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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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2
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Li Q, Huang HY, Ren T, Weschke E, Ju L, Zou C, Zhang S, Qiu Q, Liu J, Ding S, Singh A, Prokhnenko O, Huang DJ, Esterlis I, Wang Y, Xie Y, Peng Y. Prevailing Charge Order in Overdoped La_{2-x}Sr_{x}CuO_{4} beyond the Superconducting Dome. PHYSICAL REVIEW LETTERS 2023; 131:116002. [PMID: 37774302 DOI: 10.1103/physrevlett.131.116002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Revised: 04/03/2023] [Accepted: 08/24/2023] [Indexed: 10/01/2023]
Abstract
The extremely overdoped cuprates are generally considered to be Fermi liquid metals without exotic orders, whereas the underdoped cuprates harbor intertwined states. Contrary to this conventional wisdom, using Cu L_{3}-edge and O K-edge resonant x-ray scattering, we reveal a charge order (CO) correlation in overdoped La_{2-x}Sr_{x}CuO_{4} (0.35≤x≤0.6) beyond the superconducting dome. This CO has a periodicity of ∼6 lattice units with correlation lengths of ∼20 lattice units. It shows similar in-plane momentum and polarization dependence and dispersive excitations as the CO of underdoped cuprates, but its maximum intensity differs along the c direction and persists up to 300 K. This CO correlation cannot be explained by the Fermi surface instability and its origin remains to be understood. Our results suggest that CO is prevailing in the overdoped metallic regime and requires a reassessment of the picture of overdoped cuprates as weakly correlated Fermi liquids.
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Affiliation(s)
- Qizhi Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Hsiao-Yu Huang
- National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
| | - Tianshuang Ren
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Eugen Weschke
- Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin 14109, Germany
| | - Lele Ju
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Changwei Zou
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Shilong Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Qingzheng Qiu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Jiarui Liu
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - Shuhan Ding
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - Amol Singh
- National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
| | | | - Di-Jing Huang
- National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
| | - Ilya Esterlis
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Yao Wang
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
| | - Yanwu Xie
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Yingying Peng
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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3
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Stabilization of three-dimensional charge order through interplanar orbital hybridization in Pr xY 1-xBa 2Cu 3O 6+δ. Nat Commun 2022; 13:6197. [PMID: 36261435 PMCID: PMC9581994 DOI: 10.1038/s41467-022-33607-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 09/23/2022] [Indexed: 11/09/2022] Open
Abstract
The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the \documentclass[12pt]{minimal}
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\begin{document}$${d}_{{x}^{2}-{y}^{2}}$$\end{document}dx2−y2 orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using Cu L3 and Pr M5 resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa2Cu3O7, where the Pr f-electrons create a direct orbital bridge between CuO2 planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials. External perturbations can induce 3D charge order in cuprates, but the 3D correlation length is limited and the mechanism is not well understood. Ruiz et al. show that Pr substitution in YBa2Cu3O7 enhances interplanar orbital coupling and stabilizes coherent 3D charge order that coexists with superconductivity.
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Nanoscale inhomogeneity of charge density waves dynamics in La2−xSrxNiO4. Sci Rep 2022; 12:15964. [PMID: 36153400 PMCID: PMC9509336 DOI: 10.1038/s41598-022-18925-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 08/22/2022] [Indexed: 11/09/2022] Open
Abstract
AbstractWhile stripe phases with broken rotational symmetry of charge density are known to emerge in doped strongly correlated perovskites, the dynamics and heterogeneity of spatial ordering remain elusive. Here we shed light on the temperature dependent lattice motion and the spatial nanoscale phase separation of charge density wave order in the archetypal striped phase in La2−xSrxNiO4+y (LSNO) perovskite using X-ray photon correlation spectroscopy (XPCS) joint with scanning micro X-ray diffraction (SµXRD). While it is known that the CDW in 1/8 doped cuprates shows a remarkable stability we report the CDW motion dynamics by XPCS in nickelates with an anomalous quantum glass regime at low temperature, T < 65 K, and the expected thermal melting at higher temperature 65 < T < 120 K. The nanoscale CDW puddles with a shorter correlation length are more mobile than CDW puddles with a longer correlation length. The direct imaging of nanoscale spatial inhomogeneity of CDW by scanning micro X-ray diffraction (SµXRD) shows a nanoscale landscape of percolating short range dynamic CDW puddles competing with large quasi-static CDW puddles giving rise to a novel form of nanoscale phase separation of the incommensurate stripes order landscape.
