Magnetic focusing of charge carriers from spin-split bands: Semiclassics of a Zitterbewegung effect

TL;DR

This paper provides a theoretical analysis of how spin splitting affects charge carrier motion in magnetic fields, revealing that Rashba effects can dominate orbit splitting and linking Zitterbewegung oscillations to spin-dependent cyclotron dynamics.

Contribution

It introduces a semiclassical framework that incorporates Zeeman and Rashba effects, explaining experimental magnetic focusing data and highlighting the role of Zitterbewegung in spin-dependent motion.

Findings

Rashba effect can dominate cyclotron orbit splitting even when comparable to Zeeman splitting.

Spin-dependent cyclotron motion is linked to Zitterbewegung-like oscillations.

Analytical formulas accurately describe experimental magnetic focusing data.

Abstract

We present a theoretical study of the interplay between cyclotron motion and spin splitting of charge carriers in solids. While many of our results apply more generally, we focus especially on discussing the Rashba model describing electrons in the conduction band of asymmetric semiconductor heterostructures. Appropriate semiclassical limits are distinguished that describe various situations of experimental interest. Our analytical fomulae, which take full account of Zeeman splitting, are used to analyse recent magnetic-focusing data. Surprisingly, it turns out that the Rashba effect can dominate the splitting of cyclotron orbits even when the Rashba and Zeeman spin-splitting energies are of the same order. We also find that the origin of spin-dependent cyclotron motion can be traced back to Zitterbewegung-like oscillatory dynamics of charge carriers from spin-split bands. The relation between the two phenomena is discussed, and we estimate the effect of Zitterbewegung-related corrections to the charge carriers' canonical position.