1
|
Zhang HY, Wu XQ, Kong FJ, Bai YJ, Xu N. Doping evolution of the magnetic excitations in the monolayer CuO 2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:415603. [PMID: 32503012 DOI: 10.1088/1361-648x/ab99ec] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2019] [Accepted: 06/05/2020] [Indexed: 06/11/2023]
Abstract
In this paper, we study theoretically the doping evolution behaviors of the magnetic excitations (MEs) in the monolayer CuO2grown on Bi2Sr2CaCu2O8+δsubstrate. For the undoped system, the MEs exhibit the low energy commensurate behavior around (π,π). They turn to be incommensurate when the system is slightly hole-doped. In the intermediate doping regime, the low energy MEs diminish gradually. They turn to be dominated by the high energy modes. With further doping, an exotic structure transition of the MEs occurs in the heavily hole-doped regime which is directly related to the Lifshitz transition. Distinct MEs are separated by the transition point around which the low energy MEs exhibit the ring-like structure around (0, 0). Before the transition, the MEs are dominated by the broad particle-hole continuum at very high energies. In contrast, across the transition point, two new low energy modes develop around (0, 0) and (π,π) attributing to the intrapocket and interpocket particle-hole scatterings, respectively.
Collapse
Affiliation(s)
- Hai-Yang Zhang
- Department of Physics, Yancheng Institute of Technology, Yancheng 224051, People's Republic of China
| | - Xiu-Qiang Wu
- Department of Physics, Yancheng Institute of Technology, Yancheng 224051, People's Republic of China
| | - Fan-Jie Kong
- Department of Physics, Yancheng Institute of Technology, Yancheng 224051, People's Republic of China
| | - Yu-Jie Bai
- Department of Physics, Yancheng Institute of Technology, Yancheng 224051, People's Republic of China
| | - Ning Xu
- Department of Physics, Yancheng Institute of Technology, Yancheng 224051, People's Republic of China
| |
Collapse
|
2
|
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
| |
Collapse
|
3
|
Mazurenko A, Chiu CS, Ji G, Parsons MF, Kanász-Nagy M, Schmidt R, Grusdt F, Demler E, Greif D, Greiner M. A cold-atom Fermi–Hubbard antiferromagnet. Nature 2017; 545:462-466. [DOI: 10.1038/nature22362] [Citation(s) in RCA: 419] [Impact Index Per Article: 59.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Accepted: 04/03/2017] [Indexed: 11/09/2022]
|
4
|
Eberlein A, Metzner W, Sachdev S, Yamase H. Fermi Surface Reconstruction and Drop in the Hall Number due to Spiral Antiferromagnetism in High-T_{c} Cuprates. PHYSICAL REVIEW LETTERS 2016; 117:187001. [PMID: 27835021 DOI: 10.1103/physrevlett.117.187001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Indexed: 06/06/2023]
Abstract
We show that a Fermi surface reconstruction due to spiral antiferromagnetic order may explain the rapid change in the Hall number as recently observed near optimal doping in cuprate superconductors [Badoux et al., Nature (London) 531, 210 (2016)]. The single-particle spectral function in the spiral state exhibits hole pockets which look like Fermi arcs due to a strong momentum dependence of the spectral weight. Adding charge-density wave order further reduces the Fermi surface to a single electron pocket. We propose quantum oscillation measurements to distinguish between commensurate and spiral antiferromagnetic order. Similar results apply to certain metals in which topological order replaces antiferromagnetic order.
Collapse
Affiliation(s)
- Andreas Eberlein
- Department of Physics, Harvard University, Cambridge Massachusetts 02138, USA
| | - Walter Metzner
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge Massachusetts 02138, USA
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - Hiroyuki Yamase
- National Institute for Materials Science, Tsukuba 305-0047, Japan
| |
Collapse
|
5
|
Yamase H, Eberlein A, Metzner W. Coexistence of Incommensurate Magnetism and Superconductivity in the Two-Dimensional Hubbard Model. PHYSICAL REVIEW LETTERS 2016; 116:096402. [PMID: 26991188 DOI: 10.1103/physrevlett.116.096402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2015] [Indexed: 06/05/2023]
Abstract
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Néel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order.
