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 (QMC) simulations for several values of $f$ and $U$, and for system sizes ranging from $8\times 8$ to $16\times 16$, we have calculated the configurational averages of the equal-time pair structure factor $P_s$, and, for a more restricted set of variables, the helicity modulus, $\rho_s$, as functions of temperature. Two finite-size scaling {\it ansatze} for $P_s$ 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, $f_c$, 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 $f\sim 0.07$, for $2\lesssim U\lesssim 6$. 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 $f\sim 0.07$, with the highest $T_c$ increasing with $U$ in this range. We argue that, overall, the observed behavior results from both the breakdown of CDW-superconductivity degeneracy and the fact that free sites tend to "push" electrons towards attractive sites, the latter effect being more drastic at weak couplings.