Wave Packet Dynamics in a Biased Finite-Length Superlattice

TL;DR

This paper studies the behavior of specially constructed wave packets in finite superlattices, revealing their near-rigid propagation in k-space under external forces, which enhances understanding of electron dynamics in such structures.

Contribution

It introduces and analyzes 'k-compact' wave packets that minimize k-value spread and propagate with nearly rigid shape in finite superlattices.

Findings

'k-compact' wave packets exhibit minimal dispersion during propagation.

The wave packets propagate with an essentially rigid shape in k-space.

The study provides insights into electron dynamics in finite superlattices.

Abstract

In a superlattice containing a finite number of periods, the allowed values of the Bloch wave number form a discrete set, and the dynamics of an electron through k-space under the influence of an external force is necessarily that of a superposition wave packet composed of multiple Bloch waves. The present paper investigates this dynamics for a particularly simple class of "k-compact" wave packets, in which the spread over different k-values is minimized, and which propagate with an essentially rigid shape through k-space.