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Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
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Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
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Paper
Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
2022
Overview
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in \\(3\\)D with \\(C_n\\) lattice rotation symmetry along a fixed axis, in addition to either mirror symmetry or particle-hole symmetry. These insulators can realize quantized mixed geometry-charge responses. When the surface of these insulators is gapped, disclinations on the surface carry a fractional charge that is half the minimal amount that can occur in purely \\(2\\)D systems. Similarly, disclination lines in the bulk carry a fractionally quantized electric polarization. These effects, and other related phenomena, are captured by a \\(3\\)D topological response term that couples the lattice curvature to the electromagnetic field strength. Additionally, mirror symmetric insulators with this response can be smoothly deformed into a higher-order octopole insulator with quantized corner charges. We also construct a symmetry indicator form for the topological invariant that describes the quantized response of the mirror symmetric topological crystalline insulators, and discuss an unusual response quantization in time-reversal breaking systems.
Publisher
Cornell University Library, arXiv.org
Subject
