An exceptional surface and its topology

TL;DR

This paper explores the topology of exceptional surfaces in non-Hermitian three-dimensional systems, revealing new higher-dimensional topological defects and quantifying their properties with the Dixmier-Douady invariant.

Contribution

It introduces the concept of an exceptional surface in 3D non-Hermitian systems and proposes an experimental scheme to realize such models, extending the understanding of exceptional topology.

Findings

Identification of an exceptional surface where three eigenstates coalesce

Quantification of the topology using the Dixmier-Douady invariant

Proposal of an experimentally feasible scheme for engineering the model

Abstract

Non-Hermitian (NH) systems can display exceptional topological defects without Hermitian counterparts, exemplified by exceptional rings in NH two-dimensional systems. However, exceptional topological features associated with higher-dimension topological defects remain unexplored yet. We here investigate the topology for the singularities in an NH three-dimensional system. We find that the three-order singularities in the parameter space form an exceptional surface (ES), on which all the three eigenstates and eigenenergies coalesce. Such an ES corresponds to a two-dimensional extension of a point-like synthetic tensor monopole. We quantify its topology with the Dixmier-Douady invariant, which measures the quantized flux associated with the synthetic tensor field. We further propose an experimentally feasible scheme for engineering such an NH model. Our results pave the way for investigations of exceptional topology associated with topological defects with more than one dimension.