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Physical review. B, Condensed matter

Superconducting states of an extended Hubbard model

S. N. Coppersmith

Published Aug 1, 1990• 15 citations
Publisher

Abstract

The variational Monte Carlo method is used to study possible superconducting states of a two-dimensional extended Hubbard model on a copper-oxygen lattice. It is found that d-wave and extended s-wave superconducting variational wave functions can have lower energy than the corresponding normal state for different parameter regions, while simple s-wave superconductivity is never favored. Increasing the nearest-neighbor repulsion and decreasing the copper-oxygen level separation can promote extended s-wave superconductivity and inhibit d-wave superconductivity.

DOI
10.1103/physrevb.42.2259

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The variational Monte Carlo method is used to study possible superconducting states of a two-dimensional extended Hubbard model on a copper-oxygen lattice. It is found that d-wave and extended s-wave superconducting variational wave functions can have lower energy than the corresponding normal state for different parameter regions, while simple s-wave superconductivity is never favored. Increasing the nearest-neighbor repulsion and decreasing the copper-oxygen level separation can promote extended s-wave superconductivity and inhibit d-wave superconductivity.
Variational Monte Carlo calculations using extensions of the Gutzwiller variational wave function are used to study the phase diagram of an extended Hubbard model on a copper-oxygen lattice in two dimensions. Antiferromagnetism appears to occur at half-filling only when the oxygen p levels and copper d levels have substantially different energies. It is also found that strong nearest-neighbor repulsions can enhance the tendency for local-moment antiferromagnetism. The dependence of the variational parameters on the Hamiltonian parameters, particularly nearest-neighbor repulsions, is examined. The implications for models of high-temperature superconductivity are discussed.
The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6 ×6 and 10 ×10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d -wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.
We study, through the variational Monte Carlo technique, an extended Hubbard model away from half filled band density which contains two competing nearest-neighbor interactions: a superexchange J favoring d-wave superconductivity and a repulsion V opposing it. We find that the on-site repulsion U effectively enhances the strength of J while suppressing that of V, thus favoring superconductivity. This result shows that attractions which do not involve charge fluctuations are very well equipped against strong electron-electron repulsion so much to get advantage from it.
We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as ψ=exp⁡(−λK)PGψ0ψ=\exp(-λK)P_Gψ_0ψ=exp(−λK)PG​ψ0​, where ψ0ψ_0ψ0​ is a one-particle state, PGP_GPG​ is the Gutzwiller operator, KKK is the kinetic operator, and λλλ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion UUU, the band parameter t′t't′ and the electron density nen_ene​. We show a phase diagram that includes superconducting and antiferromagnetic phases and that t′=0t'=0t′=0 is most favorable for superconductivity.
A variational Monte-Carlo method is formulated to study superconductivity in strongly correlated electrons. An application is made to the strongly correlated Hubbard model on two-dimensional square lattice, by employing the simplest mean-field-type trial wave function, i.e. the Gutzwiller-projected BCS wave function. Among the various choices examined, the d-wave-type superconductivity turns out to be the most favorable. The nature of the superconducting order parameter and spin correlations is also examined.