Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions

Starting with general semiclassical equations of motion for electrons in the presence electric and magnetic fields, we extend Chambers formula to include addition a field, time-dependent fields bands Berry curvature. We thereby compute conductivity tensor ${\sigma}_{{\alpha}{\beta}}(B,{\omega})$ field two (2D) three (3D) dimensions focus then on several applications magnetotransport metals Fermi surface topological transitions 2D. In particular, consider rectangular lattice model related overdoped graphene, investigate signatures different types Hall coefficient, ${\sigma}_{xy}$ longitudinal ${\sigma}_{xx}$. The behavior those quantities as function frequency, when is time dependent, also investigated. As an example non-zero curvature, study Haldane within this context. addition, provide linear nonlinear current order $E^2$.