Collapse
Affiliation(s)
- Hiroyuki Yamase
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
- National Institute for Materials Science, Tsukuba 305-0047, Japan
| | - Andreas Eberlein
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Walter Metzner
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
| |
Collapse
|
6
|
Markiewicz RS, Lorenzana J, Seibold G, Bansil A. Short range smectic order driving long range nematic order: example of cuprates. Sci Rep 2016; 6:19678. [PMID: 26813579 PMCID: PMC4728556 DOI: 10.1038/srep19678] [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: 03/10/2015] [Accepted: 11/19/2015] [Indexed: 12/03/2022] Open
Abstract
We present a model for describing the combined presence of nematic and 'smectic' or stripe-like orders seen in recent scanning tunneling microscopy (STM) experiments on cuprates. The smectic order is treated as an electronic charge density wave with an associated Peierls distortion or a 'Pomeranchuk wave'. This primary order is restricted to nanoscale domains by disorder effects, while the secondary coupling to strain generates the nematic order with a considerably longer range. A variety of experimental results are shown to be consistent with our theoretical predictions.
Collapse
Affiliation(s)
- R. S. Markiewicz
- Physics Department, Northeastern University, Boston MA 02115, USA
| | - J. Lorenzana
- ISC-CNR and Dipartimento di Fisica, Università di Roma “La Sapienza”, P. Aldo Moro 2, 00185 Roma, Italy
- ISC-CNR, Via dei Taurini 19, I-00185 Roma, Italy
| | - G. Seibold
- Institut Für Physik, BTU Cottbus-Senftenberg, PBox 101344, 03013 Cottbus, Germany
| | - A. Bansil
- Physics Department, Northeastern University, Boston MA 02115, USA
| |
Collapse
|
7
|
Igoshev PA, Timirgazin MA, Gilmutdinov VF, Arzhnikov AK, Irkhin VY. Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:446002. [PMID: 26465091 DOI: 10.1088/0953-8984/27/44/446002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.
Collapse
Affiliation(s)
- P A Igoshev
- Institute of Metal Physics, Kovalevskaya str. 18, Ekaterinburg 620990, Russia. Ural Federal University, 620002 Ekaterinburg, Russia
| | | | | | | | | |
Collapse
|
8
|
Ma EY, Cui YT, Ueda K, Tang S, Chen K, Tamura N, Wu PM, Fujioka J, Tokura Y, Shen ZX. Mobile metallic domain walls in an all-in-all-out magnetic insulator. Science 2015; 350:538-41. [DOI: 10.1126/science.aac8289] [Citation(s) in RCA: 146] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Eric Yue Ma
- Geballe Laboratory for Advanced Materials (GLAM), Stanford University, Stanford, CA, USA
- Department of Applied Physics, Stanford University, Stanford, CA, USA
| | - Yong-Tao Cui
- Geballe Laboratory for Advanced Materials (GLAM), Stanford University, Stanford, CA, USA
| | - Kentaro Ueda
- Department of Applied Physics, University of Tokyo, Tokyo, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Saitama, Japan
| | - Shujie Tang
- Geballe Laboratory for Advanced Materials (GLAM), Stanford University, Stanford, CA, USA
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology (SIMIT), Shanghai, China
| | - Kai Chen
- Center for Advancing Materials Performance from the Nanoscale (CAMP-Nano), State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, China
| | - Nobumichi Tamura
- Advanced Light Source (ALS), Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Phillip M. Wu
- Geballe Laboratory for Advanced Materials (GLAM), Stanford University, Stanford, CA, USA
| | - Jun Fujioka
- Department of Applied Physics, University of Tokyo, Tokyo, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Saitama, Japan
| | - Yoshinori Tokura
- Department of Applied Physics, University of Tokyo, Tokyo, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Saitama, Japan
| | - Zhi-Xun Shen
- Geballe Laboratory for Advanced Materials (GLAM), Stanford University, Stanford, CA, USA
- Department of Applied Physics, Stanford University, Stanford, CA, USA
| |
Collapse
|
9
|
Laughlin RB. Fermi-liquid computation of the phase diagram of high-Tc cuprate superconductors with an orbital antiferromagnetic pseudogap. PHYSICAL REVIEW LETTERS 2014; 112:017004. [PMID: 24483922 DOI: 10.1103/physrevlett.112.017004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Indexed: 06/03/2023]
Abstract
A 4-parameter Fermi-liquid calculation of the high-Tc cuprate phase diagram is reported. Simultaneously accounted for are the special doping densities of 5% and 16%, the d-wave functional form of the (orbital antiferromagnetic) pseudogap, the measured Tc, superconducting gap, pseudogap and superfluid density as a function of doping, the particle-hole doping asymmetry and the half-filling spin wave velocity.
