Topological classification for intersection singularities of exceptional surfaces in pseudo-Hermitian systems

TL;DR

This paper classifies the topological intersection singularities of exceptional surfaces in pseudo-Hermitian systems with PT symmetry, revealing new gapless topological phases and explaining their evolution under perturbations.

Contribution

It introduces a topological classification of intersection singularities of exceptional surfaces in pseudo-Hermitian systems, predicting new non-Hermitian topological phases.

Findings

Topology described by a non-Abelian free group on three generators

Predicts a new non-Hermitian gapless topological phase

Explains evolution of exceptional surfaces under symmetry-preserving perturbations

Abstract

Exceptional points play a pivotal role in the topology of non-Hermitian systems, and significant advances have been made in classifying exceptional points and exploring the associated phenomena. Exceptional surfaces, which are hypersurfaces of exceptional degeneracies in parameter space, can support hypersurface singularities, such as cusps, intersections and swallowtail catastrophes. Here we topologically classify the intersection singularity of exceptional surfaces for a generic pseudo-Hermitian system with parity-time symmetry. By constructing the quotient space under equivalence relations of eigenstates, we reveal that the topology of such gapless structures can be described by a non-Abelian free group on three generators. Importantly, the classification predicts a new kind of non-Hermitian gapless topological phase and can systematically explain how the exceptional surfaces and their intersections evolve under perturbations with symmetries preserved. Our work opens a new pathway for designing systems with robust topological phases, and provides inspiration for applications such as sensing and lasing which can utilize the special properties inherent in exceptional surfaces and intersections.