Magnetic impurity transition in a 'd+s'-wave superconductor

TL;DR

This paper investigates how Anderson impurities affect the superconducting state of a mixed 'd+s' wave superconductor, revealing a transition in the density of states driven by impurity concentration and symmetry ratio.

Contribution

It introduces a model combining BCS-like pairing with Anderson impurities in a 'd+s' superconductor and analyzes the impurity-driven transition using a large-N mean field approach.

Findings

Transition from sharp low-energy peaks to finite density of states at the Fermi level.

Discontinuous transition when impurity resonance energy is the smallest scale.

Density of states at zero energy scales as (_s/_d)^2.

Abstract

We consider the superconducting state of $d+s$ symmetry with finite concentration of Anderson impurities in the limit $\Delta_s/\Delta_d \ll 1$. The model consists of a BCS-like term in the Hamiltonian and the Anderson impurity treated in the self-consistent large-$N$ mean field approximation. Increasing impurity concentration or lowering the ratio $\Delta_s/\Delta_d$ drives the system through a transition from a state with two sharp peaks at low energies and exponentially small density of states at the Fermi level to one with $N(0) \simeq (\Delta_s/\Delta_d)^2$. This transition is discontinuous if the energy of the impurity resonance is the smallest energy scale in the problem.