On the correct formula for the lifetime broadened superconducting density ofstates

Abstract

We argue that the well known Dynes formula (Dynes et al 1978 Phys. Rev.Lett. 41 1509) for the superconducting quasiparticle density of states, whichtries to incorporate the lifetime broadening in an approximate way, cannot bejustified microscopically for conventional superconductors. Instead, we proposea new simple formula in which the energy gap has a finite imaginary part−Δ2 and the quasiparticle energy is real. We prove that in the quasiparticle approximation2Δ2 gives the quasiparticle decay rate at the gap edge for conventional superconductors. Thisconclusion does not depend on the nature of interactions that cause the quasiparticledecay. The new formula is tested on the case of a strong coupling superconductorPb0.9Bi0.1 and an excellent agreement with theoretical predictions is obtained. While both the Dynesformula and the one proposed in this work give good fits and fit parameters forPb0.9Bi0.1, only the latter formula can be justified microscopically.