Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges

TL;DR

This paper systematically studies how non-Hermitian perturbations affect Weyl Hamiltonians with arbitrary topological charges, revealing preserved topological charges on exceptional contours and novel phase transitions involving gain and loss.

Contribution

It introduces a comprehensive analysis of non-Hermitian effects on Weyl points, showing topological charge preservation and new phase transition mechanisms in such systems.

Findings

Weyl points become exceptional contours under non-Hermitian perturbations.

Topological charge remains conserved on exceptional contours.

Oppositely charged contours can merge and dissipate charge without gap opening.

Abstract

We provide a systematic study of non-Hermitian topologically charged systems. Starting from a Hermitian Hamiltonian supporting Weyl points with arbitrary topological charge, adding a non-Hermitian perturbation transforms the Weyl points to one-dimensional exceptional contours. We analytical prove that the topological charge is preserved on the exceptional contours. In contrast to Hermitian systems, the addition of gain and loss allows for a new class of topological phase transition: when two oppositely charged exceptional contours touch, the topological charge can dissipate without opening a gap. These effects can be demonstrated in realistic photonics and acoustics systems.