On spectral flow and Fermi arcs

TL;DR

This paper uses spectral flow methods to explain the topological protection of Fermi arcs in Weyl semimetals, linking their stability to homotopy invariants of Dirac Hamiltonians.

Contribution

It introduces spectral flow techniques and a homological framework to analytically justify the topological protection of Fermi arcs in Weyl semimetals.

Findings

Spectral flow explains Fermi arc topological protection.

Homotopy invariants classify Weyl semimetal boundary states.

Dirac strings serve as global topological invariants.

Abstract

We introduce spectral flow techniques to explain why the Fermi arcs of Weyl semimetals are topologically protected against boundary condition changes and perturbations. We first analyse the topology of a certain universal space of self-adjoint half-line massive Dirac Hamiltonians, and then exploit its non-trivial and homotopy invariant spectral flow structure by pulling it back to generic Weyl semimetal models. The homological perspective of using Dirac strings/Euler chains as global topological invariants of Weyl semimetals/Fermi arcs, is thereby analytically justified.