Quantization of Fractional Corner Charge in C_n-symmetric Topological Crystalline Insulators

We show that C_n symmetries quantize the corner charge in crystalline topological insulators.
We first classify two-dimensional crystalline insulators having time-reversal and C_n symmetries and construct sets of primitive generator models that span these classifications. From these generators, we are able to characterize the existence of corner fractional charge systematically and relate it to the symmetry representations of the occupied energy bands. We find that C_n-symmetric crystalline insulators have fractional corner charges in multiples of e/n. Our findings are compiled in a set of topological indices that quantify the amount of charge robustly localized at corners. When an additional chiral symmetry is present, e/2 corner charges are accompanied by zero-energy corner-localized states. Finally, we discuss the role of fractional charges bound to disclinations as bulk probes for these topological insulators.