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arXiv:cond-mat/9707262 · Physical review. B, Condensed matter

Bogoliubov-quasiparticle spectra of the effective d -wave model for cuprate superconductivity

Y. Ohta, Masaya Yamaguchi, R. Eder

Published Nov 1, 1997• 2 citations
arXivHTMLPDF

Abstract

An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective-fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional $t\ensuremath{-}J$ model at low doping. We show that there is actually a reasonable range of parameter values where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size ${\ensuremath{\Delta}}_{d}\ensuremath{\simeq}0.13|V|$ (where $V$ is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.

DOI
10.1103/physrevb.56.11262

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An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective-fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model at low doping. We show that there is actually a reasonable range of parameter values where the dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size \ensuremathΔd\ensuremath≃0.13∣V∣{\ensuremath{\Delta}}_{d}\ensuremath{\simeq}0.13|V|\ensuremathΔd​\ensuremath≃0.13∣V∣ (where VVV is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.
Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional t-J model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in the dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2-wave channel and the energy gap has a size ${\mathrm{\ensuremath{\Delta}}}_{\mathit{d}}$\ensuremath{\simeq}0.15J--0.27J between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectra is demonstrated.
An exact-diagonalization technique on small clusters is used to study low-lying excitations and superconductivity in the two-dimensional negative-U Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum, condensation amplitude, and coherence length as functions of the coupling strength U/t, thereby working out how the picture of Bogoliubov quasiparticles in the BCS superconductors is affected by increasing the attraction. We then define the Cooper-pair operator as a spatially extended composite boson and make a variational evaluation of its internal structure. We thereby calculate the single-particle spectral function of the Cooper pair and obtain the dispersion relation for its translational motion. The dynamical density correlation function of the pairs is also calculated. We thus demonstrate the applicability of our numerical method for gaining insight into low-lying excitations of models for the intermediate coupling superconductivity relevant to cuprate materials.
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An exact-diagonalization technique on small clusters is used to study low-lying excitations and superconductivity in the two-dimensional negative-UUU Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum, condensation amplitude, and coherence length as functions of the coupling strength U/tU/tU/t, thereby working out how the picture of Bogoliubov quasiparticles in the BCS superconductors is affected by increasing the attraction. We then define the Cooper-pair operator as a spatially-extended composite boson and make a variational evaluation of its internal structure. We thereby calculate the single-particle spectral function of the Cooper pair and obtain the dispersion relation for its translational motion. The dynamical density correlation function of the pairs is also calculated. We thus demonstrate the applicability of our numerical method for gaining insight into low-lying excitations of models for the intermediate coupling superconductivity relevant to cuprate materials.
Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range ddd-wave pair field term, which precipitates a superconducting state in the ddd-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the ddd-wave pair/spin/charge-density matrices. The calculations show a ddd-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion UUU and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating ddd-wave superconductivity.
Pairing correlations are studied numerically in a hole-doped spin-fermion model. Simulations performed on up to 12 x 12 clusters provide indications of D-wave superconductivity away from half-filling comparable to those of the 2D t-J model. The pairing correlations are the strongest in the direction perpendicular to the dynamic stripes that appear in the ground state at some densities. An optimal doping, where correlations are maximized, was observed at approximately 25% doping with an estimated T(c) approximately 100-200 K, in qualitative agreement with high-T(c) cuprates' phenomenology, while pairing correlations are suppressed by static stripe inhomogeneities.