Symmetries of Weyl Superconductors with Different Pairings

TL;DR

This paper explores the symmetry properties of Weyl superconductors with different pairing types, revealing how various pairings break symmetries and lead to unique collective modes and effects.

Contribution

It identifies how specific pairing mechanisms break symmetries in Weyl superconductors and introduces the concept of a pseudo-scalar phase mode causing a pseudo-Meissner effect.

Findings

Fulde-Ferrell-Larkin-Ovchinnikov pairing breaks only U(1) gauge symmetry

Two Nambu-Goldstone modes are needed to restore broken symmetries

Emergence of a pseudo-scalar phase mode causing a pseudo-Meissner effect

Abstract

We examine the Bogoliubov-de Gennes Hamiltonian and its symmetries for a time-reversal symmetry broken three dimensional Weyl superconductor. In the limit of vanishing pairing potential, we specify that this Hamiltonian is invariant under two sets of continues symmetries, i.e. the $U(1)$ gauge symmetry and the $U(1)_A$ axial symmetry. Although a pairing of the Bardeen-Cooper-Schrieffer type spontaneously breaks both of these symmetries, we show that a Fulde-Ferrell-Larkin-Ovchinnikov type pairing spontaneously breaks only the $U(1)$ gauge symmetry (that is then restored via the well-known scalar phase mode of superconductivity). Consequently, in the former case, two Nambu-Goldstone modes are required in the system to restore the broken symmetries. We indicate that one of these two modes is an emergent pseudo-scalar phase mode. We also demonstrate that such a phase mode leads to a pseudo-Meissner effect.