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In this paper, we study the semiclassical behavior of Bloch electrons in thepresence of Weyl nodes, which are singular points in the band structure ofcertain materials. We carry out asymptotic analysis and present a rigorousderivation of the semiclassical asymptotic expansion of the current of Blochelectrons with the presence of Weyl nodes. The analysis shows that the currentcontains two parts, one independent of the Weyl nodes and the other acontribution from the singular points. This work provides a theoreticalfoundation towards a rigorous justification of recent scientific discoveries inWeyl semimetals. The main innovation of this paper is a new strategy to dealwith the singular points with quantitative estimates, which may have broaderapplications in multiscale models with singularities.

Asymptotic analysis for Bloch electrons with Weyl nodes