1
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Zhang HK, Liu S, Zhang SX. Absence of Barren Plateaus in Finite Local-Depth Circuits with Long-Range Entanglement. PHYSICAL REVIEW LETTERS 2024; 132:150603. [PMID: 38682974 DOI: 10.1103/physrevlett.132.150603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 01/24/2024] [Accepted: 03/13/2024] [Indexed: 05/01/2024]
Abstract
Ground state preparation is classically intractable for general Hamiltonians. On quantum devices, shallow parametrized circuits can be effectively trained to obtain short-range entangled states under the paradigm of variational quantum eigensolver, while deep circuits are generally untrainable due to the barren plateau phenomenon. In this Letter, we give a general lower bound on the variance of circuit gradients for arbitrary quantum circuits composed of local 2-designs. Based on our unified framework, we prove the absence of barren plateaus in training finite local-depth circuits (FLDC) for the ground states of local Hamiltonians. FLDCs are allowed to be deep in the conventional circuit depth to generate long-range entangled ground states, such as topologically ordered states, but their local depths are finite, i.e., there is only a finite number of gates acting on individual qubits. This characteristic sets FLDC apart from shallow circuits: FLDC in general cannot be classically simulated to estimate local observables efficiently by existing tensor network methods in two and higher dimensions. We validate our analytical results with extensive numerical simulations and demonstrate the effectiveness of variational training using the generalized toric code model.
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Affiliation(s)
- Hao-Kai Zhang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Shuo Liu
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Shi-Xin Zhang
- Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong 518057, China
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2
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Wang X, Zhu W. A microscopic view of checkerboard and striped charge orders through doping antiferromagnetic Mott insulator. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:265602. [PMID: 38518372 DOI: 10.1088/1361-648x/ad3709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 03/22/2024] [Indexed: 03/24/2024]
Abstract
The emergence of charge order in doped Mott insulators has received considerable attention due to its relevance to a variety of realistic materials and experiments. To investigate the interplay between magnetic and charge order, we have studied the semiclassical Kondo lattice model, which includes both electronic and magnetic degrees of freedom. By combining Langevin dynamical simulations with the kernel polynomial method, our results reveal the presence of charged stripe order, checkerboard order, and non-uniform charge disorder in the near-half-filling regime. Importantly, our simulations show that both the doping level and the strength of thes-dexchange coupling play a crucial role in facilitating charge order formation. These phases give rise to distinct electronic structures as well as excitations in the magnetic dynamics, providing insights into the underlying mechanism of charge ordering phenomena.
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Affiliation(s)
- Xuanlan Wang
- Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
| | - Wei Zhu
- Key Laboratory for Quantum Materials of Zhejiang Province, School of Science, Westlake University, Hangzhou 310024, People's Republic of China
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3
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Lu X, Chen F, Zhu W, Sheng DN, Gong SS. Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice t-J Model. PHYSICAL REVIEW LETTERS 2024; 132:066002. [PMID: 38394594 DOI: 10.1103/physrevlett.132.066002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2023] [Revised: 09/08/2023] [Accepted: 01/09/2024] [Indexed: 02/25/2024]
Abstract
The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t_{2}>0) but a dominant charge density wave (CDW) order on the hole-doped side (t_{2}<0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ=1/16-1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1/8 doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.
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Affiliation(s)
- Xin Lu
- School of Physics, Beihang University, Beijing 100191, China
| | - Feng Chen
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA
| | - W Zhu
- School of Science, Westlake University, Hangzhou 310024, China; Institute of Natural Sciences, Westlake Institute of Advanced Study, Hangzhou 310024, China; and Key Laboratory for Quantum Materials of Zhejiang Province, Westlake University, Hangzhou 310024, China
| | - D N Sheng
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA
| | - Shou-Shu Gong
- School of Physical Sciences, Great Bay University, Dongguan 523000, China and Great Bay Institute for Advanced Study, Dongguan 523000, China
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4
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Choi J, Li J, Nag A, Pelliciari J, Robarts H, Tam CC, Walters A, Agrestini S, García-Fernández M, Song D, Eisaki H, Johnston S, Comin R, Ding H, Zhou KJ. Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2307515. [PMID: 37830432 DOI: 10.1002/adma.202307515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 09/22/2023] [Indexed: 10/14/2023]
Abstract
The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.
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Affiliation(s)
- Jaewon Choi
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
| | - Jiemin Li
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Science, Beijing, 100190, China
| | - Abhishek Nag
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
| | - Jonathan Pelliciari
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - Hannah Robarts
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK
| | - Charles C Tam
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK
| | - Andrew Walters
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
| | - Stefano Agrestini
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
| | | | - Dongjoon Song
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8560, Japan
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Hiroshi Eisaki
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8560, Japan
| | - Steve Johnston
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN, 37996, USA
- Institute for Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, TN, 37996, USA
| | - Riccardo Comin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Hong Ding
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Science, Beijing, 100190, China
- Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire, OX11 0DE, UK
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5
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Amsler M, Deglmann P, Degroote M, Kaicher MP, Kiser M, Kühn M, Kumar C, Maier A, Samsonidze G, Schroeder A, Streif M, Vodola D, Wever C. Classical and quantum trial wave functions in auxiliary-field quantum Monte Carlo applied to oxygen allotropes and a CuBr2 model system. J Chem Phys 2023; 159:044119. [PMID: 37522404 DOI: 10.1063/5.0146934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 07/06/2023] [Indexed: 08/01/2023] Open
Abstract
In this work, we test a recently developed method to enhance classical auxiliary-field quantum Monte Carlo (AFQMC) calculations with quantum computers against examples from chemistry and material science, representative of classes of industry-relevant systems. As molecular test cases, we calculate the energy curve of H4 and the relative energies of ozone and singlet molecular oxygen with respect to triplet molecular oxygen, which is industrially relevant in organic oxidation reactions. We find that trial wave functions beyond single Slater determinants improve the performance of AFQMC and allow it to generate energies close to chemical accuracy compared to full configuration interaction or experimental results. In the field of material science, we study the electronic structure properties of cuprates through the quasi-1D Fermi-Hubbard model derived from CuBr2, where we find that trial wave functions with both significantly larger fidelities and lower energies over a mean-field solution do not necessarily lead to AFQMC results closer to the exact ground state energy.
