Towards the theory of types III and IV non-Hermitian Weyl fermions

TL;DR

This paper develops a non-Hermitian Hamiltonian framework to describe unconventional Weyl fermions of types III and IV, revealing anisotropic spectra with real and complex parts depending on momentum direction, and explores their topological properties.

Contribution

It introduces a formalism for non-Hermitian Weyl fermions of types III and IV, highlighting their anisotropic spectral properties and topological characteristics.

Findings

Spectrum exhibits direction-dependent real and complex parts.

Non-trivial adiabatic evolution observed.

Fractional Chern numbers identified.

Abstract

We develop the non-Hermitian Hamiltonian formalism to describe Weyl fermions of type III and IV. The spectrum of Hamiltonian has an unusual type of anisotropy. Namely, the hermiticity of Hamiltonian strongly depends on the direction in momentum space: for some directions the spectrum is real, in contrast for other directions it becomes complex. This fact leads to non-trivial adiabatic evolution and fractional Chern number. Additionally, we demonstrate that the non-Hermitian Hamiltonian can be regarded as a one-particle problem in context of topological band theory.