Quasiparticle density of states of d-wave superconductors in a disordered vortex lattice

TL;DR

This paper investigates how disorder and magnetic vortices affect the quasiparticle density of states in d-wave superconductors, revealing distinct energy regimes with different power-law behaviors.

Contribution

It introduces a detailed calculation of the density of states considering vortex pinning and scattering, highlighting two energy regimes with different power-law dependencies.

Findings

At very low energies, the density of states follows a linear plus power-law behavior with exponent near 1.

At higher energies, the density of states fits a power law with exponent close to 2.

The zero-energy density of states scales inversely with the magnetic length ( ).

Abstract

We calculate the density of states of a disordered inhomogeneous d-wave superconductor in a magnetic field. The field-induced vortices are assumed to be pinned at random positions and the effects of the scattering of the quasi-particles off the vortices are taken into account using the singular gauge transformation of Franz and Tesanovic. We find two regimes for the density of states: at very low energies the density of states follows a law \rho(\epsilon) \sim \rho_0 + |\epsilon|^{\alpha} where the exponent is close to 1. A good fit of the density of states is obtained at higher energies, excluding a narrow region around the origin, with a similar power law energy dependence but with \alpha close to 2. Both at low and at higher energies \rho_0 scales with the inverse of the magnetic length (\sqrt{B}).