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Affiliation(s)
- Maximilian Amsler
- Corporate Sector Research and Advance Engineering, Robert Bosch GmbH, Robert-Bosch-Campus 1, 71272 Renningen, Germany
| | - Peter Deglmann
- BASF SE, Quantum Chemistry, Carl-Bosch-Str. 38, 67063 Ludwigshafen, Germany
- BASF Digital Solutions GmbH, Next Generation Computing, Pfalzgrafenstr. 1, 67056 Ludwigshafen, Germany
| | | | - Michael P Kaicher
- BASF Digital Solutions GmbH, Next Generation Computing, Pfalzgrafenstr. 1, 67056 Ludwigshafen, Germany
| | - Matthew Kiser
- Volkswagen AG, Ungererstr. 69, 80805 Munich, Germany
- TUM School of Natural Sciences, Technical University of Munich, Boltzmannstr. 10, 85748 Garching, Germany
| | - Michael Kühn
- BASF SE, Quantum Chemistry, Carl-Bosch-Str. 38, 67063 Ludwigshafen, Germany
- BASF Digital Solutions GmbH, Next Generation Computing, Pfalzgrafenstr. 1, 67056 Ludwigshafen, Germany
| | - Chandan Kumar
- BMW Group, New Technology and Innovation, Parkring 19-23, 85748 Garching, Munich, Germany
| | | | - Georgy Samsonidze
- Robert Bosch LLC, Research and Technology Center, Sunnyvale, California 94085, USA
| | - Anna Schroeder
- Corporate Sector Research and Advance Engineering, Robert Bosch GmbH, Robert-Bosch-Campus 1, 71272 Renningen, Germany
- Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | - Michael Streif
- Quantum Lab, Boehringer Ingelheim, Ingelheim am Rhein, Germany
| | - Davide Vodola
- BASF Digital Solutions GmbH, Next Generation Computing, Pfalzgrafenstr. 1, 67056 Ludwigshafen, Germany
| | - Christopher Wever
- Corporate Sector Research and Advance Engineering, Robert Bosch GmbH, Robert-Bosch-Campus 1, 71272 Renningen, Germany
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6
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Huang Y, Gong SS, Sheng DN. Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators. PHYSICAL REVIEW LETTERS 2023; 130:136003. [PMID: 37067318 DOI: 10.1103/physrevlett.130.136003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2022] [Accepted: 03/06/2023] [Indexed: 06/19/2023]
Abstract
The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. In this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t-J model on the six- and eight-leg cylinders, we identify a d+id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d-wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.
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Affiliation(s)
- Yixuan Huang
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Shou-Shu Gong
- Department of Physics, Beihang University, Beijing 100191, China
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
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7
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Watanabe H, Shirakawa T, Seki K, Sakakibara H, Kotani T, Ikeda H, Yunoki S. Monte Carlo study of cuprate superconductors in a four-bandd-pmodel: role of orbital degrees of freedom. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:195601. [PMID: 36866651 DOI: 10.1088/1361-648x/acc0bf] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 03/02/2023] [Indexed: 06/18/2023]
Abstract
Understanding the various competing phases in cuprate superconductors is a long-standing challenging problem. Recent studies have shown that orbital degrees of freedom, both Cuegorbitals and Oporbitals, are a key ingredient for a unified understanding of cuprate superconductors, including the material dependence. Here we investigate a four-bandd-pmodel derived from the first-principles calculations with the variational Monte Carlo method, which allows us to elucidate competing phases on an equal footing. The obtained results can consistently explain the doping dependence of superconductivity, antiferromagnetic and stripe phases, phase separation in the underdoped region, and also novel magnetism in the heavily-overdoped region. The presence ofporbitals is critical to the charge-stripe features, which induce two types of stripe phases withs)-wave andd-wave bond stripe. On the other hand, the presence ofdz2orbital is indispensable to material dependence of the superconducting transition temperature (Tc), and enhances local magnetic moment as a source of novel magnetism in the heavily-overdoped region as well. These findings beyond one-band description could provide a major step toward a full explanation of unconventional normal state and highTcin cuprate supercondutors.
