Thermodynamic properties of the Dynes superconductors

TL;DR

This paper develops a thermodynamically consistent theory for Dynes superconductors, analyzing their specific heat, critical field, and other properties, revealing power-law behaviors and modified scaling laws near phase transitions.

Contribution

It provides a thermodynamically consistent derivation of the Dynes superconductor model, including calculations of thermodynamic properties and new scaling laws near phase transitions.

Findings

Power-law scaling of gap, specific heat, and penetration depth at low temperatures.

Modified Homes law near superconductor-normal metal transition.

Thermodynamic consistency of the Dynes superconductor theory.

Abstract

The tunneling density of states in dirty superconductors is often well described by the phenomenological Dynes formula. Recently we have shown that this formula can be derived, within the coherent potential approximation, for superconductors with simultaneously present pair-conserving and pair-breaking impurity scattering. Here we demonstrate that the theory of such so-called Dynes superconductors is thermodynamically consistent. We calculate the specific heat and critical field of the Dynes superconductors, and we show that their gap parameter, specific heat, critical field, and penetration depth exhibit power-law scaling with temperature in the low-temperature limit. We also show that, in the vicinity of a coupling constant-controlled superconductor to normal metal transition, the Homes law is replaced by a different, pair-breaking dominated scaling law.