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The physical properties of metals are often given by the sum of thecontributions from the electrons consisting the Fermi surface (FS), andtherefore, fine structures of the electronic bands and Bloch functions areoften masked by the integral over FS. As a consequence, usually, the singularstructures in the electronic bands are often not reflected to the macroscopicquantities. In this work, we investigate the anomaly-related magnetoresistancein metals with type-II Weyl nodes close to the FS, and find that theanomaly-related current increases divergently, showing a singular structure.Detailed analysis on a simple model with multiple Weyl nodes shows that thecontribution to the magnetoresistance is dominated by the electrons in thevicinity of the Weyl nodes; this is related to the fact that the current isgiven by the square of the Berry curvature, which enhances the contributionfrom the electrons around the Weyl nodes. The above results potentially allowsan estimate of the anomaly-induced current without precise information of theentire Band structure.

Singular nonlinear response in metals due to divergent Berry curvature: application to magneto-resistance in metals with type-II Weyl nodes