Collapse
Affiliation(s)
- R B Laughlin
- Department of Physics, Stanford University, Stanford, California 94305, USA
| |
Collapse
|
10
|
Xu J, Chiesa S, Walter EJ, Zhang S. Magnetic order in the Hubbard model in three dimensions and the crossover to two dimensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:415602. [PMID: 24047878 DOI: 10.1088/0953-8984/25/41/415602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Systems of fermions described by the three-dimensional (3D) repulsive Hubbard model on a cubic lattice have recently attracted considerable attention due to their possible experimental realization via cold atoms in an optical lattice. Analytical and numerical results are limited away from half-filling. We study the ground state of the doped system from weak to intermediate interaction strengths within the generalized Hartree-Fock approximation. The exact solution to the self-consistent-field equations in the thermodynamic limit is obtained and the ground state is shown to exhibit antiferromagnetic order and incommensurate spin-density waves (SDW). At low interaction strengths, the SDW has unidirectional character with a leading wavevector along the [100]-direction, and the system is metallic. As the interaction increases, the system undergoes a simultaneous structural and metal-to-insulator transition to a unidirectional SDW state along the [111]-direction, with a different wavelength. We systematically determine the real and momentum space properties of these states. The crossover from 3D to two dimensions (2D) is then studied by varying the inter-plane hopping amplitude, which can be experimentally realized by tuning the distance between a stack of square-lattice layers. Detailed comparisons are made between the exact numerical results and predictions from the pairing model, a variational ansatz based on the pairing of spins in the vicinity of the Fermi surface. Most of the numerical results can be understood quantitatively from the ansatz, which provides a simple picture for the nature of the SDW states.
Collapse
Affiliation(s)
- Jie Xu
- Department of Physics, College of William and Mary, Williamsburg, VA 23187, USA
| | | | | | | |
Collapse
|
11
|
Fink J, Schierle E, Weschke E, Geck J. Resonant elastic soft x-ray scattering. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:056502. [PMID: 23563216 DOI: 10.1088/0034-4885/76/5/056502] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site and valence specific probe to study spatial modulations of charge, spin and orbital degrees of freedom in solids on the nanoscopic length scale. It is not only used to investigate single-crystalline materials. This method also enables one to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces.
Collapse
Affiliation(s)
- J Fink
- Leibniz-Institute for Solid State and Materials Research Dresden, PO Box 270116, D-01171 Dresden, Germany.
| | | | | | | |
Collapse
|
12
|
Benjamin D, Abanin D, Abbamonte P, Demler E. Microscopic theory of resonant soft-x-ray scattering in materials with charge order: the example of charge stripes in high-temperature cuprate superconductors. PHYSICAL REVIEW LETTERS 2013; 110:137002. [PMID: 23581360 DOI: 10.1103/physrevlett.110.137002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2012] [Indexed: 06/02/2023]
Abstract
We present a microscopic theory of resonant soft-x-ray scattering that accounts for the delocalized character of valence electrons. Unlike past approaches based on local form factors, our functional determinant method treats realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. We show that the two-peak structure observed near the O K edge of stripe-ordered La1.875Ba0.125CuO4 is due to dynamical nesting within the canonical cuprate band structure. Our results provide evidence for reasonably well-defined, high-energy quasiparticles in cuprates and establish resonant soft-x-ray scattering as a bulk-sensitive probe of the electron quasiparticles.
Collapse
Affiliation(s)
- David Benjamin
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | | | | | | |
Collapse
|
13
|
Xu J, Chang CC, Walter EJ, Zhang S. Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:505601. [PMID: 22127010 DOI: 10.1088/0953-8984/23/50/505601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping, h. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is 2/h. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolve into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.
