Strong-Coupling Superconductivity with Mixed Even- and Odd-Frequency Pairing

TL;DR

This paper explores a new superconducting state combining even- and odd-frequency pairing, revealing how such mixing affects physical properties and could relate to strong-coupling superconductivity coexisting with ferromagnetism.

Contribution

It develops a Landau free energy framework for mixed parity superconducting states, highlighting the role of odd-frequency components in stabilizing novel superconducting phases.

Findings

Odd-frequency components significantly modify physical behaviors.

Mixed states can coexist with ferromagnetism in strong-coupling regimes.

The free-energy functional reveals anomalous structures due to parity mixing.

Abstract

We investigate general structure of Landau free energy for stabilizing a novel superconducting state with both even-frequency and odd-frequency components in gap function. On the basis of the Luttinger-Ward functional, we elucidate an emergent mixing between different "parities" in time. The simplest case of the conventional s-wave singlet mixed with the odd-frequency triplet state under broken time-reversal symmetry is examined to demonstrate the anomalous structure of the free-energy functional. The induced odd-frequency component alters behaviors of physical quantities from those obtained by neglecting the odd-frequency component. The novel mixed state may also be relevant to strong-coupling superconductivity coexisting with ferromagnetism.