Symmetry indicators in commensurate magnetic flux

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.

28 pages, 7 figures

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Cited by in corpus (8)

• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Topological heavy fermions in magnetic field
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Projective symmetry determined topology in flux Su-Schrieffer-Heeger model
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux
• Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux