Disordered two-dimensional superconductors: Roles of temperature and interaction strength

Abstract

We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction f of sites, while keeping a finite U on the remaining ones. Through quantum Monte Carlo simulations for several values of f and U and for system sizes ranging from 8×8 to 16×16, we have calculated the configurational averages of the equal-time pair structure factor Ps and, for a more restricted set of variables, the helicity modulus ρs, as functions of temperature. Two finite-size scaling Ansätze for Ps have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration fc, which increases with U, at least up to U=4 (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of f shows a maximum near f∼0.07 for 2≲U≲6. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of f for U=3, 4, and 6: they also show maxima near f∼0.07, with the highest Tc increasing with U in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to “push” electrons toward attractive sites; the latter effect being more drastic at weak couplings.

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