The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators

Abstract

The chiral hinge modes are the key feature of a second order topological insulator in three dimensions. Here we propose a quadrupole index in combination of a slab Chern number in the bulk to characterize the flowing pattern of chiral hinge modes along the hinges at the intersection of the surfaces of a sample. We further utilize the topological field theory to demonstrate the correspondent connection of the chiral hinge modes to the quadrupole index and the slab Chern number, and present a picture of three-dimensional quantum anomalous Hall effect as a consequence of chiral hinge modes. The two bulk topological invariants can be measured in electric transport and magneto-optical experiments. In this way we establish the bulk-hinge correspondence in a three-dimensional second order topological insulator.

arXiv comment6 pages, 3 figures

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• Signature of parity anomaly in the measurement of optical Hall conductivity in quantum anomalous Hall systems
• On the half-quantized Hall conductance of massive surface electrons in magnetic topological insulator films
• Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Effects of first- and second-order topological phases on equilibrium crystal shapes
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• RKKY interaction in helical higher-order topological insulators
• Emergent Weyl-like points in periodically modulated systems
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