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Affiliation(s)
- Hiroshi Watanabe
- Research Organization of Science and Technology, Ritsumeikan University, Shiga 525-8577, Japan
| | - Tomonori Shirakawa
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
- Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Saitama 351-0198, Japan
| | - Kazuhiro Seki
- Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Saitama 351-0198, Japan
| | - Hirofumi Sakakibara
- Advanced Mechanical and Electronic System Research Center (AMES), Faculty of Engineering, Tottori University, Tottori 680-8552, Japan
- Center of Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
- Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Saitama 351-0198, Japan
| | - Takao Kotani
- Advanced Mechanical and Electronic System Research Center (AMES), Faculty of Engineering, Tottori University, Tottori 680-8552, Japan
- Center of Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
| | - Hiroaki Ikeda
- Department of Physics, Ritsumeikan University, Shiga 525-8577, Japan
| | - Seiji Yunoki
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
- Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Saitama 351-0198, Japan
- Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Saitama 351-0198, Japan
- Computational Quantum Matter Research Team, RIKEN Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan
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8
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Wietek A. Fragmented Cooper Pair Condensation in Striped Superconductors. PHYSICAL REVIEW LETTERS 2022; 129:177001. [PMID: 36332257 DOI: 10.1103/physrevlett.129.177001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
Condensation of bosons in Bose-Einstein condensates or Cooper pairs in superconductors refers to a macroscopic occupation of a few single- or two-particle states. A condensate is called "fragmented" if not a single, but multiple states are macroscopically occupied. While fragmentation is known to occur in particular Bose-Einstein condensates, we propose that fragmentation naturally takes place in striped superconductors. To this end, we investigate the nature of the superconducting ground state realized in the two-dimensional t-t^{'}-J model. In the presence of charge density modulations, the condensate is shown to be fragmented and composed of partial condensates located on the stripes. The fragments of the condensates hybridize to form an extended macroscopic wave function across the system. The results are obtained from evaluating the singlet-pairing two-particle density matrix of the ground state on finite cylinders computed via the density matrix renormalization group method. Our results shed light on the intricate relation between stripe order and superconductivity in systems of strongly correlated electrons.
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Affiliation(s)
- Alexander Wietek
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA and Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, Dresden 01187, Germany
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9
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Yang S, Liu X, Li W, Yang J, Ying T, Li X, Sun X. Enhanced d-wave pairing in the two-dimensional Hubbard model with periodically modulated hopping amplitudes. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:375501. [PMID: 35790173 DOI: 10.1088/1361-648x/ac7e9c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 07/05/2022] [Indexed: 06/15/2023]
Abstract
Utilizing determinant quantum Monte Carlo algorithm, the evolution of thed-wave pairing in the Hubbard model on the square lattice tuned by the periodically modulated hopping amplitudes is studied. The hopping amplitudes are homogeneous in thexˆ-direction, while in theyˆ-direction the hopping amplitudes are modulated with periodP, wherety=t+dt,ty'=t-(P-1)dt, and the modulation periodPequals 2, 3 and 4 lattice spacings. The latter two modulation periods are motivated by the observation of period-3 and period-4 stripe order in cuprate superconductors. For all the periodsP, we find that the modulated hopping inhomogeneity enhances thed-wave pairing and an optimal inhomogeneity exists.
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Affiliation(s)
- Shuhui Yang
- Institute of Modern Optics, School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Xingcan Liu
- Institute of Modern Optics, School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Weiqi Li
- School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Jianqun Yang
- School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Tao Ying
- Institute of Modern Optics, School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Xingji Li
- School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Xiudong Sun
- Institute of Modern Optics, School of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Key Laboratory of Micro-Nano Optoelectronic Information System, Ministry of Industry and Information Technology, Harbin 150001, People's Republic of China
- Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China
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10
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Cohen-Stead B, Bradley O, Miles C, Batrouni G, Scalettar R, Barros K. Fast and scalable quantum Monte Carlo simulations of electron-phonon models. Phys Rev E 2022; 105:065302. [PMID: 35854479 DOI: 10.1103/physreve.105.065302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and we report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but it incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. These methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.
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Affiliation(s)
| | - Owen Bradley
- Department of Physics, University of California, Davis, California 95616, USA
| | - Cole Miles
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - George Batrouni
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, (INPHYNI), 06103 Nice, France
- Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore
| | - Richard Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - Kipton Barros
- Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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11
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Uniaxial pressure induced stripe order rotation in La1.88Sr0.12CuO4. Nat Commun 2022; 13:1795. [PMID: 35379813 PMCID: PMC8979978 DOI: 10.1038/s41467-022-29465-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 03/16/2022] [Indexed: 11/08/2022] Open
Abstract
AbstractStatic stripe order is detrimental to superconductivity. Yet, it has been proposed that transverse stripe fluctuations may enhance the inter-stripe Josephson coupling and thus promote superconductivity. Direct experimental studies of stripe dynamics, however, remain difficult. From a strong-coupling perspective, transverse stripe fluctuations are realized in the form of dynamic “kinks”—sideways shifting stripe sections. Here, we show how modest uniaxial pressure tuning reorganizes directional kink alignment. Our starting point is La1.88Sr0.12CuO4 where transverse kink ordering results in a rotation of stripe order away from the crystal axis. Application of mild uniaxial pressure changes the ordering pattern and pins the stripe order to the crystal axis. This reordering occurs at a much weaker pressure than that to detwin the stripe domains and suggests a rather weak transverse stripe stiffness. Weak spatial stiffness and transverse quantum fluctuations are likely key prerequisites for stripes to coexist with superconductivity.
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12
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Intertwined spin, charge, and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit. Proc Natl Acad Sci U S A 2022; 119:2112806119. [PMID: 35140180 PMCID: PMC8851552 DOI: 10.1073/pnas.2112806119] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/17/2021] [Indexed: 11/18/2022] Open
Abstract
The high-temperature superconducting cuprates are governed by intertwined striped magnetic and charge orders, in addition to superconductivity. Remarkably similar behavior has also been seen in numerical calculations for the Hubbard model describing the copper–oxygen layers in these materials. Finite-cluster methods typically find that spin- and charge-stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit, often conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in an embedded cluster calculation for the Hubbard model. This discovery demonstrates that striped states survive in the thermodynamic limit and allows us to study their influence on the model’s superconducting properties, where we find evidence for pair-density-wave correlations intertwined with the stripe correlations. The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite-cluster methods typically indicate that stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides an opportunity to study the influence of fluctuating stripe correlations on the model’s pairing correlations within a unified numerical framework. Using this approach, we also find evidence for pair-density-wave correlations whose strength is correlated with that of the stripes.
