Quantum anomalies and quantum geometry induced linear and non-linear transport in Weyl semimetals

Quantum geometry of the electron wave-function plays a significant role in the linear and non-linear responses of Weyl semimetals. One such geometric quantity, the Berry curvature can be used to understand the quantum anomalies in Weyl semimetal, which leads to chiral charge and energy pumping between the Weyl nodes of opposite chirality. This results in chiral charge and energy imbalance between the Weyl nodes and gives rise to several intriguing magneto-transport phenomena. In addition to the Berry curvature, other band geometric quantities such as the orbital magnetic moment, Berry curvature dipole, and the quantum metric also give rise to novel transport phenomena in Weyl semimetals.