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Wang S, Kennedy N, Fujita K, Uchida SI, Eisaki H, Johnson PD, Davis JCS, O'Mahony SM. Discovery of orbital ordering in Bi 2Sr 2CaCu 2O 8+x. NATURE MATERIALS 2024; 23:492-498. [PMID: 38438620 PMCID: PMC10990940 DOI: 10.1038/s41563-024-01817-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2023] [Accepted: 01/22/2024] [Indexed: 03/06/2024]
Abstract
The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d9 and 3d10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p6 and 3d10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO2.
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Affiliation(s)
- Shuqiu Wang
- Clarendon Laboratory, University of Oxford, Oxford, UK.
- Department of Physics, Cornell University, Ithaca, NY, USA.
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK.
| | - Niall Kennedy
- Clarendon Laboratory, University of Oxford, Oxford, UK
- School of Physics, University College Cork, Cork, Ireland
| | - Kazuhiro Fujita
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA
| | | | - Hiroshi Eisaki
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan
| | - Peter D Johnson
- Clarendon Laboratory, University of Oxford, Oxford, UK
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA
| | - J C Séamus Davis
- Clarendon Laboratory, University of Oxford, Oxford, UK.
- Department of Physics, Cornell University, Ithaca, NY, USA.
- School of Physics, University College Cork, Cork, Ireland.
- Max Planck Institute for Chemical Physics of Solids, Dresden, Germany.
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2
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Wårdh J, Granath M, Wu J, Bollinger AT, He X, Božović I. Colossal transverse magnetoresistance due to nematic superconducting phase fluctuations in a copper oxide. PNAS NEXUS 2023; 2:pgad255. [PMID: 37601309 PMCID: PMC10438889 DOI: 10.1093/pnasnexus/pgad255] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 07/25/2023] [Indexed: 08/22/2023]
Abstract
Electronic anisotropy ("nematicity") has been detected in cuprate superconductors by various experimental techniques. Using angle-resolved transverse resistance (ARTR) measurements, a very sensitive and background-free technique that can detect 0.5% anisotropy in transport, we have observed it also in La2-xSrxCuO4 (LSCO) for 0.02 ≤ x ≤ 0.25. A central enigma in LSCO is the rotation of the nematic director (orientation of the largest longitudinal resistance) with temperature; this has not been seen before in any material. Here, we address this puzzle by measuring the angle-resolved transverse magnetoresistance (ARTMR) in LSCO. We report the discovery of colossal transverse magnetoresistance (CTMR)-an order-of-magnitude drop in the transverse resistivity in the magnetic field of 6 T. We show that the apparent rotation of the nematic director is caused by anisotropic superconducting fluctuations, which are not aligned with the normal electron fluid, consistent with coexisting bond-aligned and diagonal nematic orders. We quantify this by modeling the (magneto-)conductivity as a sum of normal (Drude) and paraconducting (Aslamazov-Larkin) channels but extended to contain anisotropic Drude and Cooper-pair effective mass tensors. Strikingly, the anisotropy of Cooper-pair stiffness is much larger than that of the normal electrons. It grows dramatically on the underdoped side, where the fluctuations become quasi-one-dimensional. Our analysis is general rather than model dependent. Still, we discuss some candidate microscopic models, including coupled strongly-correlated ladders where the transverse (interladder) phase stiffness is low compared with the longitudinal intraladder stiffness, as well as the anisotropic superconducting fluctuations expected close to the transition to a pair-density wave state.
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Affiliation(s)
- Jonatan Wårdh
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
| | - Mats Granath
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
| | - Jie Wu
- Brookhaven National Laboratory, Upton, NY 11973, USA
- Present address: School of Science, Westlake University, Hangzhou, China
| | | | - Xi He
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
- Energy Sciences Institute, Yale University, West Haven, CT 06516, USA
| | - Ivan Božović
- Brookhaven National Laboratory, Upton, NY 11973, USA
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
- Energy Sciences Institute, Yale University, West Haven, CT 06516, USA
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3
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Jiang S, Romhányi J, White SR, Zhitomirsky ME, Chernyshev AL. Where is the Quantum Spin Nematic? PHYSICAL REVIEW LETTERS 2023; 130:116701. [PMID: 37001099 DOI: 10.1103/physrevlett.130.116701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Accepted: 02/23/2023] [Indexed: 06/19/2023]
Abstract
We provide strong evidence of the spin-nematic state in a paradigmatic ferro-antiferromagnetic J_{1}-J_{2} model using analytical and density-matrix renormalization group methods. In zero field, the attraction of spin-flip pairs leads to a first-order transition and no nematic state, while pair repulsion at larger J_{2} stabilizes the nematic phase in a narrow region near the pair-condensation field. A devil's staircase of multipair condensates is conjectured for weak pair attraction. A suppression of the spin-flip gap by many-body effects leads to an order-of-magnitude contraction of the nematic phase compared to naïve expectations. The proposed phase diagram should be broadly valid.
