Quaternionic vector coherent states for spin-orbit interactions

TL;DR

This paper develops quaternionic vector coherent states for a 2D electron gas with spin-orbit interactions, providing exact solutions for Landau levels and exploring quaternionic properties related to the Weyl-Heisenberg group.

Contribution

It introduces a novel construction of quaternionic vector coherent states for systems with Rashba and Dresselhaus spin-orbit interactions, offering exact eigenstates and Landau levels.

Findings

Exact analytical expressions for Landau levels and eigenstates.

Construction of quaternionic vector coherent states.

Discussion of quaternionic properties and Weyl-Heisenberg group similarity.

Abstract

This work addresses the study of two-dimensional electron gas in a perpendicular magnetic field in the presence of both Rashba and Dresselhaus spin-orbit (SO) interactions, with effective Zeeman coupling. Exact analytical expressions are found for the eigenvalue problem giving the Landau levels and the associated eigenstates, thanks to an appropriate method of parametrization used to quantize the physical system. Such a system exhibits interesting properties of quaternions for which vector coherent states are built. Similarity with the Weyl-Heisenberg group and some relevant properties of these vectors are discussed.