Bloch's theory in periodic structures with Rashba's spin-orbit interaction

TL;DR

This paper extends Bloch's theory to two-dimensional electron gases with Rashba spin-orbit interaction and arbitrary in-plane potentials, deriving a general eigenvalue problem for the band structure and analyzing specific cases.

Contribution

It introduces a general framework for Bloch's amplitude in systems with Rashba interaction and arbitrary potentials, providing new insights into their band structures.

Findings

High polarization regions correlate with large group velocities in harmonic confinement cases.

Derived a general eigenvalue problem for systems with combined periodic and arbitrary potentials.

Applied the theory to specific potential configurations to analyze band structure features.

Abstract

We consider a two-dimensional electron gas with Rashba's spin-orbit interaction and two in-plane potentials superimposed along directions perpendicular to each other. The first of these potentials is assumed to be a general periodic potential while the second one is totally arbitrary. A general form for Bloch's amplitude is found and an eigen-value problem for the band structure of the system is derived. We apply the general result to the two particular cases in which either the second potential represents a harmonic in-plane confinement or it is zero. We find that for a harmonic confinement regions of the Brillouin zone with high polarizations are associated with the ones of large group velocity.