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Wu M, Shi R, Qi R, Li Y, Du J, Gao P. Four-dimensional electron energy-loss spectroscopy. Ultramicroscopy 2023; 253:113818. [PMID: 37544270 DOI: 10.1016/j.ultramic.2023.113818] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Revised: 06/20/2023] [Accepted: 07/25/2023] [Indexed: 08/08/2023]
Abstract
Recent advances in scanning transmission electron microscopy have enabled atomic-scale focused, coherent, and monochromatic electron probes, achieving nanoscale spatial resolution, meV energy resolution, sufficient momentum resolution, and a wide energy detection range in electron energy-loss spectroscopy (EELS). A four-dimensional EELS (4D-EELS) dataset can be recorded with a slot aperture selecting the specific momentum direction in the diffraction plane and the beam scanning in two spatial dimensions. In this paper, the basic principle of the 4D-EELS technique and a few examples of its application are presented. In addition to parallelly acquired dispersion with energy down to a lattice vibration scale, it can map the real space variation of any EELS spectrum features with a specific momentum transfer and energy loss to study various locally inhomogeneous scattering processes. Furthermore, simple mathematical combinations associating the spectra at different momenta are feasible from the 4D dataset, e.g., the efficient acquisition of a reliable electron magnetic circular dichroism (EMCD) signal is demonstrated. This 4D-EELS technique provides new opportunities to probe the local dispersion and related physical properties at the nanoscale.
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Affiliation(s)
- Mei Wu
- International Center for Quantum Materials, Peking University, Beijing 100871, China; Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China
| | - Ruochen Shi
- International Center for Quantum Materials, Peking University, Beijing 100871, China; Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China
| | - Ruishi Qi
- Department of Physics, University of California at Berkeley, Berkeley 94720, United States
| | - Yuehui Li
- International Center for Quantum Materials, Peking University, Beijing 100871, China; Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China
| | - Jinlong Du
- Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China
| | - Peng Gao
- International Center for Quantum Materials, Peking University, Beijing 100871, China; Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing 100871, China.
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2
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Huber M, Lin Y, Dale N, Sailus R, Tongay S, Kaindl RA, Lanzara A. Revealing the order parameter dynamics of 1T-TiSe[Formula: see text] following optical excitation. Sci Rep 2022; 12:15860. [PMID: 36151110 PMCID: PMC9508156 DOI: 10.1038/s41598-022-19319-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 08/26/2022] [Indexed: 11/09/2022] Open
Abstract
The formation of a charge density wave state is characterized by an order parameter. The way it is established provides unique information on both the role that correlation plays in driving the charge density wave formation and the mechanism behind its formation. Here we use time and angle resolved photoelectron spectroscopy to optically perturb the charge-density phase in 1T-TiSe[Formula: see text] and follow the recovery of its order parameter as a function of energy, momentum and excitation density. Our results reveal that two distinct orders contribute to the gap formation, a CDW order and pseudogap-like order, manifested by an overall robustness to optical excitation. A detailed analysis of the magnitude of the the gap as a function of excitation density and delay time reveals the excitonic long-range nature of the CDW gap and the short-range Jahn-Teller character of the pseudogap order. In contrast to the gap, the intensity of the folded Se[Formula: see text]* band can only give access to the excitonic order. These results provide new information into the the long standing debate on the origin of the gap in TiSe[Formula: see text] and place it in the same context of other quantum materials where a pseudogap phase appears to be a precursor of long-range order.
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Affiliation(s)
- Maximilian Huber
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA
| | - Yi Lin
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA
| | - Nicholas Dale
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA
- Physics Department, University of California Berkeley, Berkeley, CA 94720 USA
| | - Renee Sailus
- Materials Science and Engineering Department, Arizona State University, Phoenix, AZ 85281 USA
| | - Sefaattin Tongay
- Materials Science and Engineering Department, Arizona State University, Phoenix, AZ 85281 USA
| | - Robert A. Kaindl
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA
- Department of Physics and CXFEL Labs, Arizona State University, Phoenix, AZ 85287 USA
| | - Alessandra Lanzara
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA
- Physics Department, University of California Berkeley, Berkeley, CA 94720 USA
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de Mello EVL. The charge-density-wave signature on the superfluid density of cuprate superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:145503. [PMID: 33395674 DOI: 10.1088/1361-648x/abd812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 01/04/2021] [Indexed: 06/12/2023]
Abstract
The superfluid density or superconducting (SC) carrier concentrationnscof cuprates has been the subject of intense investigations but there is not any single theory capable to explain all the available data. Here we show that the behavior ofnscin under and overdoped cuprates are a consequence of an SC interaction based on charge fluctuations in the incommensurate charge-density-waves (CDW) domains. We have shown that this interaction scales with the CDW amplitude or the pseudogap (PG) energy, yielding local SC amplitudes and Josephson currents. The average Josephson energyEJis proportional to the phase stiffness or superfluid densityρsc∝nsc. We find thatnsc(p) increases almost linearly with dopingpin the underdoped region and in the charge abundant overdoped only a few fractions of the holes condense leading to two kinds of carriers, a recently confirmed feature. The calculations and theρscdata uncover how the PG-CDW-SC intertwined orders operate to yield cuprates properties.
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Affiliation(s)
- E V L de Mello
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, RJ, Brazil
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4
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Heath JT, Bedell KS. Universal signatures of Majorana-like quasiparticles in strongly correlated Landau-Fermi liquids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:485602. [PMID: 32903219 DOI: 10.1088/1361-648x/abaeb0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Accepted: 08/12/2020] [Indexed: 06/11/2023]
Abstract
Motivated by recent experiments in the Kitaev honeycomb lattice, Kondo insulators, and the 'Luttinger's theorem-violating' Fermi liquid phase of the underdoped cuprates, we extend the theoretical machinery of Landau-Fermi liquid theory to a system of itinerant, interacting Majorana-like particles. Building upon a previously introduced model of 'nearly self-conjugate' fermionic polarons, a Landau-Majorana kinetic equation is introduced to describe the collective modes and Fermi surface instabilities in a fluid of particles whose fermionic degrees of freedom obey the Majorana reality condition. At large screening, we show that the Landau-Majorana liquid harbors a Lifshitz transition for specific values of the driving frequency. Moreover, we find the dispersion of the zero sound collective mode in such a system, showing that there exists a specific limit where the Landau-Majorana liquid harbors a stability against Pomeranchuk deformations unseen in the conventional Landau-Fermi liquid. With these results, our work paves the way for possible extensions of the Landau quasiparticle paradigm to nontrivial metallic phases of matter.
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Affiliation(s)
- Joshuah T Heath
- Physics Department, Boston College, Chestnut Hill, Massachusetts 02467, United States of America
| | - Kevin S Bedell
- Physics Department, Boston College, Chestnut Hill, Massachusetts 02467, United States of America
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5
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Mello EVLD. A framework for the description of charge order, pseudo and superconducting gap, critical temperature and pairing interaction in cuprate superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:40LT02. [PMID: 32580169 DOI: 10.1088/1361-648x/ab9fd5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 06/24/2020] [Indexed: 06/11/2023]
Abstract
A unified phenomenological description framework is proposed for the evaluation of some of the most important observables of the cuprate superconductors: the pseudogap (PG) ΔPG, the local superconducting amplitudes ΔSC(ri), the critical temperatureTcand charge ordering (CO) parameters. Recent detailed measurements of CO structures and CO wavelengthsλCOare faithfully reproduced by solutions of a Cahn-Hilliard differential equation with a free energy potentialVGLthat produces alternating small charge modulations. The charge oscillations induce atomic fluctuations that mediate the SC pair interaction proportional to theVGLamplitude. The local SC amplitude and phaseθiare connected by Josephson couplingEJ(rij) and the SC long-range order transition occurs whenEJ∼kBTc. The calculated results of the wavelengthλCO, ΔPG,ΔSCandTccalculations are in good agreement with a variety of experiments.
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Affiliation(s)
- E V L de Mello
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, RJ, Brazil
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Sacks W, Mauger A, Noat Y. Origin of the Fermi arcs in cuprates: a dual role of quasiparticle and pair excitations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:475703. [PMID: 30387443 DOI: 10.1088/1361-648x/aae7af] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Angle resolved photoemission spectroscopy (ARPES) mesurements in cuprates have given key information on the temperature and angle dependence of the gap (d-wave order parameter, Fermi arcs and pseudogap). We show that these features can be understood in terms of a Bose condensation of interacting pairons (preformed hole pairs which form in their local antiferromagnetic environment). Starting from the basic properties of the pairon wavefunction, we derive the corresponding k-space spectral function. The latter explains the variation of the ARPES spectra as a function of temperature and angle up to T *, the onset temperature of pairon formation. While Bose excitations dominate at the antinode, the fermion excitations dominate around the nodal direction, giving rise to the Fermi arcs at finite temperature. This dual role is the key feature distinguishing cuprate from conventional superconductivity.
