Weyl fermions in cylindrical wires

TL;DR

This paper investigates how cylindrical geometry and boundary conditions affect the spectrum of Weyl fermions in Weyl semimetals, revealing conditions for massless excitations and the impact of boundary phenomena.

Contribution

It derives the dispersion relations for Weyl fermions in cylindrical wires and identifies boundary conditions that support massless excitations.

Findings

Massless excitations occur only under specific boundary conditions.

General boundary conditions induce a mass inversely proportional to wire radius.

Boundary phenomena significantly influence excitation formation in Weyl semimetal structures.

Abstract

The key feature of Weyl semimetals (WSM) is the presence of topologically protected Dirac cones in a 3D material. We consider the effect of restricting geometry on the spectrum of excitations in WSM using as a model a cylindrical WSM wire. For the full manifold of hard boundary conditions, we derive the general form of the dispersion equation relating the energy of the excitations and their momentum along the wire. We show that only the special class of boundary conditions, corresponding to decoupled helicities or, equivalently, to pinned directions of the electron spin on the surface, support massless excitations. For a general boundary condition, these excitations acquire mass inversely proportional to the radius of the wire. This demonstrates that boundary phenomena may play a crucial role in formation of excitations in WSM based structures.