Collapse
Affiliation(s)
- Jie Xu
- Department of Physics, College of William and Mary, Williamsburg, VA 23187, USA.
| | | | | | | |
Collapse
|
14
|
Saniz R, Norman MR, Freeman AJ. Orbital mixing and nesting in the bilayer manganites La2-2xSr1+2xMn2O7. PHYSICAL REVIEW LETTERS 2008; 101:236402. [PMID: 19113571 DOI: 10.1103/physrevlett.101.236402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2008] [Indexed: 05/27/2023]
Abstract
A first principles study of La2-2xSr1+2xMn2O7 compounds for doping levels 0.3 < or = x < or = 0.5 shows that the low energy electronic structure of the majority spin carriers is determined by strong momentum-dependent interactions between the Mn eg dx2-y2 and d3z2-r2 orbitals, which, in addition to an x-dependent Jahn-Teller distortion, differ in the ferromagnetic and antiferromagnetic phases. The Fermi surface exhibits nesting behavior that is reflected by peaks in the static susceptibility, whose positions as a function of momentum have a nontrivial dependence on x.
Collapse
Affiliation(s)
- R Saniz
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | | | | |
Collapse
|
15
|
Seibold G, Lorenzana J. Magnetic fluctuations of stripes in the high temperature cuprate superconductors. PHYSICAL REVIEW LETTERS 2005; 94:107006. [PMID: 15783510 DOI: 10.1103/physrevlett.94.107006] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2004] [Indexed: 05/24/2023]
Abstract
Within the time-dependent Gutzwiller approximation for the Hubbard model we compute the magnetic fluctuations of vertical metallic stripes with parameters appropriate for La(1.875)Ba(0.125)CuO(4) (LBCO). For bond- and site-centered stripes the excitation spectra are similar, consisting of a low-energy incommensurate acoustic branch which merges into a "resonance peak" at the antiferromagnetic wave vector and several high-energy optical branches. The acoustic branch is similar to the result of theories assuming localized spins whereas the optical branches are significantly different. Results are in good agreement with a recent inelastic neutron study of LBCO.
Collapse
Affiliation(s)
- G Seibold
- Institut für Physik, BTU Cottbus, Post Box 101344, 03013 Cottbus, Germany
| | | |
Collapse
|
16
|
Pryadko LP, Kivelson SA, Zachar O. Incipient order in the t-J model at high temperatures. PHYSICAL REVIEW LETTERS 2004; 92:067002. [PMID: 14995263 DOI: 10.1103/physrevlett.92.067002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2003] [Indexed: 05/24/2023]
Abstract
We analyze the high-temperature behavior of the susceptibilities towards a number of possible ordered states in the t-J-V model using the high-temperature series expansion. From all diagrams with up to ten edges, reliable results are obtained down to temperatures of order J, or (with some optimism) to J/2. In the unphysical regime, t<J, large superconducting susceptibilities are found which, moreover, increase with decreasing temperatures, but for t>J, these susceptibilities are small and decreasing with decreasing temperature; this suggests that the t-J model does not support high-temperature superconductivity. We also find modest evidence of a tendency toward nematic and d-density wave orders.
Collapse
Affiliation(s)
- Leonid P Pryadko
- Department of Physics, University of California, Riverside, California 92521, USA.
| | | | | |
Collapse
|
17
|
Howald C, Eisaki H, Kaneko N, Kapitulnik A. Coexistence of periodic modulation of quasiparticle states and superconductivity in Bi2Sr2CaCu2O8+delta. Proc Natl Acad Sci U S A 2003; 100:9705-9. [PMID: 12913127 PMCID: PMC187829 DOI: 10.1073/pnas.1233768100] [Citation(s) in RCA: 92] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In this article we show, using scanning tunneling spectroscopy, the existence of static striped density of electronic states in nearly optimally doped Bi2Sr2CaCu2O8+delta in zero field. This modulation is aligned with the Cu-O bonds, with a periodicity of four lattice constants, and exhibits features characteristic of a two-dimensional system of line objects. We further show that the density of states modulation manifests itself as a shift of states from above to below the superconducting gap. The fact that a single energy scale (i.e., the gap) appears for both superconductivity and stripes suggests that these two effects have the same origin.
