Symmetry indicators in commensurate magnetic flux

TL;DR

This paper develops a framework for applying topological quantum chemistry to systems with magnetic flux, revealing new symmetry indicators and phase transitions in magnetic topological insulators.

Contribution

It extends symmetry indicator theory to magnetic systems by deriving the action of symmetry operators in magnetic fields, introducing new indicators at π flux, and demonstrating their use in topological phase transitions.

Findings

New symmetry indicators at π flux.

Identification of topological-to-trivial phase transition.

Confirmation via Hofstadter butterfly calculations.

Abstract

We derive a framework to apply topological quantum chemistry in systems subject to magnetic flux. We start by deriving the action of spatial symmetry operators in a uniform magnetic field, which extends Zak's magnetic translation groups to all crystal symmetry groups. Ultimately, the magnetic symmetries form a projective representation of the crystal symmetry group. As a consequence, band representations acquire an extra gauge invariant phase compared to the non-magnetic theory. Thus, the theory of symmetry indicators is distinct from the non-magnetic case. We give examples of new symmetry indicators that appear at $\pi$ flux. Finally, we apply our results to an obstructed atomic insulator with corner states in a magnetic field. The symmetry indicators reveal a topological-to-trivial phase transition at finite flux, which is confirmed by a Hofstadter butterfly calculation. The bulk phase transition provides a new probe of higher order topology in certain obstructed atomic insulators.