Superconductor-insulator quantum critical point in 1+\epsilon dimensions

Abstract

A system of spinless fermions in $d=1+\epsilon$ dimensions, at zero-temperature and in random potential is studied using the perturbative renormalization group to first order in disorder and to second order in interaction. We find a superconductor-to- Anderson insulator quantum fixed point at an infinitesimal value of disorder and calculate the correlation length and the dynamical exponents to the lowest order in $\epsilon$ and in interaction. The scaling of conductivity with temperature and the behavior of characteristic temperature scales on both sides of the transition is determined. The model may have relevance for a p-wave superconductor at low temperatures in strongly disordered media.