Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators

TL;DR

This paper develops a topological field theory for higher-order topological insulators, explaining corner and disclination charges, and predicts fractional charge responses in interacting systems.

Contribution

It introduces a unified topological description of geometry-charge responses in quadrupole insulators, including interactions and fractionalization effects.

Findings

Unified topological field theory for corner and disclination charges

Prediction of fractional charge responses in interacting quadrupole insulators

Extension of theory to systems with fractional quadrupole moments

Abstract

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 paper, we analyze these phenomena, focusing on the paradigmatic example of the quadrupole insulator with $C_4$ rotation symmetry, and 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). We extend this analysis to interacting systems, and predict the response of fractional quadrupole insulators, which exhibit charge $e/2(2k+1)$ bound to corners and disclinations.