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Affiliation(s)
- William Sacks
- Sorbonne Université, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, CNRS, UMR 7590, 4 Place Jussieu, 75005 Paris, France
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7
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Sacks W, Mauger A, Noat Y. Universal spectral signatures in pnictides and cuprates: the role of quasiparticle-pair coupling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:445601. [PMID: 28837054 DOI: 10.1088/1361-648x/aa884a] [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
Understanding the physical properties of a large variety of high-T c superconductors (SC), the cuprate family as well as the more recent iron-based superconductors, is still a major challenge. In particular, these materials exhibit the 'peak-dip-hump' structure in the quasiparticle density of states (DOS). The origin of this structure is explained within our pair-pair interaction (PPI) model: The non-superconducting state consists of incoherent pairs, a 'Cooper-pair glass' which, due to the PPI, undergoes a Bose-like condensation below T c to the coherent SC state. We derive the equations of motion for the quasiparticle operators showing that the DOS 'peak-dip-hump' is caused by the coupling between quasiparticles and excited pair states, or 'super-quasiparticles'. The renormalized SC gap function becomes energy-dependent and non retarded, reproducing accurately the experimental spectra of both pnictides and cuprates, despite the large difference in gap value.
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Affiliation(s)
- William Sacks
- Institut de Minéralogie, de Physique des Matériaux, et de Cosmochimie (IMPMC), UMR 7590, Sorbonne Universités, UPMC Paris 6, 4 place Jussieu, 75252 Paris Cedex 05, France
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8
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Miller TL, Zhang W, Eisaki H, Lanzara A. Particle-Hole Asymmetry in the Cuprate Pseudogap Measured with Time-Resolved Spectroscopy. PHYSICAL REVIEW LETTERS 2017; 118:097001. [PMID: 28306293 DOI: 10.1103/physrevlett.118.097001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Indexed: 06/06/2023]
Abstract
One of the most puzzling features of high-temperature cuprate superconductors is the pseudogap state, which appears above the temperature at which superconductivity is destroyed. There remain fundamental questions regarding its nature and its relation to superconductivity. But to address these questions, we must first determine whether the pseudogap and superconducting states share a common property: particle-hole symmetry. We introduce a new technique to test particle-hole symmetry by using laser pulses to manipulate and measure the chemical potential on picosecond time scales. The results strongly suggest that the asymmetry in the density of states is inverted in the pseudogap state, implying a particle-hole asymmetric gap. Independent of interpretation, these results can test theoretical predictions of the density of states in cuprates.
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Affiliation(s)
- Tristan L Miller
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Wentao Zhang
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Hiroshi Eisaki
- Electronics and Photonics Research Institute, National Institute of Advanced Industrial Science and Technology, Ibaraki 305-8568, Japan
| | - Alessandra Lanzara
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics, University of California, Berkeley, California 94720, USA
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9
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Bruér J, Maggio-Aprile I, Jenkins N, Ristić Z, Erb A, Berthod C, Fischer Ø, Renner C. Revisiting the vortex-core tunnelling spectroscopy in YBa2Cu3O7-δ. Nat Commun 2016; 7:11139. [PMID: 27030516 PMCID: PMC4821883 DOI: 10.1038/ncomms11139] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Accepted: 02/24/2016] [Indexed: 11/15/2022] Open
Abstract
The observation by scanning tunnelling spectroscopy of Abrikosov vortex cores in the high-temperature superconductor YBa2Cu3O7-δ (Y123) has revealed a robust pair of electron-hole symmetric states at finite subgap energy. Their interpretation remains an open question because theory predicts a different signature in the vortex cores, characterized by a strong zero-bias conductance peak. Here, we present scanning tunnelling spectroscopy data on very homogeneous Y123 at 0.4 K revealing that the subgap features do not belong to vortices: they are actually observed everywhere along the surface with high spatial and energy reproducibility, even in the absence of magnetic field. Detailed analysis and modelling show that these states remain unpaired in the superconducting phase and belong to an incoherent channel, which contributes to the tunnelling signal in parallel with the superconducting density of states.