Collapse
Affiliation(s)
- C Howald
- Department of Physics, Stanford University, Stanford, CA 94305, USA
| | | | | | | |
Collapse
|
18
|
Dumm M, Komiya S, Ando Y, Basov DN. Anisotropic electromagnetic response of lightly doped La2-xSrxCuO4 within the CuO2 planes. PHYSICAL REVIEW LETTERS 2003; 91:077004. [PMID: 12935048 DOI: 10.1103/physrevlett.91.077004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2002] [Indexed: 05/24/2023]
Abstract
Using infrared spectroscopy, we show that spin self-organization in untwinned La2-xSrxCuO4 (LSCO) crystals has profound consequences for the dynamical conductivity sigma(omega). The electronic response of CuO2 planes acquires significant anisotropy in the spin ordered state with enhancement of the conductivity along the direction of the diagonal spin stripes by up to a factor of 2. An examination of the anisotropic response indicates that the diagonal spin texture in weakly doped LSCO is also accompanied by the modulation of charge density. The electronic response of the charge stripes is found to be gapless consistent with the hypothesis of the metallic ground state. Our experiments directly show that the striped ordered systems reveal new degrees of freedom not present in ordinary one-dimensional conductors.
Collapse
Affiliation(s)
- M Dumm
- Department of Physics, University of California at San Diego, La Jolla, CA 92093-0319, USA.
| | | | | | | |
Collapse
|
19
|
Lorenzana J, Seibold G. Dynamics of metallic stripes in cuprates. PHYSICAL REVIEW LETTERS 2003; 90:066404. [PMID: 12633313 DOI: 10.1103/physrevlett.90.066404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2002] [Indexed: 05/24/2023]
Abstract
We study the dynamics of metallic vertical stripes in cuprates within the three-band Hubbard model based on a recently developed time-dependent Gutzwiller approximation. As doping increases, the optical conductivity shows transfer of spectral weight from the charge-transfer band towards (i) an incoherent band centered at 1.3 eV, (ii) a Drude peak, due mainly to motion along the stripe, and (iii) a low-energy collective mode which softens with doping and merges with (ii) at optimum doping in good agreement with experiment. The softening is related to the quasidegeneracy between Cu-centered and O-centered mean-field stripe solutions close to optimal doping.
Collapse
Affiliation(s)
- J Lorenzana
- CONICET, Centro Atómico Bariloche, 8400 S. C. de Bariloche, Argentina
| | | |
Collapse
|
20
|
Lorenzana J, Seibold G. Metallic mean-field stripes, incommensurability, and chemical potential in cuprates. PHYSICAL REVIEW LETTERS 2002; 89:136401. [PMID: 12225044 DOI: 10.1103/physrevlett.89.136401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2002] [Indexed: 05/23/2023]
Abstract
We perform a systematic slave-boson mean-field analysis of the three-band model for cuprates with first-principle parameters. Contrary to widespread belief based on earlier mean-field computations low doping stripes have a linear density close to 1/2 added hole per lattice constant. We find a dimensional crossover from 1D to 2D at doping approximately 0.1 followed by a breaking of particle-hole symmetry around doping 1/8 as doping increases. Our results explain in a simple way the behavior of the chemical potential, the magnetic incommensurability, and transport experiments as a function of doping. Bond centered and site-centered stripes become degenerate for small overdoping.
Collapse
Affiliation(s)
- J Lorenzana
- Comisión Nacional de Energía Atómica, Centro Atómico Bariloche and Instituto Balseiro, 8400 S.C. de Bariloche, Argentina
| | | |
Collapse
|
21
|
Lee DH. Duality between unidirectional harge-density-wave order and superconductivity. PHYSICAL REVIEW LETTERS 2002; 88:227003. [PMID: 12059448 DOI: 10.1103/physrevlett.88.227003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2001] [Indexed: 05/23/2023]
Abstract
The existence of a duality between a unidirectional charge-density-wave order and a superconducting order is shown. This duality predicts the existence of a charge-density wave near a superconducting vortex, and the existence of superconductivity near a charge-density-wave dislocation.
Collapse
Affiliation(s)
- Dung-Hai Lee
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| |
Collapse
|
22
|
Dumm M, Basov DN, Komiya S, Abe Y, Ando Y. Electromagnetic response of static and fluctuating stripes in cuprate superconductors. PHYSICAL REVIEW LETTERS 2002; 88:147003. [PMID: 11955170 DOI: 10.1103/physrevlett.88.147003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2001] [Indexed: 05/23/2023]
Abstract
Using infrared spectroscopy, we found that changes in the in-plane charge dynamics attributable to static stripe order in La(1.275)Nd(0.6)Sr(0.125)CuO(4) or superconductivity in La(1.875)Sr(0.125)CuO(4) are confined to energies smaller than 100 cm(-1). An absorption peak in the low- omega conductivity of the Nd-doped compound is suggestive of localization effects due to the reduced dimensionality of static charge stripes. Neither superconductivity nor static stripe ordering has a noticeable effect on the depression of the scattering rate at omega<1000 cm(-1) characteristic of the pseudogap state in other classes of moderately doped cuprates.
