Knotted Non-Hermitian Metals

TL;DR

This paper introduces stable knotted metallic band structures in non-Hermitian systems, characterized by open Fermi surfaces bounded by knotted exceptional lines, achievable without fine tuning or symmetries, and discusses their experimental realization.

Contribution

It presents the first explicit models of knotted non-Hermitian metals with short-range hopping and analyzes their topological stability and potential experimental implementations.

Findings

Knotted NH metals have stable topological phases without fine tuning.

Explicit tight-binding models for knotted NH metals are constructed.

Potential experimental realization in photonic systems is discussed.

Abstract

We report on the occurrence of knotted metallic band structures as stable topological phases in non-Hermitian (NH) systems. These knotted NH metals are characterized by open Fermi surfaces, known in mathematics as Seifert surfaces, that are bounded by knotted lines of exceptional points. Quite remarkably, and in contrast to the situation in Hermitian systems, no fine tuning or symmetries are required in order to stabilize these exotic phases of matter. By explicit construction, we derive microscopic tight-binding models hosting knotted NH metals with strictly short-ranged hopping, and investigate the stability of their topological properties against perturbations. Building up on recently developed experimental techniques for the realization of NH band structures, we discuss how the proposed models may be experimentally implemented in photonic systems.