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Journal of the Physical Society of Japan

Superconducting Condensation Energy of the Two-Chain Hubbard Model in the Bulk Limit

Soh Koike, Yamaji K., Takashi Yanagisawa

Published Jul 15, 2000• 7 citations
Publisher

Abstract

We have studied on the possibility of superconductivity in the two-chain Hubbard model by using the variational Monte Carlo method changing the interchain transfer energy t d . The energy gain per site Δ E in the variational BCS state in reference to the normal state energy, which is nothing but the superconducting condensation energy, was computed. We have fitted Δ E as a function of the inverse of the lattice size by a power-law function and found that in the bulk limit Δ E remains finite in a certain narrow range of t d . Calculated momentum distribution functions reveal that the superconductivity is most stable in the case where the electron distribution in k -space is in a one-band-like situation, on the brink of transition to a two-band-like one. The SDW-type trial wave function was also examined but we did not obtain any energy gain with it in the above-mentioned superconducting region.

DOI
10.1143/jpsj.69.2199

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We have studied on the possibility of superconductivity in the two-chain Hubbard model by using the variational Monte Carlo method changing the interchain transfer energy t d . The energy gain per site Δ E in the variational BCS state in reference to the normal state energy, which is nothing but the superconducting condensation energy, was computed. We have fitted Δ E as a function of the inverse of the lattice size by a power-law function and found that in the bulk limit Δ E remains finite in a certain narrow range of t d . Calculated momentum distribution functions reveal that the superconductivity is most stable in the case where the electron distribution in k -space is in a one-band-like situation, on the brink of transition to a two-band-like one. The SDW-type trial wave function was also examined but we did not obtain any energy gain with it in the above-mentioned superconducting region.
We investigate the two-chain Hubbard model including the next nearest-neighbor transfer energies both in the interchain and intrachain directions by use of the exact-diagonalization and the variational Monte Carlo methods. We find that superconducting correlation functions are enhanced in such a situation where the density of states of the antibonding band in the neighborhood of the Fermi level enlarges due to the above-mentioned transfer energies, especially, in the situation where the Fermi level is located a little above the bottom of the antibonding band. In such a situation we find from the calculated momentum distribution function that this system is in almost one-band situation close to the two-band one. The relevance to ladder-type superconductor Sr 14- x Ca x Cu 24 O 41 is asserted.
We investigate the ground state of the two-dimensional d-p model (three-band Hubbard model) by using a variational Monte Carlo method. The superconducting condensation energy is evaluated for the Gutzwiller-BCS wave function. We show that there is a crossover between strongly and weakly correlated regions as the level difference between d and p orbitals increases. The gap function and the condensation energy can be large in the crossover region. This result indicates a possibility of high-temperature superconductivity in the two-dimensional d-p model.
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(−S-S−S)-type where SSS is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The ddd-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the ddd-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.
We compute the superconducting condensation energies Econd of Hg1201 and Tl2201 cuprates by applying the variational Monte Carlo method to the two-dimensional Hubbard model, first, with the specific band parameters t' = -2t" = -0.25t appropriate for these highest-Tc single-CuO2-layer cuprates; t, t' and t" are the first-, second- and third-neighbor transfer energies, respectively. In the range of on-site Coulomb energy U of (7\sim10)t with optimal doping, we succeed in obtaining the bulk-limit Econd values by extrapolating the results. They sharply increase with increasing U and become comparable to experimental values when U \approx 9t. Next, Econd values at t' = -2t" = -0.18t demonstrate that with a fixed U the bulk-limit Econd quickly increases with a decrease in |t'| = 2t" in the large-|t'| region. Finally, we argue that the remoteness of the apex oxygen from the planar Cu in the two cuprates is considered to increase U and bring about the experimental magnitude of Econd. The present scheme explains the observed correlation between Tc and t' among cuprates.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.
We investigate the role of kinetic energy for the stability of superconducting state in the two-dimensional Hubbard model on the basis of an optimization variational Monte Carlo method. The wave function is optimized by multiplying by correlation operators of site off-diagonal type. This wave function is written in an exponential-type form given as ψλ=exp(−λK)ψG for the Gutzwiller wave function ψG and a kinetic operator K. The kinetic correlation operator exp(−λK) plays an important role in the emergence of superconductivity in large-U region of the two-dimensional Hubbard model, where U is the on-site Coulomb repulsive interaction. We show that the superconducting condensation energy mainly originates from the kinetic energy in the strongly correlated region. This may indicate a possibility of high-temperature superconductivity due to the kinetic energy effect in correlated electron systems.