Collapse
Affiliation(s)
- M Dumm
- Department of Physics, University of California at San Diego, La Jolla, California 92093-0319, USA.
| | | | | | | | | |
Collapse
|
23
|
Himeda A, Kato T, Ogata M. Stripe states with spatially oscillating d-wave superconductivity in the two-dimensional t-t'-J model. PHYSICAL REVIEW LETTERS 2002; 88:117001. [PMID: 11909421 DOI: 10.1103/physrevlett.88.117001] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2000] [Indexed: 05/23/2023]
Abstract
We study the interplay between stripes and d-wave superconductivity in the two-dimensional t-t'-J model using a variational Monte Carlo method. The next-nearest-neighbor hopping t'<0 stabilizes the stripe states around 1/8 hole doping rate. We find that stripes and spatially oscillating superconductivity coexist depending on parameters. The superconducting orders are enhanced at the hole stripe regions. Although the energy differences are relatively small, the stripe state in which the phases between adjacent superconducting stripes are the opposite (antiphase) is also stabilized. We consider the possibility that the antiphase coexistence may explain the weakness of the c-axis Josephson couplings in the La1.6-xNd0.4SrxCuO4.
Collapse
Affiliation(s)
- A Himeda
- Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 Japan
| | | | | |
Collapse
|
24
|
Kaneshita E, Ichioka M, Machida K. Phonon anomalies due to collective stripe modes in high T(c) cuprates. PHYSICAL REVIEW LETTERS 2002; 88:115501. [PMID: 11909406 DOI: 10.1103/physrevlett.88.115501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2001] [Indexed: 05/23/2023]
Abstract
Phonon anomalies observed in various high T(c) cuprates by neutron experiments are analyzed theoretically in terms of the stripe concept. The phonon self-energy correction is evaluated by taking into account the charge collective modes of stripes, giving rise to dispersion gap, or kink and shadow phonon modes at twice the wave number of spin stripe. These features coincide precisely with observations. The gapped branches of the phonon are found to be in-phase and out-of-phase oscillations relative to the charge collective mode.
Collapse
Affiliation(s)
- Eiji Kaneshita
- Department of Physics, Okayama University, Okayama 700-8530, Japan
| | | | | |
Collapse
|
25
|
Halboth CJ, Metzner W. d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model. PHYSICAL REVIEW LETTERS 2000; 85:5162-5165. [PMID: 11102211 DOI: 10.1103/physrevlett.85.5162] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2000] [Indexed: 05/23/2023]
Abstract
We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.
Collapse
Affiliation(s)
- CJ Halboth
- Institut fur Theoretische Physik C, Technische Hochschule Aachen, Templergraben 55, D-52056 Aachen, Germany
| | | |
Collapse
|
26
|
Matveenko SI, Mukhin SI. Analytical stripe phase solution for the Hubbard model. PHYSICAL REVIEW LETTERS 2000; 84:6066-6069. [PMID: 10991125 DOI: 10.1103/physrevlett.84.6066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/1999] [Indexed: 05/23/2023]
Abstract
The self-consistent solution for the spin-charge solitonic superstructure in a quasi-one-dimensional electron system is obtained in the framework of the Hubbard model as a function of a hole doping. Effects of interchain interactions on the ground state are discussed. Results are used for the interpretation of the observed stripe phases in doped antiferromagnets.
Collapse
Affiliation(s)
- S I Matveenko
- Landau Institute for Theoretical Physics, Kosygina Street 2, 117940 Moscow, Russia
| | | |
Collapse
|
27
|
Sadori A, Grilli M. Stripe formation in electron-doped cuprates. PHYSICAL REVIEW LETTERS 2000; 84:5375-5378. [PMID: 10990947 DOI: 10.1103/physrevlett.84.5375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/1999] [Indexed: 05/23/2023]
Abstract
We investigate the formation of charge domain walls in an electron-doped extended Hubbard model for the superconducting cuprates. Within an unrestricted Hartree-Fock approach, extended by slave bosons to obtain a better treatment of strong correlations, we demonstrate the occurrence of stripes in the (1,1) and (1,-1) directions having one doped electron per stripe site. The different filling, direction, and width of these electron-doped stripes with respect to those obtained in the hole-doped systems have interesting observable consequences.
