Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators*

Two-dimensional higher-order topological insulators can display a number of exotic phenomena, such as half-integer charges localized at corners or disclination defects. In this presentation, we analyze these phenomena, focusing on the paradigmatic example of the quadrupole insulator with C4 rotation symmetry. We present a topological field theory description of the mixed geometry-charge responses. Our theory provides a unified description of the corner and disclination charges in terms of a physical geometry (which encodes disclinations), and an effective geometry (which encodes corners).