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

Abstract

The coherent Hall effect of charge carriers is the quantum mechanical analogue of theclassical Hall effect for the case where the charge carriers are a coherent ensemble ofwavepackets. Kosevich considered this effect for the first time for semiconductorsuperlattices subjected both to an electric field along the growth direction and to aperpendicular magnetic field (Kosevich Y A 1999 Ann. Phys. 8 SI-145; 2001 Phys. Rev. B 63205313). The dynamics of the charge carriers can be described successfully by means ofa semiclassical model mapping the equation of motion to a simple pendulumequation with the deflection angle in the case of the pendulum being replaced by thek-vector of the wavepackets along the superlattice’s growth direction. While Kosevich has presented ananalytical treatment of the equation of motion, we numerically solve it and compute the real-spaceand k-space trajectories of the charge carriers. We thus arrive at a more illustrative and detailedanalysis of the wavepacket dynamics and make predictions for optical pump–probeexperiments which detect either the terahertz radiation emitted by the oscillating chargecarriers or the internal electric field as a function of time after impulsive excitation ofcharge carriers.