Microscopic interpretation of the Dynes formula for the tunneling density of states

TL;DR

This paper provides a microscopic derivation of the phenomenological Dynes formula for the tunneling density of states in disordered superconductors, linking it to a specific gap function within the coherent potential approximation.

Contribution

It introduces a consistent derivation of the Dynes formula using a causal frequency-dependent gap function and the CPA, connecting it to Lorentzian-distributed pair-breaking fields.

Findings

Dynes formula corresponds to a specific gap function with vanishing gap at Fermi level.

Superconductors with Lorentzian-distributed pair-breaking fields are described by this gap function.

Predictions of spectral and thermodynamic properties for disordered superconductors.

Abstract

Excellent fits of the tunneling density of states in disordered superconductors can be often achieved making use of the phenomenological Dynes formula. However, no consistent derivation of this formula has been available so far. The Dynes formula can be interpreted by the simplest causal frequency-dependent gap function $\Delta(\omega)$ with a vanishing gap at the Fermi level. Here we show, within the coherent potential approximation, that precisely such gap function describes superconductors with a Lorentzian distribution of pair-breaking fields and arbitrary potential disorder. We predict spectral and thermodynamic properties of such superconductors.