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Affiliation(s)
- Jens Bruér
- Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - Ivan Maggio-Aprile
- Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - Nathan Jenkins
- Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - Zoran Ristić
- Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - Andreas Erb
- Walther-Meissner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meissner-Strasse 8, D-85748 Garching, Germany
| | - Christophe Berthod
- Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - Øystein Fischer
- Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - Christoph Renner
- Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
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10
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Chatterjee U, Zhao J, Iavarone M, Di Capua R, Castellan JP, Karapetrov G, Malliakas CD, Kanatzidis MG, Claus H, Ruff JPC, Weber F, van Wezel J, Campuzano JC, Osborn R, Randeria M, Trivedi N, Norman MR, Rosenkranz S. Emergence of coherence in the charge-density wave state of 2H-NbSe2. Nat Commun 2015; 6:6313. [PMID: 25687135 PMCID: PMC4339883 DOI: 10.1038/ncomms7313] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2014] [Accepted: 01/19/2015] [Indexed: 12/02/2022] Open
Abstract
A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature Tcdw. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at Tcdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states. Charge density waves are described by a complex order parameter whose amplitude is expected to vanish at the transition temperature. This study shows that the transition in 2H-NbSe2 is driven by fluctuations of the phase of the order parameter, with a finite amplitude surviving in the disordered state.
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Affiliation(s)
- U Chatterjee
- 1] Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - J Zhao
- 1] Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA [2] Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
| | - M Iavarone
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - R Di Capua
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - J P Castellan
- 1] Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] Institute of Solid State Physics, Karlsruhe Institute of Technology, PO Box 3640, D-76021 Karlsruhe, Germany
| | - G Karapetrov
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - C D Malliakas
- 1] Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - M G Kanatzidis
- 1] Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - H Claus
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - J P C Ruff
- 1] Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] CHESS, Cornell University, Ithaca, New York 14853, USA
| | - F Weber
- 1] Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] Institute of Solid State Physics, Karlsruhe Institute of Technology, PO Box 3640, D-76021 Karlsruhe, Germany
| | - J van Wezel
- 1] Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] Institute for Theoretical Physics, University of Amsterdam, Tyndall Avenue, 1090 GL Amsterdam, The Netherlands
| | - J C Campuzano
- 1] Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA [2] Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
| | - R Osborn
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M Randeria
- Department of Physics, Ohio State University, Columbus, Ohio 43210, USA
| | - N Trivedi
- Department of Physics, Ohio State University, Columbus, Ohio 43210, USA
| | - M R Norman
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - S Rosenkranz
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
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11
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Kirzhner T, Koren G. Pairing and the phase diagram of the normal coherence length ξN(T, x) above Tc of La(2-x)Sr(x)CuO4 thin films probed by the Josephson effect. Sci Rep 2014; 4:6244. [PMID: 25175417 PMCID: PMC4150101 DOI: 10.1038/srep06244] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2014] [Accepted: 08/08/2014] [Indexed: 11/09/2022] Open
Abstract
The long range proximity effect in high-Tc c-axis Josephson junctions with a high-Tc barrier of lower Tc is still a puzzling phenomenon. It leads to supercurrents in junctions with much thicker barriers than would be allowed by the conventional proximity effect. Here we measured the T − x (Temperature-doping level) phase diagram of the barrier coherence length ξN(T, x), and found an enhancement of ξN at moderate under-doping and high temperatures. This indicates that a possible origin of the long range proximity effect in the cuprate barrier is the conjectured pre-formed pairs in the pseudogap regime, which increase the length scale over which superconducting correlations survive in the seemingly normal barrier. In more details, we measured the supercurrents Ic of Superconducting - Normal - Superconducting SNS c-axis junctions, where S was optimally doped Y Ba2Cu3O7−δ below Tc (90 K) and N was La2−xSrxCuO4 above its Tc (<25 K) but in the pseudogap regime. From the exponential decay of Ic(T) ∝ exp[−d/ξN(T)], where d is the barrier thickness, the ξN(T) values were extracted. By repeating these measurements for different barrier doping levels x, the whole phase diagram of ξN(T, x) was obtained.
