Theory of Coherent Time-dependent Transport in One-dimensional Multiband Semiconductor Superlattices

TL;DR

This paper develops an analytical framework for understanding time-dependent electron transport in one-dimensional multiband semiconductor superlattices under external electric fields, extending previous numerical studies with new theoretical insights.

Contribution

It provides an analytical derivation of energy spectra, eigenstates, and current expressions, including Zener-tunneling effects, for multiband superlattices in time-dependent fields.

Findings

Derived general results for (quasi)energies and eigenstates.

Formulated an equation of motion for the density matrix in a two-band model.

Presented an expression for the electric current and analyzed Zener-tunneling phenomena.

Abstract

We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time-dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model, and the properties of the solutions are analyzed. An expression for the current is obtained. Finally, Zener-tunneling in a two-band tight-binding model is considered. The present work gives the background and an extension of the theoretical framework underlying our recent Letter [J. Rotvig {\it et al.}, Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulations were presented.