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

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