On the Thermodynamic Stability of Odd-Frequency Superconductors

TL;DR

This paper investigates the thermodynamic stability of odd-frequency superconductors using an Eliashberg framework, concluding that stable homogeneous odd-frequency states are generally forbidden in weak coupling, with some exceptions discussed.

Contribution

It provides a rigorous analysis showing the thermodynamic instability of homogeneous odd-frequency superconductors in the weak coupling limit and discusses potential scenarios for stability.

Findings

Homogeneous odd-frequency superconductors are thermodynamically unstable in the weak coupling limit.

Strong coupling corrections do not change the instability result.

Certain scenarios might allow stable odd-frequency pairing states.

Abstract

The thermodynamic stability of odd-frequency pairing states is investigated within an Eliashberg-type framework. We find the rigorous result that in the weak coupling limit a continuous transition from the normal state to a spatially homogeneous odd-in-$\omega$ superconducting state is forbidden, irrespective of details of the pairing interaction and of the spin symmetry of the gap function. For isotropic systems, it is shown that the inclusion of strong coupling corrections does not invalidate this result. We discuss a few scenarios that might escape these thermodynamic constraints and permit stable odd-frequency pairing states.