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13
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Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors. CONDENSED MATTER 2021. [DOI: 10.3390/condmat6040052] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr2Cu2.75Mo0.25O7.54(Tc=84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.
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14
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Vaezi MS, Negari AR, Moharramipour A, Vaezi A. Amelioration for the Sign Problem: An Adiabatic Quantum Monte Carlo Algorithm. PHYSICAL REVIEW LETTERS 2021; 127:217003. [PMID: 34860094 DOI: 10.1103/physrevlett.127.217003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Revised: 03/29/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
We introduce the adiabatic quantum Monte Carlo (AQMC) method, where we gradually crank up the interaction strength, as an amelioration of the sign problem. It is motivated by the adiabatic theorem and will approach the true ground state if the evolution time is long enough. We demonstrate that the AQMC algorithm enhances the average sign exponentially such that low enough temperatures can be accessed and ground-state properties probed. It is a controlled approximation that satisfies the variational theorem and provides an upper bound for the ground-state energy. We first benchmark the AQMC algorithm vis-à-vis the undoped Hubbard model on the square lattice which is known to be sign-problem-free within the conventional quantum Monte Carlo formalism. Next, we test the AQMC algorithm against the density-matrix-renormalization-group approach for the doped four-leg ladder Hubbard model and demonstrate its remarkable accuracy. As a nontrivial example, we apply our method to the Hubbard model at p=1/8 doping for a 16×8 system and discuss its ground-state properties. We finally utilize our method and demonstrate the emergence of U(1)_{2}∼SU(2)_{1} topological order in a strongly correlated Chern insulator.
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Affiliation(s)
- Mohammad-Sadegh Vaezi
- Pasargad Institute for Advanced Innovative Solutions (PIAIS), Tehran 19916-33361, Iran
| | - Amir-Reza Negari
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
| | - Amin Moharramipour
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
| | - Abolhassan Vaezi
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
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15
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Wang Y, Chen Z, Shi T, Moritz B, Shen ZX, Devereaux TP. Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates. PHYSICAL REVIEW LETTERS 2021; 127:197003. [PMID: 34797146 DOI: 10.1103/physrevlett.127.197003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 09/22/2021] [Indexed: 06/13/2023]
Abstract
Establishing a minimal microscopic model for cuprates is a key step towards the elucidation of a high-T_{c} mechanism. By a quantitative comparison with a recent in situ angle-resolved photoemission spectroscopy measurement in doped 1D cuprate chains, our simulation identifies a crucial contribution from long-range electron-phonon coupling beyond standard Hubbard models. Using reasonable ranges of coupling strengths and phonon energies, we obtain a strong attractive interaction between neighboring electrons, whose strength is comparable to experimental observations. Nonlocal couplings play a significant role in the mediation of neighboring interactions. Considering the structural and chemical similarity between 1D and 2D cuprate materials, this minimal model with long-range electron-phonon coupling will provide important new insights on cuprate high-T_{c} superconductivity and related quantum phases.
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Affiliation(s)
- Yao Wang
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - Zhuoyu Chen
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Tao Shi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Brian Moritz
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Zhi-Xun Shen
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Thomas P Devereaux
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
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16
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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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17
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Krockenberger Y, Ikeda A, Yamamoto H. Atomic Stripe Formation in Infinite-Layer Cuprates. ACS OMEGA 2021; 6:21884-21891. [PMID: 34497883 PMCID: PMC8412913 DOI: 10.1021/acsomega.1c01720] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/10/2021] [Accepted: 07/05/2021] [Indexed: 06/13/2023]
Abstract
High-temperature superconductivity appears in cuprate materials that have been tuned in a way where the copper-oxygen bond configuration and coordination is in a state of minimal energy. In competition with the Jahn-Teller effect, which impedes the formation of infinitely connected CuO2 planes, the state of minimal energy persists for planar copper-oxygen bond length variations of up to 10%. We have synthesized the infinite-layer phases of CaCuO2 and SrCuO2 as single-crystalline films using molecular beam epitaxy and performed in-plane scanning transmission electron microscopy mapping. For the infinite-layer phase of CaCuO2 with a short Cu-O bond length, the CuO2 planes maintain their minimal energy by forming distinguished atomic stripes. In contrast, atomic stripe formation does not occur in the infinite-layer phase of SrCuO2, which has a larger Cu-O bond length. The polar field provided by the charge reservoir layer in cuprates with infinitely connected CuO2 planes holds the key over the emergence of superconductivity and is vital to maintain infinitely connected CuO2 planes themselves.
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18
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Gong S, Zhu W, Sheng DN. Robust d-Wave Superconductivity in the Square-Lattice t-J Model. PHYSICAL REVIEW LETTERS 2021; 127:097003. [PMID: 34506200 DOI: 10.1103/physrevlett.127.097003] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 07/16/2021] [Indexed: 06/13/2023]
Abstract
Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.