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Harnessing interpretable and unsupervised machine learning to address big data from modern X-ray diffraction. Proc Natl Acad Sci U S A 2022; 119:e2109665119. [PMID: 35679347 PMCID: PMC9214512 DOI: 10.1073/pnas.2109665119] [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] [Indexed: 11/18/2022] Open
Abstract
The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (CaxSr[Formula: see text])3Rh4Sn13, where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd2Re2O7, to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC-revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of [Formula: see text] Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.
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6
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Atomically-resolved interlayer charge ordering and its interplay with superconductivity in YBa 2Cu 3O 6.81. Nat Commun 2021; 12:3893. [PMID: 34162864 PMCID: PMC8222377 DOI: 10.1038/s41467-021-24003-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2020] [Accepted: 05/31/2021] [Indexed: 11/23/2022] Open
Abstract
High-temperature superconductive (SC) cuprates exhibit not only a SC phase, but also competing orders, suppressing superconductivity. Charge order (CO) has been recognized as an important competing order, but its microscopic spatial interplay with SC phase as well as the interlayer coupling in CO and SC phases remain elusive, despite being essential for understanding the physical mechanisms of competing orders and hence superconductivity. Here we report the achievement of direct real-space imaging with atomic-scale resolution of cryogenically cleaved YBa2Cu3O6.81 using cross-sectional scanning tunneling microscopy/spectroscopy. CO nanodomains are found embedded in the SC phase with a proximity-like boundary region characterized by mutual suppression of CO and superconductivity. Furthermore, SC coherence as well as CO occur on both CuO chain and plane layers, revealing carrier transport and density of states mixing between layers. The CO antiphase correlation along the c direction suggests a dominance of Coulomb repulsion over Josephson tunneling between adjacent layers. Charge ordering and superconductivity are known to compete in layered cuprates; however, precise real-space characterization of their interplay has been lacking. Here, the authors address this using atomically-resolved cross-sectional scanning tunnelling microscopy and spectroscopy on cryogenically cleaved YBa2Cu3O6.81.
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7
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Vinograd I, Zhou R, Hirata M, Wu T, Mayaffre H, Krämer S, Liang R, Hardy WN, Bonn DA, Julien MH. Locally commensurate charge-density wave with three-unit-cell periodicity in YBa 2Cu 3O y. Nat Commun 2021; 12:3274. [PMID: 34075033 PMCID: PMC8169916 DOI: 10.1038/s41467-021-23140-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 04/16/2021] [Indexed: 11/20/2022] Open
Abstract
In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW's microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa2Cu3Oy is unidirectional with a commensurate period of three unit cells (λ = 3b), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.
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Affiliation(s)
- Igor Vinograd
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France.
| | - Rui Zhou
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing, China
| | - Michihiro Hirata
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
- MPA-Q, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Tao Wu
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, China
| | - Hadrien Mayaffre
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
| | - Steffen Krämer
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
| | - Ruixing Liang
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
- Canadian Institute for Advanced Research, Toronto, Canada
| | - W N Hardy
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
- Canadian Institute for Advanced Research, Toronto, Canada
| | - D A Bonn
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
- Canadian Institute for Advanced Research, Toronto, Canada
| | - Marc-Henri Julien
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France.
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8
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Abstract
The magnetic-field scale at which superconducting vortices persist in underdoped cuprate superconductors has remained a controversial subject. Here we present an electrical transport study on three distinctly different cuprate families, at temperatures down to 0.32 K and magnetic fields up to 45 T. We reveal the presence of an anomalous vortex liquid state with a highly nonohmic resistivity in all three materials, irrespective of the level of disorder or structural details. The doping and field regime over which this anomalous vortex state persists suggests its occurrence is tied to the presence of long-range charge order under high magnetic field. Our results demonstrate that the intricate interplay between charge order and superconductivity can lead to an exotic vortex state. The interplay between charge order and d-wave superconductivity in high-Tc cuprates remains an open question. While mounting evidence from spectroscopic probes indicates that charge order competes with superconductivity, to date little is known about the impact of charge order on charge transport in the mixed state, when vortices are present. Here we study the low-temperature electrical resistivity of three distinctly different cuprate families under intense magnetic fields, over a broad range of hole doping and current excitations. We find that the electronic transport in the doping regime where long-range charge order is known to be present is characterized by a nonohmic resistivity, the identifying feature of an anomalous vortex liquid. The field and temperature range in which this nonohmic behavior occurs indicates that the presence of long-range charge order is closely related to the emergence of this anomalous vortex liquid, near a vortex solid boundary that is defined by the excitation current in the T→ 0 limit. Our findings further suggest that this anomalous vortex liquid, a manifestation of fragile superconductivity with a suppressed critical current density, is ubiquitous in the high-field state of charge-ordered cuprates.
