Non-Hermitian Hopf-Link Exceptional Line Semimetals

TL;DR

This paper explores a novel class of three-dimensional non-Hermitian topological phases characterized by Hopf-link exceptional lines, revealing new topological features and phase transitions in band structures without symmetry constraints.

Contribution

It introduces the concept of Hopf-link exceptional lines in non-Hermitian topological phases and proposes linking numbers based on Chern-Simons integrals to classify these phases.

Findings

Identification of Hopf-link exceptional lines in 3D non-Hermitian systems

Transition of Fermi surfaces from nodal lines to twisting surfaces

Proposal of linking numbers using Chern-Simons form

Abstract

We study a new class of non-Hermitian topological phases in three dimension in the absence of any symmetry, where the topological robust band degeneracies are Hopf-link exceptional lines. As a concrete example, we investigate the non-Hermitian band structures of nodal line semimetals under non-Hermitian perturbations, where the Fermi surfaces can transit from 1d nodal lines to 2d twisting surfaces with Hopf-link boundaries when the winding number defined along the nodal line is $\pm 1$. The linking numbers of these linked exceptional line phases are also proposed, based on the integral of Chern-Simons form over the Brillouin zone.