Effect of inhomogeneity on s-wave superconductivity in the attractive Hubbard model

TL;DR

This study shows that inhomogeneity in the attractive Hubbard model can enhance zero-temperature pairing and increase the critical temperature, regardless of the specific pattern of inhomogeneity, as confirmed by mean-field and Monte Carlo methods.

Contribution

It demonstrates that inhomogeneous interactions can improve superconducting properties in the attractive Hubbard model, a novel insight into the role of disorder.

Findings

Inhomogeneity increases zero-temperature pairing amplitude.

Superconducting critical temperature $T_c$ can be significantly enhanced.

Pattern of inhomogeneity (stripe, checkerboard, random) is not crucial.

Abstract

Inhomogeneous s-wave superconductivity is studied in the two-dimensional, square lattice attractive Hubbard Hamiltonian using the Bogoliubov-de Gennes (BdG) mean field approximation. We find that at weak coupling, and for densities mainly below half-filling, an inhomogeneous interaction in which the on-site interaction $U_i$ takes on two values, $U_i=0, 2U$ results in a larger zero temperature pairing amplitude, and that the superconducting $T_c$ can also be significantly increased, relative to a uniform system with $U_i=U$ on all sites. These effects are observed for stripe, checkerboard, and even random patterns of the attractive centers, suggesting that the pattern of inhomogeneity is unimportant. Monte Carlo calculations which reintroduce some of the fluctuations neglected within the BdG approach see the same effect, both for the attractive Hubbard model and a Hamiltonian with d-wave pairing symmetry.