Higher-order topology protected by latent crystalline symmetries

TL;DR

This paper shows that fractional corner charges in higher-order topological insulators can be protected by latent crystalline symmetries, not just explicit rotation symmetries, broadening the classification of topological phases.

Contribution

It introduces the concept of latent rotation symmetry and filling anomaly, extending topological classification to include hidden symmetries revealed by isospectral reduction.

Findings

Fractional corner charges can exist without explicit rotation symmetry.

Latent symmetries can protect higher-order topology.

New topological invariants are proposed for systems with latent symmetry.

Abstract

We demonstrate that rotation symmetry is not a necessary requirement for the existence of fractional corner charges in Cn-symmetric higher-order topological crystalline insulators. Instead, it is sufficient to have a latent rotation symmetry, which may be revealed upon performing an isospectral reduction on the system. We introduce the concept of a filling anomaly for latent crystalline symmetric systems, and propose modified topological invariants. The notion of higher-order topology in two dimensions protected by Cn symmetry is thus generalized to a protection by latent symmetry. Our claims are corroborated by concrete examples of models that show non-trivial corner charge in the absence of Cn-symmetry. This work extends the classification of topological crystalline insulators to include latent symmetries.