On stability of odd-frequency superconducting state

TL;DR

This paper challenges previous claims of thermodynamic instability of odd-frequency superconducting states, demonstrating through a functional integral approach that such states can be stable and exhibit a normal Meissner effect.

Contribution

It shows that odd-frequency superconductors are thermodynamically stable and physically realizable when modeled with a proper non-local-in-time effective action.

Findings

Odd-frequency state is thermodynamically stable.

Exhibits a normal Meissner effect.

Can exist as a homogeneous equilibrium phase.

Abstract

Odd-frequency pairing mechanism of superconductivity has been investigated for several decades. Nevertheless, its properties, including the thermodynamic stability, have remained unclear. In particular, it has been argued that the odd-frequency state is thermodynamically unstable, has an unphysical (anti-) Meissner effect, and thus can not exist as a homogeneous equilibrium phase. We argue that this conclusion is incorrect because it implicitly relies on the inappropriate assumption that the odd-frequency superconductor can be described by an effective Hamiltonian that breaks the particle conservation symmetry. We demonstrate that the odd-frequency state can be properly described within the functional integral approach using non-local-in-time effective action. Within the saddle point approximation, we find that this phase is thermodynamically stable, exhibits ordinary Meissner effect, and therefore can be realized as an equilibrium homogenous state of matter.