1
|
Feng Y, Lou J, Chen Y. Superconducting and charge-ordered states in the anisotropic t-J-U model. Sci Rep 2024; 14:1416. [PMID: 38228755 PMCID: PMC10792048 DOI: 10.1038/s41598-024-51829-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2023] [Accepted: 01/09/2024] [Indexed: 01/18/2024] Open
Abstract
Motivated by the effect of symmetry breaking in cuprates superconductors YBa[Formula: see text]Cu[Formula: see text]O[Formula: see text], we employ the renormalized mean-field theory to study the presence of uniform superconducting and charge-ordered states in two anisotropic t-J-U models, either with hopping strength anisotropy or antiferromagnetic interaction anisotropy. In the case of uniform superconducting state, compared with the isotropic t-J-U model with only [Formula: see text]-wave superconducting state, there is an additional s-wave superconducting state in the model with hopping strength anisotropy. Meanwhile, the hopping anisotropy may enhance the critical Coulomb interaction [Formula: see text] at the Mott insulator to the Gossamer superconductor transition point, and strong hopping anisotropy may weaken the superconducting state. In the case of a charge-ordered state, hopping anisotropy may suppress the amplitude of the charge density waves and pair density waves, which originate from local Coulomb interactions. These results indicate that the effects of hopping anisotropy and local Coulomb interactions are competitive. Moreover, the antiferromagnetic interaction anisotropy only weakly suppresses the superconducting gap and density wave amplitude. Our results show that the t-J-U model with hopping anisotropy is qualitatively consistent with experimental superconducting pair symmetry and charge density waves in the YBa[Formula: see text]Cu[Formula: see text]O[Formula: see text] system.
Collapse
Affiliation(s)
- Yifan Feng
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai, 200433, China
| | - Jie Lou
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai, 200433, China
| | - Yan Chen
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai, 200433, China.
| |
Collapse
|
2
|
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.
Collapse
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.
| |
Collapse
|
3
|
Tu WL, Wu HK, Suzuki T. Frustration-induced supersolid phases of extended Bose-Hubbard model in the hard-core limit. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:455401. [PMID: 32634790 DOI: 10.1088/1361-648x/aba383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
We investigate exotic supersolid phases in the extended Bose-Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mechanism for underlying superfluid/supersolid states to be formed. With this knowledge, we predict and realize thed-wave superfluid, which shares the same pairing symmetry with high-Tcmaterials, and its extended phases. We believe that our results contribute to preliminary understanding for desired target phases in the real-world experimental systems.
Collapse
Affiliation(s)
- Wei-Lin Tu
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Huan-Kuang Wu
- Department of Physics, Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, MD 20742, United States of America
| | - Takafumi Suzuki
- Graduate School of Engineering, University of Hyogo, Hyogo, Himeji 670-2280, Japan
| |
Collapse
|
4
|
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.
Collapse
|
5
|
Imaging the energy gap modulations of the cuprate pair-density-wave state. Nature 2020; 580:65-70. [PMID: 32238945 DOI: 10.1038/s41586-020-2143-x] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2019] [Accepted: 01/20/2020] [Indexed: 11/08/2022]
Abstract
The defining characteristic1,2 of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ(r), where r is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)3,4. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling5, the distinctive signature in single-electron tunnelling of a periodic Δ(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ(r) modulations in the canonical cuprate Bi2Sr2CaCu2O8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8) (where a0 is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state6,7. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi2Sr2CaCu2O8+δ.
Collapse
|
6
|
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.
Collapse
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.
| |
Collapse
|
7
|
Mott transition in chain structure of strained VO 2 films revealed by coherent phonons. Sci Rep 2017; 7:16038. [PMID: 29167488 PMCID: PMC5700180 DOI: 10.1038/s41598-017-16188-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2017] [Accepted: 11/08/2017] [Indexed: 11/11/2022] Open
Abstract
The characteristic of strongly correlated materials is the Mott transition between metal and insulator (MIT or IMT) in the same crystalline structure, indicating the presence of a gap formed by the Coulomb interaction between carriers. The physics of the transition needs to be revealed. Using VO2, as a model material, we observe the emergence of a metallic chain in the intermediate insulating monoclinic structure (M2 phase) of epitaxial strained films, proving the Mott transition involving the breakdown of the critical Coulomb interaction. It is revealed by measuring the temperature dynamics of coherent optical phonons with separated vibrational modes originated from two substructures in M2: one is the charge-density-wave, formed by electron-phonon (e-ph) interaction, and the other is the equally spaced insulator-chain with electron-electron (e-e) correlations.
Collapse
|
8
|
Kawasaki S, Li Z, Kitahashi M, Lin CT, Kuhns PL, Reyes AP, Zheng GQ. Charge-density-wave order takes over antiferromagnetism in Bi 2Sr 2-x La x CuO 6 superconductors. Nat Commun 2017; 8:1267. [PMID: 29097672 PMCID: PMC5668353 DOI: 10.1038/s41467-017-01465-9] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Accepted: 09/19/2017] [Indexed: 11/17/2022] Open
Abstract
Superconductivity appears in the cuprates when a spin order is destroyed, while the role of charge is less known. Recently, charge density wave (CDW) was found below the superconducting dome in YBa2Cu3Oy when a high magnetic field is applied perpendicular to the CuO2 plane, which was suggested to arise from incipient CDW in the vortex cores that becomes overlapped. Here by 63Cu-nuclear magnetic resonance, we report the discovery of CDW induced by an in-plane field, setting in above the dome in single-layered Bi2Sr2−xLaxCuO6. The onset temperature TCDW takes over the antiferromagnetic order temperature TN beyond a critical doping level at which superconductivity starts to emerge, and scales with the pseudogap temperature T*. These results provide important insights into the relationship between spin order, CDW and the pseudogap, and their connections to high-temperature superconductivity. Whilst superconductivity usually appears when magnetic order is suppressed, the role of charge is less known. Here, Kawasaki et al. report a charge density wave (CDW) above the superconducting transition induced by an in-plane magnetic field in Bi2Sr2-xLaxCuO6, with the CDW onset temperature scaling with the pseudogap temperature.
Collapse
Affiliation(s)
- S Kawasaki
- Department of Physics, Okayama University, Okayama, 700-8530, Japan
| | - Z Li
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, 100190, Beijing, China
| | - M Kitahashi
- Department of Physics, Okayama University, Okayama, 700-8530, Japan
| | - C T Lin
- Max-Planck-Institut fur Festkorperforschung, Heisenbergstrasse 1, D-70569, Stuttgart, Germany
| | - P L Kuhns
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
| | - A P Reyes
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
| | - Guo-Qing Zheng
- Department of Physics, Okayama University, Okayama, 700-8530, Japan. .,Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, 100190, Beijing, China.
| |
Collapse
|