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Affiliation(s)
- Shengtao Jiang
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Judit Romhányi
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Steven R White
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - M E Zhitomirsky
- Université Grenoble Alpes, Grenoble INP, CEA, IRIG, PHELIQS, 38000 Grenoble, France
- Institut Laue-Langevin, 71 Avenue des Martyrs, CS 20156, 38042 Grenoble Cedex 9, France
| | - A L Chernyshev
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
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4
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Nematic phases and elastoresistivity from a multiorbital non-Fermi liquid. Proc Natl Acad Sci U S A 2023; 120:e2207903120. [PMID: 36603030 PMCID: PMC9926168 DOI: 10.1073/pnas.2207903120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
We propose and study a two-orbital lattice extension of the Sachdev-Ye-Kitaev model in the large-N limit. The phase diagram of this model features a high-temperature isotropic non-Fermi liquid which undergoes first-order thermal transition into a nematic insulator or continuous thermal transition into a nematic metal phase, separated by a tunable tricritical point. These phases arise from spontaneous partial orbital polarization of the multiorbital non-Fermi liquid. We explore the spectral and transport properties of this model, including d.c. elastoresistivity, which exhibits a peak near nematic transition, as well as nonzero frequency elastoconductivity. Our work offers a useful perspective on nematic phases and transport in correlated multiorbital systems.
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5
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How pressure enhances the critical temperature of superconductivity in YBa 2Cu 3O 6+y. Proc Natl Acad Sci U S A 2023; 120:e2215458120. [PMID: 36608293 PMCID: PMC9926205 DOI: 10.1073/pnas.2215458120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
High-temperature superconducting cuprates respond to doping with a dome-like dependence of their critical temperature (Tc). But the family-specific maximum Tc can be surpassed by application of pressure, a compelling observation known for decades. We investigate the phenomenon with high-pressure anvil cell NMR and measure the charge content at planar Cu and O, and with it the doping of the ubiquitous CuO2 plane with atomic-scale resolution. We find that pressure increases the overall hole doping, as widely assumed, but when it enhances Tc above what can be achieved by doping, pressure leads to a hole redistribution favoring planar O. This is similar to the observation that the family-specific maximum Tc is higher for materials where the hole content at planar O is higher at the expense of that at planar Cu. The latter reflects dependence of the maximum Tc on the Cu-O bond covalence and the charge-transfer gap. The results presented here indicate that the pressure-induced enhancement of the maximum Tc points to the same mechanism.
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6
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Harrison N, Chan MK. Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity. PHYSICAL REVIEW LETTERS 2022; 129:017001. [PMID: 35841553 DOI: 10.1103/physrevlett.129.017001] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Revised: 03/22/2022] [Accepted: 05/24/2022] [Indexed: 06/15/2023]
Abstract
Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.
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Affiliation(s)
- N Harrison
- National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - M K Chan
- National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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7
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González-Herrero H, Mendieta-Moreno JI, Edalatmanesh S, Santos J, Martín N, Écija D, de la Torre B, Jelinek P. Atomic Scale Control and Visualization of Topological Quantum Phase Transition in π-Conjugated Polymers Driven by Their Length. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2104495. [PMID: 34536048 DOI: 10.1002/adma.202104495] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Revised: 08/06/2021] [Indexed: 06/13/2023]
Abstract
Quantum phase transitions (QPTs) driven by quantum fluctuations are transitions between distinct quantum phases of matter. At present, they are poorly understood and not readily controlled. Here, scanning tunneling microscopy (STM) and noncontact atomic force microscopy (nc-AFM) are used to explore atomic scale control over quantum phase transitions between two different topological quantum states of a well-defined π-conjugated polymer. The phase transition is driven by a pseudo Jahn-Teller effect that is activated above a certain polymer chain length. In addition, theoretical calculations indicate the presence of long-lasting coherent fluctuations between the polymer's two quantum phases near the phase transition, at finite temperature. This work thus presents a new way of exploring atomic-scale control over QPTs and indicates that emerging quantum criticality in the vicinity of a QPT can give rise to new states of organic matter.
