Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators

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.

11 pages, 2 figures

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Cited by in corpus (9)

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• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Effective action approach to the filling anomaly in crystalline topological matter
• Rotational Symmetry Protected Edge and Corner States in Abelian topological phases
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Topological Dipole Insulator
• Disclinations, dislocations, and emanant flux at Dirac criticality
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges