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

TL;DR

This paper introduces a new topological invariant called the quadrupole index, linking bulk properties to chiral hinge modes in 3D second order topological insulators, and demonstrates their connection to the quantum anomalous Hall effect.

Contribution

It proposes a novel quadrupole index combined with a slab Chern number to characterize hinge modes and establishes the bulk-hinge correspondence in 3D second order topological insulators.

Findings

Quadrupole index characterizes chiral hinge modes.

Connection between hinge modes and bulk invariants demonstrated.

Bulk invariants measurable via transport and magneto-optical experiments.

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.