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Affiliation(s)
- Tal Kirzhner
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Gad Koren
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
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12
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Sugai S, Takayanagi Y, Hayamizu N, Muroi T, Shiozaki R, Nohara J, Takenaka K, Okazaki K. Superconducting pairing and the pseudogap in the nematic dynamical stripe phase of La2-xSrxCuO4. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:475701. [PMID: 24166932 DOI: 10.1088/0953-8984/25/47/475701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Fully absorption coefficient corrected Raman spectra were obtained in La2-xSrxCuO4. The B1g spectra have a Fleury-Loudon type two-magnon peak (resonant term) whose energy decreases from 3180 cm(-1) (394 meV) to 440 cm(-1) (55 meV) on increasing the carrier density from x = 0 to 0.25, while the B2g spectra have a 1000-3500 cm(-1) (124-434 meV) hump (hill) whose lower-edge energy increases from x = 0 to 0.115 and then stays constant to x = 0.25. The B2g hump is assigned to the electronic scattering (non-resonant term) of the spectral function with magnetic self-energy. The completely different carrier density dependence arises from anisotropic magnetic excitations of spin-charge stripes. The B1g spectra were assigned to the sum of k ∥ and k⊥ stripe excitations and the B2g spectra to k⊥ stripe excitations according to the calculation by Seibold and Lorenzana (2006 Phys. Rev. B 73 144515). The k ∥ and k⊥ stripe excitations in fluctuating spin-charge stripes were separately detected for the first time. The appearance of only k⊥ stripe excitations in the electronic scattering arises from the charge hopping perpendicular to the stripe. This is the same direction as the Burgers vector of the edge dislocation in metal. The successive charge hopping in the Burgers vector direction across the charge stripes may cause Cooper pairs as predicted by Zaanen et al (2004 Ann. Phys. 310 181). Indeed, this is supported by the experimental fact that the superconducting coherent length coincides with the inter-charge stripe distance in the wide carrier density range. The one-directional charge hopping perpendicular to the stripe causes the flat Fermi surface and the pseudogap near (π,0) and (0,π), but the states around (π/2,π/2) cannot be produced. The low-energy Raman scattering disclosed that the electronic states at the Fermi arc around (π/2,π/2) are coupled to the A1g soft phonon of the tetragonal-orthorhombic phase transition. This suggests that the Fermi arc is produced by the electron-phonon interaction. All the present Raman data suggest that Cooper pairs are formed at moving edge dislocations of dynamical charge stripes.
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Affiliation(s)
- S Sugai
- Department of Physics, Arts and Science, Petroleum Institute, PO Box 2533, Abu Dhabi, UAE. Department of Physics, Faculty of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
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13
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Sakai S, Blanc S, Civelli M, Gallais Y, Cazayous M, Méasson MA, Wen JS, Xu ZJ, Gu GD, Sangiovanni G, Motome Y, Held K, Sacuto A, Georges A, Imada M. Raman-scattering measurements and theory of the energy-momentum spectrum for underdoped Bi2Sr2CaCuO(8+δ) superconductors: evidence of an s-wave structure for the pseudogap. PHYSICAL REVIEW LETTERS 2013; 111:107001. [PMID: 25166695 DOI: 10.1103/physrevlett.111.107001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2013] [Indexed: 06/03/2023]
Abstract
We reveal the full energy-momentum structure of the pseudogap of underdoped high-Tc cuprate superconductors. Our combined theoretical and experimental analysis explains the spectral-weight suppression observed in the B2g Raman response at finite energies in terms of a pseudogap appearing in the single-electron excitation spectra above the Fermi level in the nodal direction of momentum space. This result suggests an s-wave pseudogap (which never closes in the energy-momentum space), distinct from the d-wave superconducting gap. Recent tunneling and photoemission experiments on underdoped cuprates also find a natural explanation within the s-wave pseudogap scenario.
