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

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 ρ(ε) \sim ρ_0 + |ε|^α 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 αclose to 2. Both at low and at higher energies ρ_0 scales with the inverse of the magnetic length (\sqrt{B}).