Semiclassical Time Evolution of the Holes from Luttinger Hamiltonian

TL;DR

This paper investigates the semi-classical dynamics of holes in the Luttinger model, revealing oscillatory behaviors similar to relativistic Zitterbewegung and discussing helicity conservation issues.

Contribution

It provides a numerical analysis of hole trajectories that align with advanced adiabatic theories, highlighting oscillations and helicity non-conservation.

Findings

Trajectories match higher-order adiabatic corrections

Holes exhibit Zitterbewegung-like oscillations

Helicity of light holes is not conserved

Abstract

We study the semi-classical motion of holes by exact numerical solution of the Luttinger model. The trajectories obtained for the heavy and light holes agree well with the higher order corrections to the abelian and the non-abelian adiabatic theories in Ref. [1] [S. Murakami et al., Science 301, 1378(2003)], respectively. It is found that the hole trajectories contain rapid oscillations reminiscent of the "Zitterbewegung" of relativistic electrons. We also comment on the non-conservation of helicity of the light holes.