Superconductivity in Weyl metals

TL;DR

This paper investigates the types of superconducting states possible in Weyl metals, analyzing their stability, physical properties, and the challenges in realizing certain states like the FFLO state.

Contribution

It provides a comparative analysis of BCS and FFLO-like superconducting states in Weyl metals, highlighting conditions for their stability and physical characteristics.

Findings

Odd-parity BCS state is energetically favored in inversion-symmetric Weyl metals.

FFLO state may be lower in energy in noncentrosymmetric Weyl metals.

Realizing the FFLO state is generally very difficult due to lack of symmetry relations.

Abstract

We report on a study of intrinsic superconductivity in a Weyl metal, i.e. a doped Weyl semimetal. Two distinct superconducting states are possible in this system in principle: a zero-momentum pairing BCS state, with point nodes in the gap function; and a finite-momentum FFLO-like state, with a full nodeless gap. We find that, in an inversion-symmetric Weyl metal the odd-parity BCS state has a lower energy than the FFLO state, despite the nodes in the gap. The FFLO state, on the other hand, may have a lower energy in a noncentrosymmetric Weyl metal, in which Weyl nodes of opposite chirality have different energy. However, realizing the FFLO state is in general very difficult since the paired states are not related by any exact symmetry, which precludes a weak-coupling superconducting instability. We also discuss some of the physical properties of the nodal BCS state, in particular Majorana and Fermi arc surface states.