Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the $\it{\textbf{k}}$-space

TL;DR

This paper compares two theoretical approaches to studying the Larkin-Ovchinnikov state in Weyl metals, revealing significant differences in their bulk and surface spectra due to how pairing interactions are modeled in momentum space.

Contribution

It demonstrates how restricting or extending pairing in momentum space affects the topological and spectral properties of Weyl metals, highlighting fundamental differences.

Findings

Different pairing approaches lead to distinct bulk spectra in Weyl metals.

Line nodes are robust in the extended pairing approach for two Weyl pairs.

Surface states and topological features vary significantly between the two methods.

Abstract

Two common approaches of studying theoretically the property of a superconductor are shown to have significant differences, when they are applied to the Larkin-Ovchinnikov state of Weyl metals. In the first approach the pairing term is restricted by a cutoff energy to the neighborhood of the Fermi surface, whereas in the second approach the pairing term is extended to the whole Brillouin zone. We explore their difference by considering two minimal models for the Weyl metal. For a model giving a single pair of Weyl pockets, both two approaches give a partly-gapped (fully-gapped) bulk spectrum for small (large) pairing amplitude. However, for very small cutoff energy, a portion of the Fermi surface can be completely unaffected by the pairing term in the first approach. For the other model giving two pairs of Weyl pockets, while the bulk spectrum for the first approach can be fully gapped, the one from the second approach has a robust line node, and the surface states are also changed qualitatively by the pairing. We elucidate the above differences by topological arguments and analytical analyses. A factor common to both of the two models is the tilting of the Weyl cones which leads to asymmetric normal state band structure with respect to the Weyl nodes. For the Weyl metal with two pairs of Weyl pockets, the band folding leads to a double degeneracy in the effective model, which distinguishes the pairing of the second approach from all others.