  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.
