Lifshitz Tail in the Density of States of a Superconductor with Magnetic Impurities

Abstract

We argue that any superconductor with magnetic impurities is gapless due to a Lifshitz tail in the density of states extending to zero energy. At low energy the density of states $\nu (E\to 0)$ remains finite. We show that fluctuations in the impurity distribution produce regions of suppressed superconductivity, which are responsible for the low energy density of states.