
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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45
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Resolving transitions in the mesoscale domain configuration in VO2 using laser speckle pattern analysis. Sci Rep 2014; 4:6259. [PMID: 25178929 PMCID: PMC4151099 DOI: 10.1038/srep06259] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2014] [Accepted: 08/11/2014] [Indexed: 12/02/2022] Open
Abstract
The configuration and evolution of coexisting mesoscopic domains with contrasting material properties are critical in creating novel functionality through emergent physical properties. However, current approaches that map the domain structure involve either spatially resolved but protracted scanning probe experiments without real time information on the domain evolution, or time resolved spectroscopic experiments lacking domain-scale spatial resolution. We demonstrate an elegant experimental technique that bridges these local and global methods, giving access to mesoscale information on domain formation and evolution at time scales orders of magnitude faster than current spatially resolved approaches. Our straightforward analysis of laser speckle patterns across the first order phase transition of VO2 can be generalized to other systems with large scale phase separation and has potential as a powerful method with both spatial and temporal resolution to study phase separation in complex materials.
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46
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Enayat M, Sun Z, Singh UR, Aluru R, Schmaus S, Yaresko A, Liu Y, Lin C, Tsurkan V, Loidl A, Deisenhofer J, Wahl P. Real-space imaging of the atomic-scale magnetic structure of Fe
1+
y
Te. Science 2014; 345:653-6. [DOI: 10.1126/science.1251682] [Citation(s) in RCA: 65] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Mostafa Enayat
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Zhixiang Sun
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Udai Raj Singh
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Ramakrishna Aluru
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Stefan Schmaus
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Alexander Yaresko
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Yong Liu
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Chengtian Lin
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Vladimir Tsurkan
- Center for Electronic Correlations and Magnetism, Experimental Physics V, University of Augsburg, D-86159 Augsburg, Germany
- Institute of Applied Physics, Academy of Sciences of Moldova, MD 2028, Chisinau, Republica Moldova
| | - Alois Loidl
- Center for Electronic Correlations and Magnetism, Experimental Physics V, University of Augsburg, D-86159 Augsburg, Germany
| | - Joachim Deisenhofer
- Center for Electronic Correlations and Magnetism, Experimental Physics V, University of Augsburg, D-86159 Augsburg, Germany
| | - Peter Wahl
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
- Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, UK
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47
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Corboz P, Rice TM, Troyer M. Competing states in the t-J model: uniform D-wave state versus stripe state. PHYSICAL REVIEW LETTERS 2014; 113:046402. [PMID: 25105638 DOI: 10.1103/physrevlett.113.046402] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2014] [Indexed: 06/03/2023]
Abstract
Variational studies of the t-J model on the square lattice based on infinite projected-entangled pair states confirm an extremely close competition between a uniform d-wave superconducting state and different stripe states. The site-centered stripe with an in-phase d-wave order has an equal or only slightly lower energy than the stripe with antiphase d-wave order. The optimal stripe filling is not constant but increases with J/t. A nematic anisotropy reduces the pairing amplitude and the energies of stripe phases are lowered relative to the uniform state with increasing nematicity.
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Affiliation(s)
- Philippe Corboz
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland and Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam, Netherlands
| | - T M Rice
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
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48
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Först M, Tobey RI, Bromberger H, Wilkins SB, Khanna V, Caviglia AD, Chuang YD, Lee WS, Schlotter WF, Turner JJ, Minitti MP, Krupin O, Xu ZJ, Wen JS, Gu GD, Dhesi SS, Cavalleri A, Hill JP. Melting of charge stripes in vibrationally driven La(1.875)Ba(0.125)CuO4: assessing the respective roles of electronic and lattice order in frustrated superconductors. PHYSICAL REVIEW LETTERS 2014; 112:157002. [PMID: 24785066 DOI: 10.1103/physrevlett.112.157002] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Indexed: 05/19/2023]
Abstract
We report femtosecond resonant soft x-ray diffraction measurements of the dynamics of the charge order and of the crystal lattice in nonsuperconducting, stripe-ordered La1.875Ba0.125CuO4. Excitation of the in-plane Cu-O stretching phonon with a midinfrared pulse has been previously shown to induce a transient superconducting state in the closely related compound La1.675Eu0.2Sr0.125CuO4. In La1.875Ba0.125CuO4, we find that the charge stripe order melts promptly on a subpicosecond time scale. Surprisingly, the low temperature tetragonal (LTT) distortion is only weakly reduced, reacting on significantly longer time scales that do not correlate with light-induced superconductivity. This experiment suggests that charge modulations alone, and not the LTT distortion, prevent superconductivity in equilibrium.
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Affiliation(s)
- M Först
- Max-Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - R I Tobey
- Zernike Institute for Advanced Materials, University of Groningen, 9747AG Groningen, Netherlands
| | - H Bromberger
- Max-Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - S B Wilkins
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - V Khanna
- Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom and Diamond Light Source, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom
| | - A D Caviglia
- Max-Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Y-D Chuang
- Advanced Light Source, Lawrence Berkeley Laboratory, Berkeley 94720, California, USA
| | - W S Lee
- SIMES, SLAC National Accelerator Laboratory and Stanford University, Menlo Park 94025, California, USA
| | - W F Schlotter
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park 94025, California, USA
| | - J J Turner
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park 94025, California, USA
| | - M P Minitti
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park 94025, California, USA
| | - O Krupin
- European XFEL GmbH, 22761 Hamburg, Germany
| | - Z J Xu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - J S Wen
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - G D Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - S S Dhesi
- Diamond Light Source, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom
| | - A Cavalleri
- Max-Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany and Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom and Center for Free Electron Laser Science and University of Hamburg, 22761 Hamburg, Germany
| | - J P Hill
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
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49
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Direct observation of dynamic charge stripes in La2-xSrxNiO4. Nat Commun 2014; 5:3467. [PMID: 24632780 DOI: 10.1038/ncomms4467] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2013] [Accepted: 02/18/2014] [Indexed: 11/08/2022] Open
Abstract
The insulator-to-metal transition continues to be a challenging subject, especially when electronic correlations are strong. In layered compounds, such as La2-xSrxNiO4 and La2-xBaxCuO4, the doped charge carriers can segregate into periodically spaced charge stripes separating narrow domains of antiferromagnetic order. Although there have been theoretical proposals of dynamically fluctuating stripes, direct spectroscopic evidence of charge-stripe fluctuations has been lacking. Here we report the detection of critical lattice fluctuations, driven by charge-stripe correlations, in La2-xSrxNiO4 using inelastic neutron scattering. This scattering is detected at large momentum transfers where the magnetic form factor suppresses the spin fluctuation signal. The lattice fluctuations associated with the dynamic charge stripes are narrow in q and broad in energy. They are strongest near the charge-stripe melting temperature. Our results open the way towards the quantitative theory of dynamic stripes and for directly detecting dynamical charge stripes in other strongly correlated systems, including high-temperature superconductors such as La2-xSrxCuO4.
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50
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Barci DG, Mendoza-Coto A, Stariolo DA. Nematic phase in stripe-forming systems within the self-consistent screening approximation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062140. [PMID: 24483418 DOI: 10.1103/physreve.88.062140] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2013] [Indexed: 06/03/2023]
Abstract
We show that in order to describe the isotropic-nematic transition in stripe-forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of a two-point correlation function characteristic of a nematic phase.
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Affiliation(s)
- Daniel G Barci
- Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013 Rio de Janeiro, Brazil
| | - Alejandro Mendoza-Coto
- Departamento de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, RS, Brazil
| | - Daniel A Stariolo
- Departamento de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, RS, Brazil
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