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Affiliation(s)
- Héctor González-Herrero
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University, Olomouc, 78371, Czech Republic
| | | | - Shayan Edalatmanesh
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University, Olomouc, 78371, Czech Republic
- Institute of Physics, Czech Academy of Sciences, Prague, 162 00, Czech Republic
| | - José Santos
- Department of Organic Chemistry, Faculty of Chemistry, University Complutense of Madrid, Madrid, 28040, Spain
- IMDEA-Nanociencia, C/Faraday 9, Ciudad Universitaria de Cantoblanco, Madrid, 28049, Spain
| | - Nazario Martín
- Department of Organic Chemistry, Faculty of Chemistry, University Complutense of Madrid, Madrid, 28040, Spain
- IMDEA-Nanociencia, C/Faraday 9, Ciudad Universitaria de Cantoblanco, Madrid, 28049, Spain
| | - David Écija
- IMDEA-Nanociencia, C/Faraday 9, Ciudad Universitaria de Cantoblanco, Madrid, 28049, Spain
| | - Bruno de la Torre
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University, Olomouc, 78371, Czech Republic
- Institute of Physics, Czech Academy of Sciences, Prague, 162 00, Czech Republic
| | - Pavel Jelinek
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University, Olomouc, 78371, Czech Republic
- Institute of Physics, Czech Academy of Sciences, Prague, 162 00, Czech Republic
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8
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Kowalski N, Dash SS, Sémon P, Sénéchal D, Tremblay AM. Oxygen hole content, charge-transfer gap, covalency, and cuprate superconductivity. Proc Natl Acad Sci U S A 2021; 118:e2106476118. [PMID: 34593641 PMCID: PMC8501840 DOI: 10.1073/pnas.2106476118] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/21/2021] [Indexed: 11/18/2022] Open
Abstract
Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping [D. Rybicki et al., Nat. Commun. 7, 1-6 (2016)]. They have also shown that a large charge-transfer gap [W. Ruan et al., Sci. Bull. (Beijing) 61, 1826-1832 (2016)], a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role among doped charge-transfer insulators of transition metal oxides because copper has the largest covalent bonding with oxygen. Experiments [L. Wang et al., arXiv [Preprint] (2020). https://arxiv.org/abs/2011.05029 (Accessed 10 November 2020)] also suggest that superexchange is at the origin of superconductivity in cuprates. Our results reveal the consistency of these experiments with the above two experimental findings. Indeed, we show that covalency and a charge-transfer gap lead to an effective short-range superexchange interaction between copper spins that ultimately explains pairing and superconductivity in the three-band Hubbard model of cuprates.
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Affiliation(s)
- Nicolas Kowalski
- Département de physique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Institut quantique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Regroupement québécois sur les matériaux de pointe, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - Sidhartha Shankar Dash
- Département de physique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Institut quantique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Regroupement québécois sur les matériaux de pointe, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - Patrick Sémon
- Département de physique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Regroupement québécois sur les matériaux de pointe, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - David Sénéchal
- Département de physique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Institut quantique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Regroupement québécois sur les matériaux de pointe, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - André-Marie Tremblay
- Département de physique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada;
- Institut quantique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Regroupement québécois sur les matériaux de pointe, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
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9
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Vanishing nematic order beyond the pseudogap phase in overdoped cuprate superconductors. Proc Natl Acad Sci U S A 2021; 118:2106881118. [PMID: 34413195 DOI: 10.1073/pnas.2106881118] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
During the last decade, translational and rotational symmetry-breaking phases-density wave order and electronic nematicity-have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant X-ray scattering in a cuprate high-temperature superconductor [Formula: see text] (Nd-LSCO) to navigate the cuprate phase diagram, probing the relationship between electronic nematicity of the Cu 3d orbitals, charge order, and the pseudogap phase as a function of doping. We find evidence for a considerable decrease in electronic nematicity beyond the pseudogap phase, either by raising the temperature through the pseudogap onset temperature T* or increasing doping through the pseudogap critical point, p*. These results establish a clear link between electronic nematicity, the pseudogap, and its associated quantum criticality in overdoped cuprates. Our findings anticipate that electronic nematicity may play a larger role in understanding the cuprate phase diagram than previously recognized, possibly having a crucial role in the phenomenology of the pseudogap phase.
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10
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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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11
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Worasaran T, Ikeda MS, Palmstrom JC, Straquadine JAW, Kivelson SA, Fisher IR. Nematic quantum criticality in an Fe-based superconductor revealed by strain-tuning. Science 2021; 372:973-977. [PMID: 34045352 DOI: 10.1126/science.abb9280] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 04/17/2021] [Indexed: 11/02/2022]
Abstract
Quantum criticality may be essential to understanding a wide range of exotic electronic behavior; however, conclusive evidence of quantum critical fluctuations has been elusive in many materials of current interest. An expected characteristic feature of quantum criticality is power-law behavior of thermodynamic quantities as a function of a nonthermal tuning parameter close to the quantum critical point (QCP). Here, we observed power-law behavior of the critical temperature of the coupled nematic/structural phase transition as a function of uniaxial stress in a representative family of iron-based superconductors, providing direct evidence of quantum critical nematic fluctuations in this material. These quantum critical fluctuations are not confined within a narrow regime around the QCP but rather extend over a wide range of temperatures and compositions.
