Anomalous Hall velocity, transient weak supercurrent, and coherent Meissner effect in semiconductor superlattices

Abstract

Complex evolution equations are derived for the macroscopic-average electron velocity and kinetic energy in biased semiconductor superlattices and coupled quantum wells. On this basis, we describe transient coherent oscillations of an electronic wave packet in crossed electric and magnetic fields as well as the temporal transition to dc transport and the nonlinear ac response in a biased semiconductor superlattice. We show that the coherent, excitation-dependent dynamics of a Bloch-oscillating wave packet is strongly affected by the carrier scattering and coupling with coherent plasmons. The possibility is predicted for optical excitation of Bloch-oscillating coherent heavy quasiparticles, whose minimal dipole oscillation amplitude depends on the ratio between the frequency and scattering rate and is much smaller than the single-electron spatial amplitude of Bloch oscillations. The separatrix is described that separates the full-miniband Bloch oscillations and the bottom-miniband cyclotron, plasma, or hybrid magnetoplasma coherent charge oscillations in the superlattice layer. Close to the separatrix, the frequency of Bloch oscillations of the electronic wave packet decreases, the oscillations become strongly anharmonic, and their spatial amplitude can greatly exceed the single-electron value. For incoherent oscillations, the separatrix is transformed into a separatrix domain in which oscillations are strongly damped and which separates the low-damped Bloch and (magneto)plasma oscillations. The frequencies of the coherent cyclotron, plasma, or hybrid magnetoplasma oscillations of the electronic wave packet depend on the wave packet excitation conditions and bias. The coupling and the form of the avoided crossing between the coherent Bloch oscillations and longitudinal optical phonon resonance in a wide-miniband superlattice also depend on the wave jacket excitation conditions. It is shown that the full-miniband Bloch oscillations of an electronic wave packet in a moderate parallel magnetic field give rise to an anomalous Hall velocity, which is proportional to the magnetic field but inversely proportional to the electric one, and whose magnitude and sign depend on the excitation conditions. The anomalous Hall velocity depends on the carrier effective mass and therefore the Hall current can be nonzero for equal densities of electrons and holes in a relatively thin superlattice layer clad by metal electrodes. It is shown that the interaction between a Bloch-oscillating electronic wave packet and the self-induced field results in a transient quasi-dc current that depends on the gauge-invariant phase difference and causes a coherent Meissner effect. A Fraunhofer diffraction pattern for the coherent ac and quasi-dc vertical currents is predicted; it is caused by quantum interference and magnetic flux quantization in the semiconductor superlattice layer. The occurrence of the coherent quasi-dc current results also in an excitation-dependent change of the wave packet dynamical relaxation rate.