Weyl and Dirac Loop Superconductors

TL;DR

This paper explores novel three-dimensional superconducting states emerging from Weyl and Dirac loop materials, highlighting topologically non-trivial phases like the meron and skyrmion superconductors driven by Fermi surface topology.

Contribution

It introduces a minimal Hamiltonian for Weyl and Dirac loops, classifies possible superconducting instabilities, and predicts new topological superconducting states influenced by symmetry and topology.

Findings

Doped Weyl loop materials favor a fully gapped chiral superconductor.

The meron superconductor state is topologically non-trivial and unique to Fermi surface topology.

Complex superconducting states, including skyrmion phases, can arise in Dirac loop systems.

Abstract

We study three dimensional systems where the parent metallic state contains a loop of Weyl or Dirac points. We introduce the minimal $\vec{k} \cdot \vec{p}$ Hamiltonian , and discuss its symmetries. Guided by this symmetry analysis, we classify the superconducting instabilities that may arise. For a doped Weyl loop material, we argue that - independent of microscopic details - the leading superconducting instability should be to a fully gapped chiral superconductor in three dimensions- an unusual state made possible only by the non-trivial topology of the Fermi surface. This state - which we dub the `meron superconductor' - is neither fully topological nor fully trivial. Meanwhile, at perfect compensation additional states are possible (including some that are fully topological), but the leading instability depends on microscopic details. We discuss the influence of disorder on pairing. In the presence of a spin degeneracy (`Dirac loops') still more complex superconducting states can arise, including a `skyrmion' superconductor with topological properties similar to superfluid He III-B, which additionally breaks lattice rotation symmetry and exhibits nematic order.