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Journal of the Physical Society of Japan

Superconducting Phase Diagram of the Two-Band Model Investigated by the Exact-Diagonalization Method

Yamaji K., Kikuo Harigaya, Takashi Yanagisawaand Yukihiro Shimoi

Published Oct 15, 1992• 7 citations
Publisher

Abstract

By means of the exact-diagonalization method we have studied the finite-size two-band model with the interband pair-transfer interaction by calculating the superconducting (SC) correlation function P s etc. in the ground state. Occurrence of SC was clearly indicated by the increase of P s . The diagram of the observed SC region was constructed in the plane of the relative position of the second band versus on-site Coulomb energy U . In the low-density limit it proved close to the region where a negative- U situation is realized by the pair-transfer interaction. On the high-density side, the SC region was found to be more extended than the latter in accord with the previous interband-ladder-diagram results. Inclusion of the exchange interaction was found to reduce the SC region in a restricted region where two bands substantially share electrons. The two-band situations in cuprates are argued to be relevant to the high T c through the present mechanism.

DOI
10.1143/jpsj.61.3689

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By means of the exact-diagonalization method we have studied the finite-size two-band model with the interband pair-transfer interaction by calculating the superconducting (SC) correlation function P s etc. in the ground state. Occurrence of SC was clearly indicated by the increase of P s . The diagram of the observed SC region was constructed in the plane of the relative position of the second band versus on-site Coulomb energy U . In the low-density limit it proved close to the region where a negative- U situation is realized by the pair-transfer interaction. On the high-density side, the SC region was found to be more extended than the latter in accord with the previous interband-ladder-diagram results. Inclusion of the exchange interaction was found to reduce the SC region in a restricted region where two bands substantially share electrons. The two-band situations in cuprates are argued to be relevant to the high T c through the present mechanism.
Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.
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.
Abstract We investigate the ground state of the two-dimensional three-band d-p model for for high-temperature superconductors on the basis of a variational Monte Carlo method. We employ an optimization variational Monte Carlo method that we have developed recently. The many-body wave function is improved beyond the Gutzwiller ansatz by adopting the wave function in the form ψ = exp(−S)ψG where ψG represents the Gutzwiller function and S is a kinetic operator. The strong magnetic correlation and also superconductivity (SC) are induced by the on-site Coulomb repulsive interaction. It is important to clarify the phase diagram that includes superconductive phase and antiferromagnetic phase. We show the phase diagram to show the antiferromagnetic region in the parameter space. High-temperature superconductivity may occur in the strongly correlated region near the antiferromagnetic boundary.
A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes ttt (and ${t}^{\ensuremath{'}}$) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (UUU, $\ensuremath{\delta}$, ${t}^{\ensuremath{'}}$) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, $U/t\ensuremath{\gtrsim}3$, and for not too large hole doping, $\ensuremath{\delta}\ensuremath{\lesssim}0.32$ for ${t}^{\ensuremath{'}}=0.25t$; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.
Phase diagram of the two-band Fermi gas with repulsive intraband and interband interactions is obtained with the bosonization technique. In the forward-scattering model, there is a region for the superconductivity (SC) within a band due to charge fluctuations in the accompanying band. When the backward scattering is relevant the SC region becomes wider, while when the umklapp scattering is relevant the system is renormalized into two independent single bands, which is considered to cover the regime where superconductivity a\ifmmode\acute\else\textasciiacute\fi{} la single-band attractive Hubbard model is found from quantum Monte Carlo results in the multiband model on discrete lattices.
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.