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9
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Nag A, Zhu M, Bejas M, Li J, Robarts HC, Yamase H, Petsch AN, Song D, Eisaki H, Walters AC, García-Fernández M, Greco A, Hayden SM, Zhou KJ. Detection of Acoustic Plasmons in Hole-Doped Lanthanum and Bismuth Cuprate Superconductors Using Resonant Inelastic X-Ray Scattering. PHYSICAL REVIEW LETTERS 2020; 125:257002. [PMID: 33416344 DOI: 10.1103/physrevlett.125.257002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2020] [Revised: 10/18/2020] [Accepted: 11/13/2020] [Indexed: 06/12/2023]
Abstract
High T_{c} superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic x-ray scattering to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors (La_{1.84}Sr_{0.16}CuO_{4} and Bi_{2}Sr_{1.6}La_{0.4}CuO_{6+δ}), crucially completing the picture. Interestingly, in contrast to the quasistatic charge ordering which manifests at both Cu and O sites, the observed acoustic plasmons are predominantly associated with the O sites, revealing a unique dichotomy in the behavior of valence charges in hole-doped cuprates.
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Affiliation(s)
- Abhishek Nag
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
| | - M Zhu
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Matías Bejas
- Facultad de Ciencias Exactas, Ingeniería y Agrimensura and Instituto de Física de Rosario (UNR-CONICET), Avenida Pellegrini 250, 2000 Rosario, Argentina
| | - J Li
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - H C Robarts
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Hiroyuki Yamase
- International Center of Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0047, Japan
- Department of Condensed Matter Physics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
| | - A N Petsch
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - D Song
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8560, Japan
| | - H Eisaki
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8560, Japan
| | - A C Walters
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
| | | | - Andrés Greco
- Facultad de Ciencias Exactas, Ingeniería y Agrimensura and Instituto de Física de Rosario (UNR-CONICET), Avenida Pellegrini 250, 2000 Rosario, Argentina
| | - S M Hayden
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
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McMahon C, Achkar AJ, da Silva Neto EH, Djianto I, Menard J, He F, Sutarto R, Comin R, Liang R, Bonn DA, Hardy WN, Damascelli A, Hawthorn DG. Orbital symmetries of charge density wave order in YBa 2Cu 3O 6+x. SCIENCE ADVANCES 2020; 6:6/45/eaay0345. [PMID: 33158874 PMCID: PMC7673704 DOI: 10.1126/sciadv.aay0345] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/14/2019] [Accepted: 09/24/2020] [Indexed: 06/11/2023]
Abstract
Charge density wave (CDW) order has been shown to compete and coexist with superconductivity in underdoped cuprates. Theoretical proposals for the CDW order include an unconventional d-symmetry form factor CDW, evidence for which has emerged from measurements, including resonant soft x-ray scattering (RSXS) in YBa2Cu3O6+x (YBCO). Here, we revisit RSXS measurements of the CDW symmetry in YBCO, using a variation in the measurement geometry to provide enhanced sensitivity to orbital symmetry. We show that the (0 0.31 L) CDW peak measured at the Cu L edge is dominated by an s form factor rather than a d form factor as was reported previously. In addition, by measuring both (0.31 0 L) and (0 0.31 L) peaks, we identify a pronounced difference in the orbital symmetry of the CDW order along the a and b axes, with the CDW along the a axis exhibiting orbital order in addition to charge order.