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Affiliation(s)
- S Sakai
- Centre de Physique Théorique, École Polytechnique, CNRS, 91128 Palaiseau, France and Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan and JST-CREST, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - S Blanc
- Laboratoire Matériaux et Phénomnes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, Bâtiment Condorcet, 75205 Paris Cedex 13, France
| | - M Civelli
- Laboratoire de Physique des Solides, Université Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France
| | - Y Gallais
- Laboratoire Matériaux et Phénomnes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, Bâtiment Condorcet, 75205 Paris Cedex 13, France
| | - M Cazayous
- Laboratoire Matériaux et Phénomnes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, Bâtiment Condorcet, 75205 Paris Cedex 13, France
| | - M-A Méasson
- Laboratoire Matériaux et Phénomnes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, Bâtiment Condorcet, 75205 Paris Cedex 13, France
| | - J S Wen
- Matter Physics and Materials Science, Brookhaven National Laboratory (BNL), Upton, New York 11973, USA
| | - Z J Xu
- Matter Physics and Materials Science, Brookhaven National Laboratory (BNL), Upton, New York 11973, USA
| | - G D Gu
- Matter Physics and Materials Science, Brookhaven National Laboratory (BNL), Upton, New York 11973, USA
| | - G Sangiovanni
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany and Institute for Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria
| | - Y Motome
- Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan
| | - K Held
- Institute for Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria
| | - A Sacuto
- Laboratoire Matériaux et Phénomnes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, Bâtiment Condorcet, 75205 Paris Cedex 13, France
| | - A Georges
- Centre de Physique Théorique, École Polytechnique, CNRS, 91128 Palaiseau, France and JST-CREST, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan and Collège de France, 11 Place Marcelin Berthelot, 75005 Paris, France and DPMC, Université de Genève, 24 Quai Ernest Ansermet, CH-1211 Genève, Suisse
| | - M Imada
- Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan and JST-CREST, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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14
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Coslovich G, Giannetti C, Cilento F, Dal Conte S, Abebaw T, Bossini D, Ferrini G, Eisaki H, Greven M, Damascelli A, Parmigiani F. Competition between the Pseudogap and superconducting states of Bi2Sr2Ca0.92Y0.08Cu2O8+δ single crystals revealed by ultrafast broadband optical reflectivity. PHYSICAL REVIEW LETTERS 2013; 110:107003. [PMID: 23521283 DOI: 10.1103/physrevlett.110.107003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2012] [Indexed: 06/01/2023]
Abstract
Ultrafast broadband transient reflectivity experiments are performed to study the interplay between the nonequilibrium dynamics of the pseudogap and the superconducting phases in Bi(2)Sr(2}Ca(0.92)Y(0.08)Cu(2)O(8+δ). Once superconductivity is established, the relaxation of the pseudogap proceeds ~2 times faster than in the normal state, and the corresponding transient reflectivity variation changes sign after ~0.5 ps. The results can be described by a set of coupled differential equations for the pseudogap and for the superconducting order parameter. The sign and strength of the coupling term suggest a remarkably weak competition between the two phases, allowing their coexistence.
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Affiliation(s)
- G Coslovich
- Department of Physics, Università degli Studi di Trieste, Trieste I-34127, Italy
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15
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d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry. Symmetry (Basel) 2011. [DOI: 10.3390/sym3040699] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the two-dimensional geometry of the Fermi surface (FS). Phase diagrams on the σ0 − α plane—here, σ0 is the ratio between the energy gaps in the parent pure CDW and superconducting states, and the quantity 2α is connected with the degree of dielectric (CDW) FS gapping—were obtained for various possible configurations of the order parameters in the momentum space. Relevant tunnel and photoemission experimental data for high-Tc oxides are compared with theoretical predictions. A brief review of the results obtained earlier for the coexistence between s-wave superconductivity and CDWs is also given.
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16
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Lubashevsky Y, Garg A, Sassa Y, Shi M, Kanigel A. Insensitivity of the superconducting gap to variations in the critical temperature of Zn-substituted Bi2Sr2CaCu2O(8+δ) superconductors. PHYSICAL REVIEW LETTERS 2011; 106:047002. [PMID: 21405348 DOI: 10.1103/physrevlett.106.047002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2010] [Indexed: 05/30/2023]
Abstract
The phase diagram of the superconducting high-T(c) cuprates is governed by two energy scales: T*, the temperature below which a gap is opened in the excitation spectrum, and T(c), the superconducting transition temperature. The way these two energy scales are reflected in the low-temperature energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing we prepared a set of samples having the same T* but different T(c)'s, and measured their gap using angle-resolved photoemission spectroscopy (ARPES). We show that T(c) is not related to the gap shape or size, but it controls the size of the coherence peak at the gap edge.
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17
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Koren G, Kirzhner T. Observation of two Andreev-like energy scales in La2-xSrxCuO4 superconductor-normal-metal-superconductor junctions. PHYSICAL REVIEW LETTERS 2011; 106:017002. [PMID: 21231767 DOI: 10.1103/physrevlett.106.017002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2010] [Indexed: 05/30/2023]
Abstract
Conductance spectra measurements of highly transparent junctions made of superconducting La2-xSrxCuO4 electrodes and a nonsuperconducting La1.65Sr0.35CuO4 barrier are reported. At low temperatures below Tc, these junctions have two prominent Andreev-like conductance peaks with clear steps at energies Δ1 and Δ2 with Δ2>2Δ1. No such peaks appear above Tc. The doping dependence at 2 K shows that both Δ1 and Δ2 scale roughly as Tc. Δ1 is identified as the superconducting energy gap, while a few scenarios are proposed as for the origin of Δ2.
