Chiral charge pumping via the anomalous zeroth Landau level in Weyl semimetals
In Weyl semimetals, chiral (Weyl) nodes carry opposite topological charges ±1. Under a magnetic field B, each node forms Landau levels; uniquely, the zeroth Landau level is chiral — it disperses with a definite sign of velocity v·sign(chirality). A parallel electric field E·B ≠ 0 pumps charge between nodes (chiral anomaly), producing an anomalous Hall current proportional to E·B. This is the condensed matter realization of the Adler-Bell-Jackiw axial anomaly in quantum field theory.