Critical Anomalous Metals Near Superconductivity In Models With Random Interactions

Anomalous metals are observed in numerous experiments on disordered two-dimensional systems proximate to superconductivity. A characteristic feature of an anomalous metal is that its low-temperature conductivity has a weakly temperature dependent value, significantly higher than that of a disordered Fermi liquid. We propose a dynamical mean-field model of an anomalous metal: interacting electrons similar in structure to that of the well-studied universal Hamiltonian of mesoscopic metallic grains, but with independent random interactions between pairs of sites, involving Cooper pair hopping and spin exchange. We find evidence for critical anomalous phases or points between a superconducting phase and a disordered Fermi liquid phase in this model. Our results are obtained by a renormalization group analysis in a weak coupling limit, and a complementary solution at large M when the spin symmetry is generalized to USp(M). The large M limit describes the anomalous metal by fractionalization of the electron into spinons, holons, and doublons, with these partons forming critical non-Fermi liquids in the Sachdev-Ye-Kitaev class. We compute the low-temperature conductivity in the large M limit and find temperature-independent values moderately enhanced from that in the disordered metal.