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 $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, 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 ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze 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 $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. 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 $f\ensuremath{\sim}0.07$, with the highest ${T}_{c}$ increasing with $U$ in this range. We argue that, overall, the observed behavior results from both the breakdown of 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.