Broken-symmetry phases of interacting nested Weyl and Dirac loops

TL;DR

This paper investigates how interactions induce various broken symmetry phases, such as density waves and superconductivity, in systems with nested Weyl and Dirac loops, revealing their dependence on symmetry properties and extending to nodal lines.

Contribution

It provides a comprehensive analysis of interaction-induced phases in nested Weyl and Dirac loops, including the effects of symmetries and extensions to nodal lines and spinful systems.

Findings

Density-wave phases lower total energy and can be metallic, insulating, or semimetallic.

Superconductivity from interloop pairing is fully gapped only in semimetallic systems.

Ordered phases include nodal point and nodal chain semimetals depending on symmetry.

Abstract

We study interaction-induced broken symmetry phases that can arise in metallic or semimetallic band structures with two nested Weyl or Dirac loops. The odered phases can be of the charge or (pseudo)spin density wave type, or superconductivity from interloop pairing. A general analysis for two types of Weyl loops is given, according to whether a local reflection symmetry in momentum space exists or not, for Hamiltonians having a global PT symmetry. The resulting density-wave phases always have lower total energy, and can be metallic, insulating, or semimetallic (with nodal loops), depending on both the reflection symmetry of the loops and the symmetry transformation that maps one loop onto the other. We extend this study to nested $\mathbb{Z}_2$ nodal lines, for which the ordered phases include also nodal point and nodal chain semimetals, and to spinful Dirac nodal lines. Superconductivity from interloop pairing can be fully gapped only if the initial double loop system is semimetallic.