Higher-order topology protected by latent crystalline symmetries

We demonstrate that rotation symmetry is not a necessary requirement for the existence of fractional corner charges in C_n <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> -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 C_n <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> 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 C_n <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> -symmetry. This work extends the classification of topological crystalline insulators to include latent symmetries.