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Affiliation(s)
- Thanapat Worasaran
- Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA. .,Department of Applied Physics and Geballe Laboratory of Advanced Materials, Stanford University, Stanford, CA 94305, USA
| | - Matthias S Ikeda
- Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.,Department of Applied Physics and Geballe Laboratory of Advanced Materials, Stanford University, Stanford, CA 94305, USA
| | - Johanna C Palmstrom
- Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.,Department of Applied Physics and Geballe Laboratory of Advanced Materials, Stanford University, Stanford, CA 94305, USA
| | - Joshua A W Straquadine
- Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.,Department of Applied Physics and Geballe Laboratory of Advanced Materials, Stanford University, Stanford, CA 94305, USA
| | - Steven A Kivelson
- Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.,Department of Physics and Geballe Laboratory of Advanced Materials, Stanford University, Stanford, CA 94305, USA
| | - Ian R Fisher
- Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA. .,Department of Applied Physics and Geballe Laboratory of Advanced Materials, Stanford University, Stanford, CA 94305, USA
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12
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Andrei EY, MacDonald AH. Graphene bilayers with a twist. NATURE MATERIALS 2020; 19:1265-1275. [PMID: 33208935 DOI: 10.1038/s41563-020-00840-0] [Citation(s) in RCA: 159] [Impact Index Per Article: 39.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 09/24/2020] [Indexed: 05/02/2023]
Abstract
Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive to carrier density and to controllable environmental factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena, magic-angle twisted bilayer graphene hosts superconductivity, interaction-induced insulating states, magnetism, electronic nematicity, linear-in-temperature low-temperature resistivity and quantized anomalous Hall states. We highlight some key research results in this field, point to important questions that remain open and comment on the place of magic-angle twisted bilayer graphene in the strongly correlated quantum matter world.
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Affiliation(s)
- Eva Y Andrei
- Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ, USA.
| | - Allan H MacDonald
- Department of Physics, The University of Texas at Austin, Austin, TX, USA
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13
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Abstract
Planar oxygen nuclear magnetic resonance (NMR) relaxation and shift data from all cuprate superconductors available in the literature are analyzed. They reveal a temperature-independent pseudogap at the Fermi surface, which increases with decreasing doping in family-specific ways, i.e., for some materials, the pseudogap is substantial at optimal doping while for others it is nearly closed at optimal doping. The states above the pseudogap, or in its absence are similar for all cuprates and doping levels, and Fermi liquid-like. If the pseudogap is assumed exponential it can be as large as about 1500 K for the most underdoped systems, relating it to the exchange coupling. The pseudogap can vary substantially throughout a material, being the cause of cuprate inhomogeneity in terms of charge and spin, so consequences for the NMR analyses are discussed. This pseudogap appears to be in agreement with the specific heat data measured for the YBaCuO family of materials, long ago. Nuclear relaxation and shift show deviations from this scenario near Tc, possibly due to other in-gap states.
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14
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Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity. Proc Natl Acad Sci U S A 2020; 117:14805-14811. [PMID: 32546526 PMCID: PMC7334493 DOI: 10.1073/pnas.2002429117] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
By making a variety of quantitative comparisons between electronic visualization experiments and a theory describing coexisting pair density wave and superconductive states in cuprates, we find striking correspondence throughout. Our model can thus explain the microscopic origins of many key atomic-scale phenomena of the cuprate broken-symmetry state. These observations are consistent with the possibility that a short-range pair density wave (PDW) state coexists with superconductivity below a critical hole density in Bi2Sr2CaCu2O8, that the charge density wave modulations in cuprates are a consequence of the PDW state, that the cuprate pseudogap is the antinodal gap of the PDW, and that the critical point in the cuprate phase diagram occurs due to disappearance of the PDW. The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states Nr,E is predicted at the terminal BiO surface of Bi2Sr2CaCu2O8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of Nr,E, the modulations of the coherence peak energy Δpr, and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space q-space. Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi2Sr2CaCu2O8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.
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Song Y, Yuan D, Lu X, Xu Z, Bourret-Courchesne E, Birgeneau RJ. Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2×2 Fe Clusters in KFe_{0.8}Ag_{1.2}Te_{2}. PHYSICAL REVIEW LETTERS 2019; 123:247205. [PMID: 31922861 DOI: 10.1103/physrevlett.123.247205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Indexed: 06/10/2023]
Abstract
Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter.
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Affiliation(s)
- Yu Song
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Dongsheng Yuan
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Xingye Lu
- Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Zhijun Xu
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg Maryland 20899, USA
- Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA
| | - Edith Bourret-Courchesne
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Robert J Birgeneau
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
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Linking the pseudogap in the cuprates with local symmetry breaking: A commentary. Proc Natl Acad Sci U S A 2019; 116:14395-14397. [PMID: 31285324 PMCID: PMC6642401 DOI: 10.1073/pnas.1908786116] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022] Open
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