Collapse
Affiliation(s)
- A Sadori
- Istituto Nazionale di Fisica della Materia and Dipartimento di Fisica, Universita di Roma "La Sapienza," Piazzale A. Moro 2, Roma, Italy 00185, USA
| | | |
Collapse
|
28
|
Bao W, McQueeney RJ, Heffner R, Sarrao JL, Dai P, Zarestky JL. Commensurate dynamic magnetic correlations in La2Cu0.9Li0.1O4. PHYSICAL REVIEW LETTERS 2000; 84:3978-3981. [PMID: 11019254 DOI: 10.1103/physrevlett.84.3978] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/1999] [Indexed: 05/23/2023]
Abstract
When sufficient numbers of holes are introduced into the two-dimensional CuO2 square lattice, dynamic magnetic correlations become incommensurate with underlying lattice in all previously investigated La(2-x)A(x)Cu(1-z)B(z)O(4+y) ( A = Sr or Nd, B = Zn) including high T(c) superconductors and insulators, and in bilayered superconducting YBa2Cu3O6.6 and Bi2Sr2CaCu2O8. Magnetic correlations also become incommensurate in structurally related La2NiO4 when doped with Sr or O. We report an exception to this so-far well-established experimental "rule" in La(2)Cu(1-z)Li(z)O4 in which magnetic correlations remain commensurate.
Collapse
Affiliation(s)
- W Bao
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | | | |
Collapse
|
29
|
Abstract
The high-temperature copper oxide superconductors are of fundamental and enduring interest. They not only manifest superconducting transition temperatures inconceivable 15 years ago, but also exhibit many other properties apparently incompatible with conventional metal physics. The materials expand our notions of what is possible, and compel us to develop new experimental techniques and theoretical concepts. This article provides a perspective on recent developments and their implications for our understanding of interacting electrons in metals.
Collapse
Affiliation(s)
- J Orenstein
- Department of Physics, University of California, Berkeley, CA 94720, USA, and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ
| | | |
Collapse
|
30
|
Abstract
The growing body of experimental evidence for the existence of complex textures of charges and spins in the high-temperature superconductors has drawn attention to the so-called 'stripe-phase' models as a possible basis for the mechanism of superconductivity in these materials. Such observations have until now been restricted to systems where the texture dynamics are slow or suppressed altogether, and do not include the important case of YBa2Cu3O(7-delta). It seems likely that the dynamic behaviour of stripes, which has been suggested to undergo several phase transitions as a function of temperature, should also be reflected in the lattice properties of the host materials, and this forms the motivation for our present experiments. Specifically, we use MeV helium ion channelling, an ultrafast real-space probe of atomic displacements (with sub-picometre resolution), to probe incoherent lattice fluctuations in YBa2Cu3O(7-delta) as a function of temperature and oxygen doping. We detect lattice fluctuations that are larger than the expected thermal vibration component, and which show anomalies characteristic of the phase transitions anticipated for a dynamic stripe phase. Comparison of our lattice results with single-particle-tunnelling and photoemission data highlights the importance of spin-charge separation phenomena in the copper oxide superconductors.
Collapse
|
31
|
Emery VJ, Kivelson SA, Tranquada JM. Stripe phases in high-temperature superconductors. Proc Natl Acad Sci U S A 1999; 96:8814-7. [PMID: 10430848 PMCID: PMC33690 DOI: 10.1073/pnas.96.16.8814] [Citation(s) in RCA: 317] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Stripe phases are predicted and observed to occur in a class of strongly correlated materials describable as doped antiferromagnets, of which the copper-oxide superconductors are the most prominent representatives. The existence of stripe correlations necessitates the development of new principles for describing charge transport and especially superconductivity in these materials.