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Affiliation(s)
- Shoushu Gong
- Department of Physics, Beihang University, Beijing 100191, China
| | - W Zhu
- School of Science, Westlake University, Hangzhou 310024, China; Institute of Natural Sciences, Westlake Institute of Advanced Study, Hangzhou 310024, China; and Key Laboratory for Quantum Materials of Zhejiang Province, Westlake University, Hangzhou 310024, China
| | - D N Sheng
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA
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19
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Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane. Nat Commun 2021; 12:597. [PMID: 33500415 PMCID: PMC7838423 DOI: 10.1038/s41467-020-20824-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 12/21/2020] [Indexed: 11/08/2022] Open
Abstract
In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi2Sr2CaCu2O8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern. Knowledge of effective Coulomb interactions is central to understand emergent quantum phases in strongly correlated systems. Here, Boschini et al. report a dynamic quasi-circular spectrum of charge density wave fluctuations in the CuO2 plane of Bi2Sr2CaCu2O8+δ, shedding a light on understanding how Coulomb interactions can lead to rotational and translational symmetry breaking in the cuprates.
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20
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Christensen MH, Wang X, Schattner Y, Berg E, Fernandes RM. Modeling Unconventional Superconductivity at the Crossover between Strong and Weak Electronic Interactions. PHYSICAL REVIEW LETTERS 2020; 125:247001. [PMID: 33412040 DOI: 10.1103/physrevlett.125.247001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Accepted: 10/22/2020] [Indexed: 06/12/2023]
Abstract
High-temperature superconductivity emerges in many different quantum materials, often in regions of the phase diagram where the electronic kinetic energy is comparable to the electron-electron repulsion. Describing such intermediate-coupling regimes has proven challenging as standard perturbative approaches are inapplicable. Here, we employ quantum Monte Carlo methods to solve a multiband Hubbard model that does not suffer from the sign problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free studies, we treat magnetic, superconducting, and charge degrees of freedom on an equal footing. We find an antiferromagnetic dome accompanied by a metal-to-insulator crossover line in the intermediate-coupling regime, with a smaller superconducting dome appearing in the metallic region. Across the antiferromagnetic dome, the magnetic fluctuations change from overdamped in the metallic region to propagating in the insulating region. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.
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Affiliation(s)
- Morten H Christensen
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Xiaoyu Wang
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - Yoni Schattner
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Rafael M Fernandes
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
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21
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Gao H, Coulthard JR, Jaksch D, Mur-Petit J. Anomalous Spin-Charge Separation in a Driven Hubbard System. PHYSICAL REVIEW LETTERS 2020; 125:195301. [PMID: 33216562 DOI: 10.1103/physrevlett.125.195301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Accepted: 10/05/2020] [Indexed: 06/11/2023]
Abstract
Spin-charge separation (SCS) is a striking manifestation of strong correlations in low-dimensional quantum systems, whereby a fermion splits into separate spin and charge excitations that travel at different speeds. Here, we demonstrate that periodic driving enables control over SCS in a Hubbard system near half filling. In one dimension, we predict analytically an exotic regime where charge travels slower than spin and can even become "frozen," in agreement with numerical calculations. In two dimensions, the driving slows both charge and spin and leads to complex interferences between single-particle and pair-hopping processes.
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Affiliation(s)
- Hongmin Gao
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Jonathan R Coulthard
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Dieter Jaksch
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore
| | - Jordi Mur-Petit
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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22
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Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi 2Sr 2LaCuO 6+δ. Proc Natl Acad Sci U S A 2020; 117:16219-16225. [PMID: 32586955 PMCID: PMC7368327 DOI: 10.1073/pnas.2001755117] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Charge-density waves (CDWs) are a ubiquitous form of electron density modulation in cuprate superconductors. Unveiling the nature of quasistatic CDWs and their dynamical excitations is crucial for understanding their origin––similar to the study of antiferromagnetism in cuprates. However, dynamical CDW excitations remain largely unexplored due to the limited availability of suitable experimental probes. Here, using resonant inelastic X-ray scattering, we observe dynamical CDW excitations in Bi2Sr2LaCuO6+δ (Bi2201) superconductors through its interference with the lattice. The distinct anomalies of the bond-buckling and the bond-stretching phonons allow us to draw a clear picture of funnel-shaped dynamical CDW excitations in Bi2201. Our results of the interplay between CDWs and the phonon anomalies shed light on the nature of CDWs in cuprates. Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi2Sr1.4La0.6CuO6+δ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi2Sr1.8La0.2CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW. Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.
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23
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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: 6] [Impact Index Per Article: 1.5] [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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24
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Lin JQ, Miao H, Mazzone DG, Gu GD, Nag A, Walters AC, García-Fernández M, Barbour A, Pelliciari J, Jarrige I, Oda M, Kurosawa K, Momono N, Zhou KJ, Bisogni V, Liu X, Dean MPM. Strongly Correlated Charge Density Wave in La_{2-x}Sr_{x}CuO_{4} Evidenced by Doping-Dependent Phonon Anomaly. PHYSICAL REVIEW LETTERS 2020; 124:207005. [PMID: 32501068 DOI: 10.1103/physrevlett.124.207005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
The discovery of charge-density-wave-related effects in the resonant inelastic x-ray scattering spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. Here, we report a comprehensive resonant inelastic x-ray scattering study of La_{2-x}Sr_{x}CuO_{4} finding that charge-density wave effects persist up to a remarkably high doping level of x=0.21 before disappearing at x=0.25. The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross section for phonons and charge-density-wave-induced phonon softening. We interpret our results in terms of a charge-density wave that is generated by strong correlations and a phonon response that is driven by the charge-density-wave-induced modification of the lattice.
