Exceptional topological insulators with crystal symmetries

Exceptional topological insulators are a non-Hermitian three-dimensional phase of matter with nontrivial point-gap topology. Their topological index, a 3D winding number, is well-defined without any symmetries, and implies that the surface of the open system hosts anomalous topologically protected modes. I will explain how this non-Hermitian topological phase can be inferred using symmetry-indicators of the bulk Hamiltonian. Furthermore, I will demonstrate how exceptional topological insulators represent a pumping between a two-dimensional phase with a higher-order non-Hermitian skin effect and a trivial two-dimensional phase. This implies an anomalous localization of the surface states of an exceptional topological insulator.