Collapse
Affiliation(s)
- V J Emery
- Department of Physics, Brookhaven National Laboratory, Upton, NY 11973-5000, USA
| | | | | |
Collapse
|
32
|
Kivelson SA, Fradkin E, Emery VJ. Electronic liquid-crystal phases of a doped Mott insulator. Nature 1998. [DOI: 10.1038/31177] [Citation(s) in RCA: 941] [Impact Index Per Article: 36.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
|
33
|
Ortiz G, Ordejón P, Martin RM, Chiappe G. Quantum phase transitions involving a change in polarization. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:13515-13528. [PMID: 9985260 DOI: 10.1103/physrevb.54.13515] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
34
|
Gan J, Lee DH, Hedegård P. Composite quasiparticle formation and the low-energy effective Hamiltonians for the one- and two-dimensional Hubbard model. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:7737-7757. [PMID: 9984447 DOI: 10.1103/physrevb.54.7737] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
35
|
Dongen PG. Phase diagram of the extended Hubbard model at weak coupling. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:1584-1596. [PMID: 9986002 DOI: 10.1103/physrevb.54.1584] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
36
|
Eskes H, Grimberg R, Zaanen J. Quantizing charged magnetic domain walls: Strings on a lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:R724-R727. [PMID: 9985419 DOI: 10.1103/physrevb.54.r724] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
37
|
Salkola MI, Emery VJ, Kivelson SA. Implications of Charge Ordering for Single-Particle Properties of High-Tc Superconductors. PHYSICAL REVIEW LETTERS 1996; 77:155-158. [PMID: 10061795 DOI: 10.1103/physrevlett.77.155] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
38
|
Daré AM, Vilk YM, Tremblay A. Crossover from two- to three-dimensional critical behavior for nearly antiferromagnetic itinerant electrons. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:14236-14251. [PMID: 9983220 DOI: 10.1103/physrevb.53.14236] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
39
|
Zaanen J, Horbach ML. Charged domain-wall dynamics in doped antiferromagnets and spin fluctuations in cuprate superconductors. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:8671-8680. [PMID: 9982380 DOI: 10.1103/physrevb.53.8671] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
40
|
Rendell JM, Carbotte JP. Effects of gap and band anisotropy on spin susceptibility in the oxide superconductors. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:5889-5900. [PMID: 9984198 DOI: 10.1103/physrevb.53.5889] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
41
|
Ramirez AP, Gammel PL, Cheong SW, Bishop DJ, Chandra P. Charge modulation in La1.67Sr0.33NiO4: A bulk thermodynamic study. PHYSICAL REVIEW LETTERS 1996; 76:447-450. [PMID: 10061459 DOI: 10.1103/physrevlett.76.447] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
42
|
Tranquada JM, Lorenzo JE, Buttrey DJ, Sachan V. Cooperative ordering of holes and spins in La2NiO4.125. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:3581-3595. [PMID: 9981483 DOI: 10.1103/physrevb.52.3581] [Citation(s) in RCA: 62] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
43
|
Eriksson AB, Einarsson T, Östlund S. Symmetries and mean-field phases of the extended Hubbard model. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:3662-3675. [PMID: 9981494 DOI: 10.1103/physrevb.52.3662] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
44
|
Kato M. Simulated-annealing method for fermion systems at finite temperature. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:16046-16051. [PMID: 9978586 DOI: 10.1103/physrevb.51.16046] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
45
|
Chubukov AV, Musaelian KA. Magnetic phases of the two-dimensional Hubbard model at low doping. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:12605-12617. [PMID: 9978031 DOI: 10.1103/physrevb.51.12605] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
46
|
Ferrer J. Crossover from a spin-density wave to the quantum Néel ground state. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:8310-8317. [PMID: 9977440 DOI: 10.1103/physrevb.51.8310] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
47
|
Liu BG. Effect of strong correlation on the in-plane electronic properties of the high-Tc superconductors. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:3949-3952. [PMID: 9979223 DOI: 10.1103/physrevb.51.3949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
48
|
Freericks JK, Jarrell M. Magnetic phase diagram of the Hubbard model. PHYSICAL REVIEW LETTERS 1995; 74:186-189. [PMID: 10057730 DOI: 10.1103/physrevlett.74.186] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
49
|
van Dongen PGJ. Phase Separation in the Extended Hubbard Model at Weak Coupling. PHYSICAL REVIEW LETTERS 1995; 74:182-185. [PMID: 10057729 DOI: 10.1103/physrevlett.74.182] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
50
|
Hu F, Sarker SK, Jayaprakash C. Domain walls, spiral states, and phase separation in the extended Hubbard model: A Hartree-Fock analysis. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:17901-17909. [PMID: 9976223 DOI: 10.1103/physrevb.50.17901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|