Density of states in unconventional superconductors: Impurity-scattering effects

Abstract

The density of states in unconventional superconductors, ${\mathit{N}}_{\mathit{s}}$(E), is very sensitive to impurity scattering, especially at low energies. We investigate the behavior of ${\mathit{N}}_{\mathit{s}}$(E), using both numerical calculations and analytic approximations; we discuss the Born limit, the unitarity limit, and the crossover between these two cases. We consider a two-dimensional electron gas with a d-wave order parameter of the form \ensuremath{\Delta}(k^)=\ensuremath{\Delta}(k${\mathrm{^}}_{\mathit{x}}^{2}$-k${\mathrm{^}}_{\mathit{y}}^{2}$). The low-energy structure in ${\mathit{N}}_{\mathit{s}}$(E) should be quite general, applying to all gaps with the same general behavior.