Non-Abelian band topology in noninteracting metals

TL;DR

This paper introduces non-Abelian topological charges for line nodes in crystalline metals with $ ext{PT}$ symmetry, revealing new constraints on nodal-line configurations and predicting novel topological phases beyond existing classifications.

Contribution

It develops a comprehensive many-band framework for non-Abelian topological charges in metals, extending band topology beyond standard approaches.

Findings

Non-Abelian quaternion charges characterize line nodes.

Constraints on nodal-line configurations are established.

Prediction of new one-dimensional topological phases.

Abstract

Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of crystalline metals with space-time inversion ($\mathcal{PT}$) symmetry and with weak spinorbit coupling. We show that these are quaternion charges, similar to those describing disclinations in biaxial nematics. Starting from two-band considerations, we develop the complete many-band description of nodes in the presence of $\mathcal{PT}$ and mirror symmetries, which allows us to investigate the topological stability of nodal chains in metals. The non-Abelian charges put strict constraints on the possible nodal-line configurations. Our analysis goes beyond the standard approach to band topology and implies the existence of one-dimensional topological phases not present in existing classifications.