Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals

TL;DR

This paper investigates how disorder affects the bandstructure topology in tilted Weyl semimetals, revealing the emergence of flat bands and nodal lines in the non-Hermitian spectrum due to electron scattering.

Contribution

It introduces a novel analysis of disorder-induced flat bands and nodal lines in non-Hermitian Weyl semimetals with tilt, connecting to non-Hermitian topological theory.

Findings

Tilt induces flat bands or nodal line segments at electron-hole interfaces.

Flat bands have fully imaginary spectra separated by exceptional nodal rings.

Tilt in two directions can shrink flat bands into nodal line segments with exceptional edge points.

Abstract

We study the interplay of disorder and bandstructure topology in a Weyl semimetal with a tilted conical spectrum around the Weyl points. The spectrum of particles is given by the eigenvalues of a non-Hermitian matrix, which contains contributions from a Weyl Hamiltonian and complex self-energy due to electron elastic scattering on disorder. We find that the tilt-induced matrix structure of the self-energy gives rise to either a flat band or a nodal line segment at the interface of the electron and hole pockets in the bulk bandstructure of type-II Weyl semimetals depending on the Weyl cone inclination. For the tilt in a single direction in momentum space, each Weyl point expands into a flat band lying on the plane, which is transverse to the direction of the tilt. The spectrum of the flat band is fully imaginary and is separated from the in-plane dispersive part of the spectrum by the "exceptional nodal ring" where the matrix of the Green function in momentum-frequency space is defective. The tilt in two directions might shrink a flat band into a nodal line segment with "exceptional edge points". We discuss the connection to the non-Hermitian topological theory.