Coriolis force, geometric phase, and spin-electric coupling in semiconductors

We consider the response of an effective spin of a charge carrier to an adiabatic rotation of its crystal momentum induced by electric field. This rotation gives rise to Coriolis pseudo-force that is responsible for torque acting on the orbital momentum of a particle. Mediated by a spin-orbit coupling in the valence band this perturbation leads to a spin-electric coupling that may affect the coherent transport properties of a charge carrier and cause a spin precession in zero magnetic fields. In the static uniform electric field the derived effective spin-Hamiltonians of the carriers in the conduction and light hole bands are homologous to the Rashba Hamiltonian. These effects may be also interpreted as a manifestation of, in general, a non-Abelian gauge potential and can be described in purely geometric terms as a consequence of the corresponding holonomy. We demonstrate that in the conduction band the strength of the associated covariant gauge field is proportional to the effective electron g-tensor and is controllable by gate fields or a strain applied to the crystal.