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Affiliation(s)
- Christopher McMahon
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - A J Achkar
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - E H da Silva Neto
- Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- CIFAR, Toronto, Ontario M5G 1Z8, Canada
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
- Department of Physics, University of California, Davis, CA 95616, USA
- Department of Physics, Yale University, New Haven, CT 06511, USA
| | - I Djianto
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - J Menard
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - F He
- Canadian Light Source, Saskatoon, Saskatchewan S7N 2V3, Canada
| | - R Sutarto
- Canadian Light Source, Saskatoon, Saskatchewan S7N 2V3, Canada
| | - R Comin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Ruixing Liang
- CIFAR, Toronto, Ontario M5G 1Z8, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - D A Bonn
- Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- CIFAR, Toronto, Ontario M5G 1Z8, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - W N Hardy
- CIFAR, Toronto, Ontario M5G 1Z8, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - A Damascelli
- Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- CIFAR, Toronto, Ontario M5G 1Z8, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - D G Hawthorn
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
- CIFAR, Toronto, Ontario M5G 1Z8, Canada
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11
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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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12
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Robinson NJ, Johnson PD, Rice TM, Tsvelik AM. Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:126501. [PMID: 31300626 DOI: 10.1088/1361-6633/ab31ed] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Over the past two decades, advances in computational algorithms have revealed a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. On the one hand, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. On the other hand, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reflects a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.
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Affiliation(s)
- Neil J Robinson
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1098 XH Amsterdam, The Netherlands
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13
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Bikondoa O, Bouchenoire L, Brown SD, Thompson PBJ, Wermeille D, Lucas CA, Cooper MJ, Hase TPA. XMaS @ the ESRF. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20180237. [PMID: 31030656 PMCID: PMC6501888 DOI: 10.1098/rsta.2018.0237] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/27/2019] [Indexed: 05/27/2023]
Abstract
This paper describes the motivation for the design and construction of a beamline at the European Synchrotron Radiation Facility (ESRF) for the use of UK material scientists. Although originally focused on the study of magnetic materials, the beamline has been running for 20 years and currently supports a very broad range of science as evidenced by the research topics highlighted in this article. We describe how the beamline will adapt to align with the ESRF's upgrade to a diffraction limited storage ring. This article is part of the theme issue 'Fifty years of synchrotron science: achievements and opportunities'.
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Affiliation(s)
- Oier Bikondoa
- XMaS Beamline, European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble 38043, France
- Department of Physics, University of Warwick, Coventry CV4 7AL, UK
| | - Laurence Bouchenoire
- XMaS Beamline, European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble 38043, France
- Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK
| | - Simon D. Brown
- XMaS Beamline, European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble 38043, France
- Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK
| | - Paul B. J. Thompson
- XMaS Beamline, European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble 38043, France
- Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK
| | - Didier Wermeille
- XMaS Beamline, European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble 38043, France
- Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK
| | - Chris A. Lucas
- Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK
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14
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Evidence for a vestigial nematic state in the cuprate pseudogap phase. Proc Natl Acad Sci U S A 2019; 116:13249-13254. [PMID: 31160468 DOI: 10.1073/pnas.1821454116] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The CuO2 antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E| < [Formula: see text], where [Formula: see text] is the PG energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite-Q density-wave (DW) state and a Q = 0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken-symmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures T DW and T NE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy [Formula: see text] Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi2Sr2CaCu2O8.
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15
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Kim HH, Souliou SM, Barber ME, Lefrançois E, Minola M, Tortora M, Heid R, Nandi N, Borzi RA, Garbarino G, Bosak A, Porras J, Loew T, König M, Moll PJW, Mackenzie AP, Keimer B, Hicks CW, Le Tacon M. Uniaxial pressure control of competing orders in a high-temperature superconductor. Science 2019; 362:1040-1044. [PMID: 30498124 DOI: 10.1126/science.aat4708] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Accepted: 10/25/2018] [Indexed: 11/02/2022]
Abstract
Cuprates exhibit antiferromagnetic, charge density wave (CDW), and high-temperature superconducting ground states that can be tuned by means of doping and external magnetic fields. However, disorder generated by these tuning methods complicates the interpretation of such experiments. Here, we report a high-resolution inelastic x-ray scattering study of the high-temperature superconductor YBa2Cu3O6.67 under uniaxial stress, and we show that a three-dimensional long-range-ordered CDW state can be induced through pressure along the a axis, in the absence of magnetic fields. A pronounced softening of an optical phonon mode is associated with the CDW transition. The amplitude of the CDW is suppressed below the superconducting transition temperature, indicating competition with superconductivity. The results provide insights into the normal-state properties of cuprates and illustrate the potential of uniaxial-pressure control of competing orders in quantum materials.