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Affiliation(s)
- G Koren
- Physics Department, Technion - Israel Institute of Technology Haifa, 32000, Israel.
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18
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Norman M. Fermi-surface reconstruction and the origin of high-temperature superconductivity. PHYSICS 2010. [DOI: 10.1103/physics.3.86] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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19
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Hu H, Liu XJ, Drummond PD, Dong H. Pseudogap pairing in ultracold Fermi atoms. PHYSICAL REVIEW LETTERS 2010; 104:240407. [PMID: 20867287 DOI: 10.1103/physrevlett.104.240407] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2010] [Revised: 06/01/2010] [Indexed: 05/29/2023]
Abstract
The Bose-Einstein condensate to Bardeen-Cooper-Schrieffer crossover in ultracold Fermi gases creates an ideal environment to enrich our knowledge of many-body systems. It is relevant to a wide range of fields from condensed matter to astrophysics. The nature of pairing in strongly interacting Fermi gases can be readily studied. This aids our understanding of related problems in high-Tc superconductors, whose mechanism is still under debate due to the large interaction parameter. Here, we calculate the dynamical properties of a normal, trapped strongly correlated Fermi gas, by developing a quantum cluster expansion. Our calculations for the single-particle spectral function agree with recent rf spectroscopy measurements, and clearly demonstrate pseudogap pairing in the strongly interacting regime.
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Affiliation(s)
- Hui Hu
- ARC Centre of Excellence for Quantum-Atom Optics, Swinburne University of Technology, Melbourne 3122, Australia
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20
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Sonier JE. High-field μSR studies of superconducting and magnetic correlations in cuprates above T(c). JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:203202. [PMID: 21393701 DOI: 10.1088/0953-8984/22/20/203202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The advent of high transverse field muon spin rotation (TF-μSR) has led to recent μSR investigations of the magnetic field response of cuprates above the superconducting transition temperature T(c). Here the results of such experiments on hole-doped cuprates are reviewed. Although these investigations are currently ongoing, it is clear that the effects of high field on the internal magnetic field distribution of these materials is dependent upon competition between superconductivity and magnetism. In La(2 - x)Sr(x)CuO(4) the response to the external field above T(c) is dominated by heterogeneous spin magnetism. However, the magnetism that dominates the observed inhomogeneous line broadening below x ∼ 0.19 is overwhelmed by the emergence of a completely different kind of magnetism in the heavily overdoped regime. The origin of the magnetism above x ∼ 0.19 is probably related to intrinsic disorder, but the systematic evolution of the magnetism with doping changes in the doping range beyond the superconducting 'dome'. In contrast, the width of the internal field distribution of underdoped Y Ba(2)Cu(3)O(y) above T(c) is observed to track T(c) and the density of superconducting carriers. This observation suggests that the magnetic response above T(c) is not dominated by electronic moments, but rather inhomogeneous fluctuating superconductivity. The spatially inhomogeneous response of Y Ba(2)Cu(3)O(y) to the applied field may be a means of minimizing energy, rather than being caused by intrinsic disorder.
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Affiliation(s)
- J E Sonier
- Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada.
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21
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Greco A. Evidence for two competing order parameters in underdoped cuprate superconductors from a model analysis of Fermi-Arc effects. PHYSICAL REVIEW LETTERS 2009; 103:217001. [PMID: 20366060 DOI: 10.1103/physrevlett.103.217001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2009] [Indexed: 05/29/2023]
Abstract
Preformed pairs above T{c} and the two-gap scenarios are two main proposals for describing the low-doping pseudogap phase of high-T{c} cuprates. Very recent angle-resolved photoemission experiments have shown features which were interpreted as evidence for preformed pairs. Here it is shown that those results can be explained also in the context of the two-gap scenario if self-energy effects are considered. The discussion is based on the d charge-density wave theory or the flux phase of the t-J model.
