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

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.