  In this paper, we study the semiclassical behavior of Bloch electrons in the
presence of Weyl nodes, which are singular points in the band structure of
certain materials. We carry out asymptotic analysis and present a rigorous
derivation of the semiclassical asymptotic expansion of the current of Bloch
electrons with the presence of Weyl nodes. The analysis shows that the current
contains two parts, one independent of the Weyl nodes and the other a
contribution from the singular points. This work provides a theoretical
foundation towards a rigorous justification of recent scientific discoveries in
Weyl semimetals. The main innovation of this paper is a new strategy to deal
with the singular points with quantitative estimates, which may have broader
applications in multiscale models with singularities.