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Affiliation(s)
- J Q Lin
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - H Miao
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - D G Mazzone
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - G D Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - A Nag
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - A C Walters
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - M García-Fernández
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - A Barbour
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - J Pelliciari
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - I Jarrige
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - M Oda
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - K Kurosawa
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - N Momono
- Department of Sciences and Informatics, Muroran Institute of Technology, Muroran 050-8585, Japan
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - V Bisogni
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - X Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - M P M Dean
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
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25
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Zhang Y, Lane C, Furness JW, Barbiellini B, Perdew JP, Markiewicz RS, Bansil A, Sun J. Competing stripe and magnetic phases in the cuprates from first principles. Proc Natl Acad Sci U S A 2020; 117:68-72. [PMID: 31843896 PMCID: PMC6955329 DOI: 10.1073/pnas.1910411116] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Realistic description of competing phases in complex quantum materials has proven extremely challenging. For example, much of the existing density-functional-theory-based first-principles framework fails in the cuprate superconductors. Various many-body approaches involve generic model Hamiltonians and do not account for the interplay between the spin, charge, and lattice degrees of freedom. Here, by deploying the recently constructed strongly constrained and appropriately normed (SCAN) density functional, we show how the landscape of competing stripe and magnetic phases can be addressed on a first-principles basis both in the parent insulator YBa2Cu3O6 and the near-optimally doped YBa2Cu3O7 as archetype cuprate compounds. In YBa2Cu3O7, we find many stripe phases that are nearly degenerate with the ground state and may give rise to the pseudogap state from which the high-temperature superconducting state emerges. We invoke no free parameters such as the Hubbard U, which has been the basis of much of the existing cuprate literature. Lattice degrees of freedom are found to be crucially important in stabilizing the various phases.
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Affiliation(s)
- Yubo Zhang
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118
| | - Christopher Lane
- Department of Physics, Northeastern University, Boston, MA 02115
| | - James W Furness
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118
| | - Bernardo Barbiellini
- Department of Physics, School of Engineering Science, LUT University, FI-53851 Lappeenranta, Finland
- Department of Physics, Northeastern University, Boston, MA 02115
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, PA 19122;
- Department of Chemistry, Temple University, Philadelphia, PA 19122
| | | | - Arun Bansil
- Department of Physics, Northeastern University, Boston, MA 02115;
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118;
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26
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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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27
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Amoretti A, Areán D, Goutéraux B, Musso D. Universal Relaxation in a Holographic Metallic Density Wave Phase. PHYSICAL REVIEW LETTERS 2019; 123:211602. [PMID: 31809185 DOI: 10.1103/physrevlett.123.211602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Revised: 09/04/2019] [Indexed: 06/10/2023]
Abstract
In this Letter, we uncover a universal relaxation mechanism of pinned density waves, combining gauge-gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (e.g., by disorder or lattice effects), these phonons are pinned with a mass m and damped at a rate Ω, which we explicitly compute. This contribution to Ω is distinct from that of topological defects. We show that Ω≃Gm^{2}Ξ, where G is the shear modulus and Ξ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high T_{c} superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.
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Affiliation(s)
- Andrea Amoretti
- Dipartimento di Fisica, Università di Genova, via Dodecaneso 33, I-16146 Genova, Italy and I.N.F.N.-Sezione di Genova and Physique Théorique et Mathématique and International Solvay Institutes Université Libre de Bruxelles, C.P. 231, 1050 Brussels, Belgium
| | - Daniel Areán
- Instituto de Física Teórica UAM/CSIC, Calle Nicolás Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain
| | - Blaise Goutéraux
- CPHT, CNRS, Ecole polytechnique, IP Paris, F-91128 Palaiseau, France and Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
| | - Daniele Musso
- Departamento de Física de Partículas, Universidade de Santiago de Compostela and Instituto Galego de Física de Altas Enerxías (IGFAE), Santiago de Compostela, 15705, Spain
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28
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Jiang HC, Devereaux TP. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping
t
′. Science 2019; 365:1424-1428. [DOI: 10.1126/science.aal5304] [Citation(s) in RCA: 78] [Impact Index Per Article: 15.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2018] [Accepted: 08/20/2019] [Indexed: 11/02/2022]
Affiliation(s)
- Hong-Chen Jiang
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, CA 94025, USA
| | - Thomas P. Devereaux
- Stanford Institute for Materials and Energy Sciences, SLAC and Stanford University, Menlo Park, CA 94025, USA
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
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29
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Li Y, Terzic J, Baity PG, Popović D, Gu GD, Li Q, Tsvelik AM, Tranquada JM. Tuning from failed superconductor to failed insulator with magnetic field. SCIENCE ADVANCES 2019; 5:eaav7686. [PMID: 31214648 PMCID: PMC6570505 DOI: 10.1126/sciadv.aav7686] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/17/2018] [Accepted: 05/07/2019] [Indexed: 06/09/2023]
Abstract
Do charge modulations compete with electron pairing in high-temperature copper oxide superconductors? We investigated this question by suppressing superconductivity in a stripe-ordered cuprate compound at low temperature with high magnetic fields. With increasing field, loss of three-dimensional superconducting order is followed by reentrant two-dimensional superconductivity and then an ultraquantum metal phase. Circumstantial evidence suggests that the latter state is bosonic and associated with the charge stripes. These results provide experimental support to the theoretical perspective that local segregation of doped holes and antiferromagnetic spin correlations underlies the electron-pairing mechanism in cuprates.