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Affiliation(s)
- H-H Kim
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - S M Souliou
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France
| | - M E Barber
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - E Lefrançois
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany.,European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France
| | - M Minola
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - M Tortora
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - R Heid
- Institute for Solid State Physics, Karlsruhe Institute of Technology, Hermann-v.-Helmholtz-Platz 176344 Karlsruhe, Germany
| | - N Nandi
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - R A Borzi
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), La Plata, Argentina and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), c.c. 16, suc. 4, 1900 La Plata, Argentina
| | - G Garbarino
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France
| | - A Bosak
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France
| | - J Porras
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - T Loew
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - M König
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - P J W Moll
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - A P Mackenzie
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany.,Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UK
| | - B Keimer
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - C W Hicks
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
| | - M Le Tacon
- Institute for Solid State Physics, Karlsruhe Institute of Technology, Hermann-v.-Helmholtz-Platz 176344 Karlsruhe, Germany.
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16
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Stabilization of three-dimensional charge order in YBa 2Cu 3O 6+x via epitaxial growth. Nat Commun 2018; 9:2978. [PMID: 30061634 PMCID: PMC6065363 DOI: 10.1038/s41467-018-05434-8] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2018] [Accepted: 07/04/2018] [Indexed: 11/25/2022] Open
Abstract
Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has confounded investigations of its impact on the transport and thermodynamic properties. The three-dimensional (3D) CO observed in YBa2Cu3O6+x in high magnetic fields is of particular interest, because quantum transport measurements have revealed detailed information about the corresponding Fermi surface. Here we use resonant X-ray scattering to demonstrate 3D-CO in underdoped YBa2Cu3O6+x films grown epitaxially on SrTiO3 in the absence of magnetic fields. The resonance profiles indicate that Cu sites in the charge-reservoir layers participate in the CO state, and thus efficiently transmit CO correlations between adjacent CuO2 bilayer units. The results offer fresh perspectives for experiments elucidating the influence of 3D-CO on the electronic properties of cuprates without the need to apply high magnetic fields. In many cuprates the high temperature superconducting state competes with a charge ordered phase that has been difficult to investigate in detail. Here the authors show three-dimensional charge order can be stabilized in YBCO films and studied without using the high magnetic fields that are necessary in the bulk material.
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17
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Ekino T, Gabovich AM, Suan Li M, Szymczak H, Voitenko AI. Quasiparticle conductance-voltage characteristics for break junctions involving d-wave superconductors: charge-density-wave effects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:505602. [PMID: 29105650 DOI: 10.1088/1361-648x/aa9867] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Quasiparticle tunnel conductance-voltage characteristics (CVCs), [Formula: see text], were calculated for break junctions (BJs) made up of layered d-wave superconductors partially gapped by charge-density waves (CDWs). The current is assumed to flow in the ab-plane of electrodes. The influence of CDWs is analyzed by comparing the resulting CVCs with CVCs calculated for BJs made up of pure d-wave superconductors with relevant parameters. The main CDW-effects were found to be the appearance of new CVC peculiarities and the loss of CVC symmetry with respect to the V-sign. Tunnel directionality was shown to be one of the key factors in the formation of [Formula: see text] dependences. In particular, the orientation of electrodes with respect to the current channel becomes very important. As a result, [Formula: see text] can acquire a large variety of forms similar to those for tunnel junctions between superconductors with s-wave, d-wave, and mixed symmetry of their order parameters. The diversity of peculiarities is especially striking at finite temperatures. In the case of BJs made up of pure d-wave superconductors, the resulting CVC can include a two-peak gap-driven structure. The results were compared with the experimental BJ data for a number of high-T c oxides. It was shown that the large variety of the observed current-voltage characteristics can be interpreted in the framework of our approach. Thus, quasiparticle tunnel currents in the ab-plane can be used as an additional mean to detect CDWs competing with superconductivity in cuprates or other layered superconductors.
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Affiliation(s)
- T Ekino
- Hiroshima University, Graduate School of Integrated Arts and Sciences, Higashi-Hiroshima, 739-8521, Japan
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18
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Caplan Y, Orgad D. Dimensional Crossover of Charge-Density Wave Correlations in the Cuprates. PHYSICAL REVIEW LETTERS 2017; 119:107002. [PMID: 28949186 DOI: 10.1103/physrevlett.119.107002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Indexed: 06/07/2023]
Abstract
Short-range charge-density wave correlations are ubiquitous in underdoped cuprates. They are largely confined to the copper-oxygen planes and typically oscillate out of phase from one unit cell to the next in the c direction. Recently, it was found that a considerably longer-range charge-density wave order develops in YBa_{2}Cu_{3}O_{6+x} above a sharply defined crossover magnetic field. This order is more three-dimensional and is in-phase along the c axis. Here, we show that such behavior is a consequence of the conflicting ordering tendencies induced by the disorder potential and the Coulomb interaction, where the magnetic field acts to tip the scales from the former to the latter. We base our conclusion on analytic large-N analysis and Monte Carlo simulations of a nonlinear sigma model of competing superconducting and charge-density wave orders. Our results are in agreement with the observed phenomenology in the cuprates, and we discuss their implications to other members of this family, which have not been measured yet at high magnetic fields.
