Regularized framework of a Weyl equation for describing a Weyl semimetal: Application to the case with a screw dislocation

TL;DR

This paper introduces a regularized Weyl equation framework that captures surface and dislocation-bound chiral states in Weyl semimetals, overcoming limitations of the standard Weyl equation.

Contribution

A new combined Weyl and supplementary equation framework derived from microscopic models, enabling accurate description of boundary and dislocation states.

Findings

Successfully describes chiral surface states in cylindrical geometries.

Analytically determines local charge currents from chiral modes.

Validates the framework with application to screw dislocation cases.

Abstract

The term Weyl semimetal originates from the fact that its energy dispersion obeys a Weyl equation. However, a Weyl equation itself cannot fully describe the electron states in an actual bounded geometry. For example, the appearance of chiral surface states, which is a characteristic feature of a Weyl semimetal, cannot be captured with a Weyl equation. This indicates that some degree of freedom is lost when a Weyl equation is derived from a microscopic model of a Weyl semimetal. To overcome this difficulty, we present a framework consisting of a Weyl equation and a supplementary equation, which can be derived from a microscopic model. Applying this framework to a cylindrical system in the presence of a screw dislocation, we show that it appropriately describes the chiral surface states and one-dimensional chiral modes along a dislocation line. The local charge current induced by these chiral states is determined in an analytical manner.