Chiral Anomaly in Non-Relativistic Systems: Berry Curvature and Chiral Kinetic Theory

Chiral anomaly and the novel quantum phenomena it induces have been widely studied for Dirac Weyl fermions. In most typical cases, Lorentz covariance is assumed thus linear dispersion relations are maintained. However, in realistic materials, such as semimetals, non-linear appear naturally. We develop a kinetic framework to study chiral fermions with dispersions by using methods of Wigner function semi-classical equations motion. this framework, sourced Berry monopoles momentum space could be enhanced or suppressed due windings around monopoles. Our results can help understand anomaly-induced transport non-relativistic systems.