Anomalous transport phenomena from dissipative charge pumping

The Berry curvature involving time and momentum derivatives, which we term emergent electric field, induces a nondisspative current known as the adiabatic charge pumping or Thouless pumping in periodically driven systems. We study dissipative currents originated from the interplay between emergent electric fields and electric/magnetic fields in two and three dimensions on the basis of the Boltzmann transport theory. As an example of two-dimensional models, we study the Rashba Hamiltonian with time-dependent and anisotropic spin-orbit coupling. We show that the interplay between emergent electric fields and electric fields leads to a current transverse to electric fields, which is symmetric and contributes to the entropy production. As an example of three-dimensional models, we study the Weyl Hamiltonian under AC electric fields. We show that the interplay between emergent electric fields and magnetic fields leads to a Hall-type current at zero DC electric fields, which is now transverse to DC magnetic fields: $j_{x}=\sigma_{xy}B_y$ ($\sigma_{xy}=-\sigma_{yx}$). The Hall photocurrent is relevant in the inversion symmetry breaking Weyl semimetals such as TaAs or SrSi$_2$.