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Affiliation(s)
- Yosef Caplan
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Dror Orgad
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
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19
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Mangin-Thro L, Li Y, Sidis Y, Bourges P. a-b Anisotropy of the Intra-Unit-Cell Magnetic Order in YBa_{2}Cu_{3}O_{6.6}. PHYSICAL REVIEW LETTERS 2017; 118:097003. [PMID: 28306306 DOI: 10.1103/physrevlett.118.097003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2016] [Indexed: 06/06/2023]
Abstract
Within the complex phase diagram of the hole-doped cuprates, seizing the nature of the mysterious pseudogap phase is essential for unraveling the microscopic origin of high-temperature superconductivity. Below the pseudogap temperature T^{⋆}, evidence for intra-unit-cell orders breaking the fourfold rotation symmetry have been provided by neutron diffraction and scanning tunneling spectroscopy. Using polarized neutron diffraction on a detwinned YBa_{2}Cu_{3}O_{6.6} sample, we here report a distinct a-b anisotropy of the intra-unit-cell magnetic structure factor below T^{⋆}, highlighting that intra-unit-cell order in this material breaks the mirror symmetry of the CuO_{2} bilayers. This is likely to originate from a crisscrossed arrangement of loop currents within the CuO_{2} bilayer, resulting in a bilayer mean toroidal axis along the b direction.
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Affiliation(s)
- Lucile Mangin-Thro
- Laboratoire Léon Brillouin, CEA-CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - Yuan Li
- Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Yvan Sidis
- Laboratoire Léon Brillouin, CEA-CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - Philippe Bourges
- Laboratoire Léon Brillouin, CEA-CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
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20
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Fermi liquid behavior of the in-plane resistivity in the pseudogap state of YBa2Cu4O8. Proc Natl Acad Sci U S A 2016; 113:13654-13659. [PMID: 27856753 DOI: 10.1073/pnas.1602709113] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that, inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations [Doiron-Leyraud N, et al. (2007) Nature 447(7144):565-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110(15):5774-5778], and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys Rev B 93:064513] point to a Fermi liquid regime at low temperature in the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity at low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field-induced normal state of underdoped YBa2Cu4O8 that are consistent with a T2 resistivity extending down to 1.5 K. The magnitude of the T2 coefficient, however, is much smaller than expected for a single pocket of the mass and size observed in quantum oscillations, implying that the reconstructed Fermi surface must consist of at least one additional pocket.
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21
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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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22
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Kharkov YA, Sushkov OP. The amplitudes and the structure of the charge density wave in YBCO. Sci Rep 2016; 6:34551. [PMID: 27721385 PMCID: PMC5056359 DOI: 10.1038/srep34551] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Accepted: 09/14/2016] [Indexed: 11/28/2022] Open
Abstract
We find unknown s- and d-wave amplitudes of the recently discovered charge density wave (CDW) in underdoped cuprates. To do so we perform a combined analysis of experimental data for ortho-II YBa2Cu3Oy. The analysis includes data on nuclear magnetic resonance, resonant inelastic X-ray scattering, and hard X-ray diffraction. The amplitude of doping modulation found in our analysis is 3.5 · 10−3 in a low magnetic field and T = 60 K, the amplitude is 6.5 · 10−3 in a magnetic field of 30T and T = 1.3 K. The values are in units of elementary charge per unit cell of a CuO2 plane. We show that the data rule out a checkerboard pattern, and we also show that the data might rule out mechanisms of the CDW which do not include phonons.
