Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures

TL;DR

This paper introduces symmetry indicator topological invariants for non-Hermitian band structures with inversion symmetry, simplifying the calculation of complex topological invariants and linking them to observable surface states.

Contribution

It develops a method to compute non-Hermitian topological invariants using symmetry eigenvalues, reducing computational complexity and providing new insights into surface states.

Findings

Symmetry indicators can determine the 3D winding number from high-symmetry points.

Indicators characterize the Chern-Simons form in time-reversal symmetric systems.

Surface states are linked to nontrivial symmetry indicators.

Abstract

We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological invariants. In particular, we express the three-dimensional winding number of point-gapped non-Hermitian systems, which is defined as an integral over the whole Brillouin zone, in terms of symmetry eigenvalues at high-symmetry momenta. Furthermore, for time-reversal symmetric non-Hermitian topological insulators, we find that symmetry indicators characterize the associated Chern-Simons form, whose evaluation usually requires a computationally expensive choice of smooth gauge. In each case, we discuss the non-Hermitian surface states associated with nontrivial symmetry indicators.