Instabilities of Weyl-loop semi-metals

TL;DR

This paper investigates the interaction-driven instabilities in Weyl-loop semi-metals using a controlled weak coupling renormalization group approach, identifying potential phases like chiral superconductivity, Pomeranchuk, and insulating states.

Contribution

It introduces an epsilon expansion regularization scheme and performs an analytical functional renormalization group analysis for Weyl-loop semi-metals, revealing their possible ordered phases.

Findings

Leading instability in particle-particle channel is chiral superconductivity.

Potential instabilities include Pomeranchuk phase and insulating phase.

The dominant instability depends on microscopic interaction parameters.

Abstract

We study Weyl-loop semi-metals with short range interactions, focusing on the possible interaction driven instabilities. We introduce an $\epsilon$ expansion regularization scheme by means of which the possible instabilities may be investigated in an unbiased manner through a controlled weak coupling renormalization group calculation. The problem has enough structure that a `functional' renormalization group calculation (necessary for an extended Fermi surface) can be carried out analytically. The leading instabilities are identified, and when there are competing degenerate instabilities a Landau-Ginzburg calculation is performed to determine the most likely phase. In the particle-particle channel, the leading instability is found to be to a fully gapped chiral superconducting phase which spontaneously breaks time reversal symmetry, in agreement with general symmetry arguments suggesting that Weyl loops should provide natural platforms for such exotic forms of superconductivity. In the particle hole channel, there are two potential instabilities - to a gapless Pomeranchuk phase which spontaneously breaks rotation symmetry, or to a fully gapped insulating phase which spontaneously breaks mirror symmetry. The dominant instability in the particle hole channel depends on the specific values of microscopic interaction parameters.