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Affiliation(s)
- Y A Kharkov
- School of Physics, University of New South Wales, Sydney 2052, Australia
| | - O P Sushkov
- School of Physics, University of New South Wales, Sydney 2052, Australia
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23
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Chang J, Blackburn E, Ivashko O, Holmes AT, Christensen NB, Hücker M, Liang R, Bonn DA, Hardy WN, Rütt U, Zimmermann MV, Forgan EM, Hayden SM. Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x. Nat Commun 2016; 7:11494. [PMID: 27146255 PMCID: PMC4858734 DOI: 10.1038/ncomms11494] [Citation(s) in RCA: 116] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2016] [Accepted: 04/01/2016] [Indexed: 11/09/2022] Open
Abstract
The application of magnetic fields to layered cuprates suppresses their high-temperature superconducting behaviour and reveals competing ground states. In widely studied underdoped YBa2Cu3O6+x (YBCO), the microscopic nature of field-induced electronic and structural changes at low temperatures remains unclear. Here we report an X-ray study of the high-field charge density wave (CDW) in YBCO. For hole dopings ∼0.123, we find that a field (B∼10 T) induces additional CDW correlations along the CuO chain (b-direction) only, leading to a three-dimensional (3D) ordered state along this direction at B∼15 T. The CDW signal along the a-direction is also enhanced by field, but does not develop an additional pattern of correlations. Magnetic field modifies the coupling between the CuO2 bilayers in the YBCO structure, and causes the sudden appearance of the 3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW at low and high fields, allowing Fermi surface reconstruction, as recently suggested.
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Affiliation(s)
- J Chang
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, Zürich CH-8057, Switzerland
| | - E Blackburn
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK
| | - O Ivashko
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, Zürich CH-8057, Switzerland
| | - A T Holmes
- European Spallation Source ERIC, Box 176, Lund SE-221 00, Sweden
| | - N B Christensen
- Department of Physics, Technical University of Denmark, Kongens Lyngby DK-2800, Denmark
| | - M Hücker
- Condensed Matter Physics &Materials Science Department, Brookhaven National Lab, Upton, New York 11973, USA
| | - Ruixing Liang
- Department of Physics &Astronomy, University of British Columbia, Vancouver V6T-1Z1, Canada.,Canadian Institute for Advanced Research, Toronto M5G-1Z8, Canada
| | - D A Bonn
- Department of Physics &Astronomy, University of British Columbia, Vancouver V6T-1Z1, Canada.,Canadian Institute for Advanced Research, Toronto M5G-1Z8, Canada
| | - W N Hardy
- Department of Physics &Astronomy, University of British Columbia, Vancouver V6T-1Z1, Canada.,Canadian Institute for Advanced Research, Toronto M5G-1Z8, Canada
| | - U Rütt
- Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany
| | - M V Zimmermann
- Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany
| | - E M Forgan
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK
| | - S M Hayden
- H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK
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24
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Hamidian MH, Edkins SD, Joo SH, Kostin A, Eisaki H, Uchida S, Lawler MJ, Kim EA, Mackenzie AP, Fujita K, Lee J, Davis JCS. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x. Nature 2016; 532:343-7. [PMID: 27074504 DOI: 10.1038/nature17411] [Citation(s) in RCA: 169] [Impact Index Per Article: 21.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2015] [Accepted: 02/08/2016] [Indexed: 11/09/2022]
Abstract
The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold (6)Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a 'pair density wave' state. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi2Sr2CaCu2O8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. This phenomenology is consistent with Ginzburg-Landau theory when a charge density wave with d-symmetry form factor and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase.
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Affiliation(s)
- M H Hamidian
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S D Edkins
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA.,School of Physics and Astronomy, University of St Andrews, Fife KY16 9SS, UK
| | - Sang Hyun Joo
- Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, South Korea.,Center for Correlated Electron Systems, Institute of Basic Science, Seoul 151-742, South Korea
| | - A Kostin
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - H Eisaki
- Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
| | - S Uchida
- Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan.,Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0011, Japan
| | - M J Lawler
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA.,Department of Physics, Binghamton University, Binghamton, New York 13902-6000, USA
| | - E-A Kim
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - A P Mackenzie
- School of Physics and Astronomy, University of St Andrews, Fife KY16 9SS, UK.,Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
| | - K Fujita
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Jinho Lee
- Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, South Korea.,Center for Correlated Electron Systems, Institute of Basic Science, Seoul 151-742, South Korea
| | - J C Séamus Davis
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA.,School of Physics and Astronomy, University of St Andrews, Fife KY16 9SS, UK.,Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA.,Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA
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25
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Abstract
We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S = 1/2, charge +e fermionic dimers. The model realizes a "fractionalized Fermi liquid" with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8 × 8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.
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