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Affiliation(s)
- Yangmu Li
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - J. Terzic
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
| | - P. G. Baity
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
| | - Dragana Popović
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
| | - G. D. Gu
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Qiang Li
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - A. M. Tsvelik
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - J. M. Tranquada
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY 11973, USA
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30
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Singh A, Lee JCT, Avila KE, Chen Y, Montoya SA, Fullerton EE, Fischer P, Dahmen KA, Kevan SD, Sanyal MK, Roy S. Scaling of domain cascades in stripe and skyrmion phases. Nat Commun 2019; 10:1988. [PMID: 31040276 PMCID: PMC6491444 DOI: 10.1038/s41467-019-09934-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2017] [Accepted: 04/09/2019] [Indexed: 11/30/2022] Open
Abstract
The origin of deterministic macroscopic properties often lies in microscopic stochastic motion. Magnetic fluctuations that manifest as domain avalanches and chaotic magnetization jumps exemplify such stochastic motion and have been studied in great detail. Here we report Fourier space studies of avalanches in a system exhibiting competing magnetic stripe and skyrmion phase using a soft X-ray speckle metrology technique. We demonstrate the existence of phase boundaries and underlying critical points in the stripe and skyrmion phases. We found that distinct scaling and universality classes are associated with these domain topologies. The magnitude and frequency of abrupt magnetic domain jumps observed in the stripe phase are dramatically reduced in the skyrmion phase. Our results provide an incisive way to probe and understand phase stability in systems exhibiting complex spin topologies. Switching of magnetic materials often occurs through discrete random avalanches. Singh et al. observe sharply reduced avalanches in the topologically protected skyrmion phase of a Fe/Gd heterostructure and obtain different critical behaviour in the stripe and skyrmion phases, suggesting distinct universality classes.
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Affiliation(s)
- A Singh
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata, West Bengal, 700064, India
| | - J C T Lee
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA.,Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA
| | - K E Avila
- Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA
| | - Y Chen
- Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA
| | - S A Montoya
- Center for Memory and Recording Research, University of California San Diego, La Jolla, CA, 92093, USA
| | - E E Fullerton
- Center for Memory and Recording Research, University of California San Diego, La Jolla, CA, 92093, USA
| | - P Fischer
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA.,Department of Physics, University of California, Santa Cruz, CA, 95064, USA
| | - K A Dahmen
- Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA
| | - S D Kevan
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA
| | - M K Sanyal
- Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata, West Bengal, 700064, India
| | - S Roy
- Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA, 94720, USA.
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31
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Chen XM, Mazzoli C, Cao Y, Thampy V, Barbour AM, Hu W, Lu M, Assefa TA, Miao H, Fabbris G, Gu GD, Tranquada JM, Dean MPM, Wilkins SB, Robinson IK. Charge density wave memory in a cuprate superconductor. Nat Commun 2019; 10:1435. [PMID: 30926816 PMCID: PMC6440992 DOI: 10.1038/s41467-019-09433-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2018] [Accepted: 03/11/2019] [Indexed: 11/09/2022] Open
Abstract
Although CDW correlations are a ubiquitous feature of the superconducting cuprates, their disparate properties suggest a crucial role for pinning the CDW to the lattice. Here, we report coherent resonant X-ray speckle correlation analysis, which directly determines the reproducibility of CDW domain patterns in La1.875Ba0.125CuO4 (LBCO 1/8) with thermal cycling. While CDW order is only observed below 54 K, where a structural phase transition creates inequivalent Cu-O bonds, we discover remarkably reproducible CDW domain memory upon repeated cycling to far higher temperatures. That memory is only lost on cycling to 240(3) K, which recovers the four-fold symmetry of the CuO2 planes. We infer that the structural features that develop below 240 K determine the CDW pinning landscape below 54 K. This opens a view into the complex coupling between charge and lattice degrees of freedom in superconducting cuprates.
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Affiliation(s)
- X M Chen
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA. .,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.
| | - C Mazzoli
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - Y Cao
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - V Thampy
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA.,Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - A M Barbour
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - W Hu
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - M Lu
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - T A Assefa
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - H Miao
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - G Fabbris
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - G D Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - J M Tranquada
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - M P M Dean
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA.
| | - S B Wilkins
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA.
| | - I K Robinson
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA. .,London Centre for Nanotechnology, University College, Gower St., London, WC1E 6BT, UK.
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32
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Zhao Z, Zhang S, Yu T, Xu H, Bergara A, Yang G. Predicted Pressure-Induced Superconducting Transition in Electride Li_{6}P. PHYSICAL REVIEW LETTERS 2019; 122:097002. [PMID: 30932540 DOI: 10.1103/physrevlett.122.097002] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Indexed: 06/09/2023]
Abstract
Electrides are unique compounds where most of the electrons reside at interstitial regions of the crystal behaving as anions, which strongly determines its physical properties. Interestingly, the magnitude and distribution of interstitial electrons can be effectively modified either by modulating its chemical composition or external conditions (e.g., pressure). Most of the electrides under high pressure are nonmetallic, and superconducting electrides are very rare. Here we report that a pressure-induced stable Li_{6}P electride, identified by first-principles swarm structure calculations, becomes a superconductor with a predicted superconducting transition temperature T_{c} of 39.3 K, which is the highest among the already known electrides. The interstitial electrons in Li_{6}P, with dumbbell-like connected electride states, play a dominant role in the superconducting transition. Other Li-rich phosphides, Li_{5}P, Li_{11}P_{2}, Li_{15}P_{2}, and Li_{8}P, are also predicted to be superconducting electrides, but with a lower T_{c}. Superconductivity in all these compounds can be attributed to a combination of a weak electronegativity of phosphorus (P) with a strong electropositivity of lithium (Li), and opens up the interest to explore high-temperature superconductivity in similar binary compounds.
