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

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.

References in corpus (7)

• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• New topological invariants in non-Hermitian systems
• Discovery of a new type of topological Weyl fermion semimetal state in Mo${}_x$W${}_{1-x}$Te${}_2$
• Emergent Weyl spinors in multi-fermion systems
• Black and White Holes at Material Junctions
• Artificial event horizons in Weyl semimetal heterostructures and their non-equilibrium signatures

Cited by in corpus (1)

• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes