Evolution and tunneling time of electron wave packets through a superlattice

Abstract

We present a formalism to study the evolution of a wave packet inside and outside a scattering superlattice. Time series of specific Gaussian packets, centered at an arbitrary energy ${E}_{o},$ exhibit interesting back-scattering, trapping, and transmission effects. These effects depend on whether the energy ${E}_{o}$ is in a gap, coincides with a resonance, or is an arbitrary point in a band of the superlattice. The time evolution depends strongly on the transmission coefficient and on the superlattice tunneling time. We show that because of the reduced wave-packet distortion and the high intensity difference between the back-scattered and the transmitted wave, for ${E}_{o}$ in a gap, it is convenient to look at the back-scattered wave packet to study the superlattice tunneling time.