Semiclassical Landau quantization of spin-orbit coupled systems

TL;DR

This paper develops a semiclassical quantization method for Landau levels in spin-orbit coupled systems, incorporating a matrix phase to describe spin dynamics, and compares it with exact solutions.

Contribution

It generalizes the Onsager quantization condition to include spin-orbit interactions using a matrix-valued phase, enabling better understanding of spin effects in Landau quantization.

Findings

Derived a matrix-valued phase for spin dynamics in Landau levels

Proposed experimental methods to measure the matrix phase

Validated the semiclassical spectrum against exact solutions

Abstract

A semiclassical quantization condition is derived for Landau levels in general spin-orbit coupled systems. This generalizes the Onsager quantization condition via a matrix-valued phase which describes spin dynamics along the classical cyclotron trajectory. We discuss measurement of the matrix phase via magnetic oscillations and electron spin resonance, which may be used to probe the spin structure of the precessing wavefunction. We compare the resulting semiclassical spectrum with exact results which are obtained for a variety of spin-orbit interactions in 2D systems.