Quantization of fractional corner charge in Cn-symmetric higher-order topological crystalline insulators

Building upon the concepts of band representations and their relation to localized Wannier functions, the authors systematically study charge fractionalization in higher-order topological insulators. They show that, when protected by ${C}_{n}$ rotation symmetries, charge can be fractionally quantized in units of $e/n$. The authors build topological indices for ${C}_{n}$-symmetric higher-order topological insulators in class AI. Due to an algebraic structure of the topological classification of these phases, these indices apply even to fragile phases, which lack a Wannier description, but for which a ``generalized'' Wannier description can be formulated.