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Affiliation(s)
- Ziyuan Zhao
- Centre for Advanced Optoelectronic Functional Materials Research and Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
| | - Shoutao Zhang
- Centre for Advanced Optoelectronic Functional Materials Research and Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
| | - Tong Yu
- Centre for Advanced Optoelectronic Functional Materials Research and Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
| | - Haiyang Xu
- Centre for Advanced Optoelectronic Functional Materials Research and Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
| | - Aitor Bergara
- Departamento de Física de la Materia Condensada, Universidad del País Vasco-Euskal Herriko Unibertsitatea, UPV/EHU, 48080 Bilbao, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia, Spain
- Centro de Física de Materiales CFM, Centro Mixto CSIC-UPV/EHU, 20018 Donostia, Spain
| | - Guochun Yang
- Centre for Advanced Optoelectronic Functional Materials Research and Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
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33
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Tu WL, Lee TK. Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors. Sci Rep 2019; 9:1719. [PMID: 30737472 PMCID: PMC6368576 DOI: 10.1038/s41598-018-38288-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Accepted: 12/10/2018] [Indexed: 11/09/2022] Open
Abstract
One of the most puzzling problems of high temperature cuprate superconductor is the pseudogap phase (PG) at temperatures above the superconducting transition temperature in the underdoped regime. The PG phase is found by the angle-resolved photoemission spectra (ARPES) to have a gap at some regions in momentum space and a fraction of Fermi surface remained, known as Fermi arcs. The arc turns into a d-wave SC gap with a node below the SC transition temperature. Here, by studying a strongly correlated model at low temperatures, we obtained a phase characterized by two kinds of pairing order parameters with the total momentum of the Cooper pair to be zero and finite. The finite momentum pairing is accompanied with a spatial modulation of pairing order, i.e. a pair density wave (PDW). These PDW phases are intertwined with modulations of charge density and intra-unit cell form factors. The coexistence of the two different pairing orders provides the unique two-gaps like spectra observed by ARPES for superconducting cuprates. As temperature raises, the zero-momentum pairing order vanishes while the finite momentum pairing orders are kept, thus Fermi arcs are realized. The calculated quasiparticle spectra have the similar doping and temperature dependence as reported by ARPES and scanning tunneling spectroscopy (STS). The consequence of breaking symmetry between x and y due to the unidirectional PDW and the possibility to probe such a PDW state in the PG phase is discussed.
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Affiliation(s)
- Wei-Lin Tu
- Department of Physics, National Taiwan University, Daan, Taipei, 10617, Taiwan
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, Toulouse, France
- Institute of Physics, Academia Sinica, Nankang, Taipei, 11529, Taiwan
| | - Ting-Kuo Lee
- Institute of Physics, Academia Sinica, Nankang, Taipei, 11529, Taiwan.
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34
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Zhao H, Ren Z, Rachmilowitz B, Schneeloch J, Zhong R, Gu G, Wang Z, Zeljkovic I. Charge-stripe crystal phase in an insulating cuprate. NATURE MATERIALS 2019; 18:103-107. [PMID: 30559411 DOI: 10.1038/s41563-018-0243-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 11/06/2018] [Indexed: 06/09/2023]
Abstract
High-temperature (high-Tc) superconductivity in cuprates arises from carrier doping of an antiferromagnetic Mott insulator. This carrier doping leads to the formation of electronic liquid-crystal phases1. The insulating charge-stripe crystal phase is predicted to form when a small density of holes is doped into the charge-transfer insulator state1-3, but this phase is yet to be observed experimentally. Here, we use surface annealing to extend the accessible doping range in Bi-based cuprates and realize the lightly doped charge-transfer insulating state of the cuprate Bi2Sr2CaCu2O8+x. In this insulating state with a charge transfer gap on the order of ~1 eV, our spectroscopic imaging scanning tunnelling microscopy measurements provide strong evidence for a unidirectional charge-stripe order with a commensurate 4a0 period along the Cu-O-Cu bond. Notably, this insulating charge-stripe crystal phase develops before the onset of the pseudogap and formation of the Fermi surface. Our work provides fresh insight into the microscopic origin of electronic inhomogeneity in high-Tc cuprates.
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Affiliation(s)
- He Zhao
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | - Zheng Ren
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | | | | | | | - Genda Gu
- Brookhaven National Laboratory, Upton, NY, USA
| | - Ziqiang Wang
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | - Ilija Zeljkovic
- Department of Physics, Boston College, Chestnut Hill, MA, USA.
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35
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Hohenadler M, Assaad FF. Fractionalized Metal in a Falicov-Kimball Model. PHYSICAL REVIEW LETTERS 2018; 121:086601. [PMID: 30192610 DOI: 10.1103/physrevlett.121.086601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Indexed: 06/08/2023]
Abstract
Quantum Monte Carlo simulations reveal an exotic metallic phase with a single-particle gap but gapless spin and charge excitations and a nonsaturating resistivity in a two-dimensional SU(2) Falicov-Kimball model. An exact duality between this model and an unconstrained slave-spin theory leads to a classification of the phase as a fractionalized or orthogonal metal whose low-energy excitations have different quantum numbers than the original electrons. Whereas the fractionalized metal corresponds to the regime of disordered slave spins, the regime of ordered slave spins is a Fermi liquid. At a critical temperature, an Ising phase transition to a spontaneously generated constrained slave-spin theory of the Hubbard model is observed.
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Affiliation(s)
- Martin Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
| | - Fakher F Assaad
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
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