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Affiliation(s)
- Andrés Greco
- Facultad de Ciencias Exactas, Ingeniería y Agrimensura and Instituto de Física Rosario (UNR-CONICET), Av. Pellegrini 250, 2000 Rosario, Argentina
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22
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Yuli O, Asulin I, Kalcheim Y, Koren G, Millo O. Proximity-induced pseudogap: evidence for preformed pairs. PHYSICAL REVIEW LETTERS 2009; 103:197003. [PMID: 20365947 DOI: 10.1103/physrevlett.103.197003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2009] [Indexed: 05/29/2023]
Abstract
The temperature evolution of the proximity effect in Au/La(2-x)Sr(x)CuO(4) and La(1.55)Sr(0.45)CuO(4)/La(2-x)Sr(x)CuO(4) bilayers was investigated using scanning tunneling microscopy. Proximity-induced gaps, centered at the chemical potential, were found to persist above the superconducting transition temperature, T(c), and up to nearly the pseudogap crossover temperature in both systems. Such independence of the spectra on the details of the normal-metal cap layer is incompatible with a density-wave order origin. However, our results can be accounted for by a penetration of incoherent Cooper pairs into the normal metal above T(c).
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Affiliation(s)
- Ofer Yuli
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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23
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de Mello EVL, Kasal RB, Passos CAC. Electronic phase separation transition as the origin of the superconductivity and pseudogap phase of cuprates. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:235701. [PMID: 21825593 DOI: 10.1088/0953-8984/21/23/235701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
To deal with the physics of cuprate superconductivity we propose an electronic phase separation transition that segregates the holes into high and low density domains. The calculated grain boundary potential favors the development of intragrain superconducting amplitudes. The zero resistivity transition arises only when the intergrain Josephson coupling E(J) is of the order of the thermal energy and phase locking takes place among the superconducting grains. We show that this approach explains the pseudogap and superconducting phases and it also reproduces some recent scanning tunneling microscopy data.
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Affiliation(s)
- E V L de Mello
- Instituto de Física, Universidade Federal Fluminense, Niterói, RJ 24210-340, Brazil
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24
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Chen Q, Levin K. Momentum resolved radio frequency spectroscopy in trapped fermi gases. PHYSICAL REVIEW LETTERS 2009; 102:190402. [PMID: 19518929 DOI: 10.1103/physrevlett.102.190402] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2008] [Indexed: 05/27/2023]
Abstract
We address recent momentum-resolved radio frequency (rf) spectroscopy experiments, showing how they yield more stringent tests than other comparisons with theory, associated with the ultracold Fermi gases. We demonstrate that, by providing a clear dispersion signature of pairing, they remove the ambiguity plaguing the interpretation of previous rf experiments. Our calculated spectral intensities are in semiquantitative agreement with the data. Even in the presence of a trap, the spectra are predicted to exhibit two BCS-like branches.
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Affiliation(s)
- Qijin Chen
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
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25
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Kondo T, Khasanov R, Takeuchi T, Schmalian J, Kaminski A. Competition between the pseudogap and superconductivity in the high-T(c) copper oxides. Nature 2009; 457:296-300. [PMID: 19148096 DOI: 10.1038/nature07644] [Citation(s) in RCA: 222] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2008] [Accepted: 11/10/2008] [Indexed: 11/09/2022]
Abstract
In a classical Bardeen-Cooper-Schrieffer superconductor, pairing and coherence of electrons are established simultaneously below the critical transition temperature (T(c)), giving rise to a gap in the electronic energy spectrum. In the high-T(c) copper oxide superconductors, however, a pseudogap extends above T(c). The relationship between the pseudogap and superconductivity is one of the central issues in this field. Spectral gaps arising from pairing precursors are qualitatively similar to those caused by competing electronic states, rendering a standard approach to their analysis inconclusive. The issue can be settled, however, by studying the correlation between the weights associated with the pseudogap and superconductivity spectral features. Here we report a study of two spectral weights using angle-resolved photoemission spectroscopy. The weight of the superconducting coherent peak increases away from the node following the trend of the superconducting gap, but starts to decrease in the antinodal region. This striking non-monotonicity reveals the presence of a competing state. We demonstrate a direct correlation, for different values of momenta and doping, between the loss in the low-energy spectral weight arising from the opening of the pseudogap and a decrease in the spectral weight associated with superconductivity. We therefore conclude that the pseudogap competes with the superconductivity by depleting the spectral weight available for pairing.
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Affiliation(s)
- Takeshi Kondo
- Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA.
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