Quantized Response and Topology of Insulators with Inversion Symmetry

TL;DR

This paper classifies three-dimensional inversion-symmetric insulators using parity eigenvalues and Chern numbers, revealing constraints on topological invariants and quantized magneto-electric responses, with implications for magnetic topological insulators.

Contribution

It provides a new classification scheme for inversion-symmetric insulators based on TRIM parities and Chern numbers, including a geometric derivation using entanglement spectra.

Findings

TRIM parities satisfy a product constraint of +1.

Chern numbers are constrained modulo two by TRIM parities.

Magneto-electric response theta is quantized and determined by TRIM parities.

Abstract

We study three dimensional insulators with inversion symmetry, in which other point group symmetries, such as time reversal, are generically absent. Their band topology is found to be classified by the parities of occupied states at time reversal invariant momenta (TRIM parities), and by three Chern numbers. The TRIM parities of any insulator must satisfy a constraint: their product must be +1. The TRIM parities also constrain the Chern numbers modulo two. When the Chern numbers vanish, a magneto-electric response parameterized by "theta" is defined and is quantized to theta= 0, 2pi. Its value is entirely determined by the TRIM parities. These results may be useful in the search for magnetic topological insulators with large theta. A classification of inversion symmetric insulators is also given for general dimensions. An alternate geometrical derivation of our results is obtained by using the entanglement spectrum of the ground state wave-function.