Non-Hermitian spatial symmetries and their stabilized exceptional topological semimetals

Authors:
Preprint
Publisher website
Google Scholar
Abstract
Without the constraint imposed by Hermiticity, non-Hermitian systems enjoy greater freedom than Hermitian ones. While internal symmetries enriched by non-Hermiticity have been revealed, the interplay between spatial symmetries and non-Hermiticity remains to be explored. Here we study non-Hermitian spatial symmetries -- a class of symmetries that have no counterparts in Hermitian systems -- and study how exceptional semimetals can be stabilized by these symmetries. Different from internal ones, spatial symmetries act non-locally in momentum space and enforce global constraints on quantities at different momentum locations. We derive general constraints on geometric and topological invariants imposed by non-Hermitian spatial symmetries, which differ from those by Hermitian spatial symmetries. With these constraints, we reveal that certain exceptional manifold is only compatible with and stabilized by non-Hermitian spatial symmetries but is intrinsically incompatible with Hermitian spatial symmetries. We illustrate our theory using two three-dimensional (3D) models, dubbed exceptional unconventional Weyl semimetal and exceptional triple-point semimetal, respectively. Experimental cold-atom realization of the former is also proposed.

This publication has 58 references indexed in Scilit: