Ioffe and Mezard have recently proposed a replica-symmetry breaking phase in disorder superconductors using a cavity method approach. Here we study the disordered attractive Hubbard model by solving the Bogolubov-de Gennes equations on two-dimensional finite clusters at zero temperature. By analyzing the on-site order parameter distribution (OPD) we find anomalous tails, which agree qualitatively with the predictions based on the presence of a broken replica-symmetry phase and suggests the relevance of the 2d Directed Polymer physics at strong disorder. Finally, by introducing a flux through the sample, we find that the current density is strongly inhomogeneous and appears to follows almost one-dimensional patterns, while the optical conductivity shows an intra-gap absorption due to collective modes which become optically active in the presence of strong disorder.

Dipartimento di Fisica, Università di Roma “La Sapienza”