The coherent Hall effect of charge carriers in a superlattice: semiclassical description of the wavepacket dynamics

The coherent Hall effect of charge carriers is the quantum mechanical analogue of the classical Hall effect for the case where the charge carriers are a coherent ensemble of wavepackets. Kosevich considered this effect for the first time for semiconductor superlattices subjected both to an electric field along the growth direction and to a perpendicular magnetic field (Kosevich Y A 1999 Ann. Phys. 8 SI-145; 2001 Phys. Rev. B 63 205313). The dynamics of the charge carriers can be described successfully by means of a semiclassical model mapping the equation of motion to a simple pendulum equation with the deflection angle in the case of the pendulum being replaced by the k-vector of the wavepackets along the superlattice's growth direction. While Kosevich has presented an analytical treatment of the equation of motion, we numerically solve it and compute the real-space and k-space trajectories of the charge carriers. We thus arrive at a more illustrative and detailed analysis of the wavepacket dynamics and make predictions for optical pump-probe experiments which detect either the terahertz radiation emitted by the oscillating charge carriers or the internal electric field as a function of time after impulsive excitation of charge carriers