Interplay of disorder and magnetic field in the superconducting vortex state

TL;DR

This study investigates how disorder and magnetic fields influence the low energy density of states in inhomogeneous superconductors with s-wave and d-wave pairing, revealing distinct behaviors at low energies.

Contribution

It provides a detailed analysis of the density of states in disordered vortex configurations for both pairing symmetries, highlighting the effects of vortex density and anisotropy.

Findings

Disorder or increased vortex density enhances low energy states.

In s-wave superconductors, the gap is filled, leading to a power-law density of states.

In d-wave superconductors, the density of states is finite at zero energy and varies with Dirac anisotropy.

Abstract

We calculate the density of states of an inhomogeneous superconductor in a magnetic field where the positions of vortices are distributed completely at random. We consider both the cases of s-wave and d-wave pairing. For both pairing symmetries either the presence of disorder or increasing the density of vortices enhances the low energy density of states. In the s-wave case the gap is filled and the density of states is a power law at low energies. In the d-wave case the density of states is finite at zero energy and it rises linearly at very low energies in the Dirac isotropic case (\alpha_D=t/\Delta_0=1, where t is the hopping integral and \Delta_0 is the amplitude of the order parameter). For slightly higher energies the density of states crosses over to a quadratic behavior. As the Dirac anisotropy increases (as \Delta_0 decreases with respect to the hopping term) the linear region decreases in width. Neglecting this small region the density of states interpolates between quadratic and back to linear as \alpha_D increases. The low energy states are strongly peaked near the vortex cores.