Spin-orbit coupling in a Quantum Dot at high magnetic field

TL;DR

This paper investigates how spin-orbit coupling and high magnetic fields influence the electronic states and spin textures in a disk-shaped quantum dot, revealing symmetry breaking and state hierarchy dependencies on quantum dot size.

Contribution

It demonstrates the interplay of magnetic field, spin-orbit coupling, and electron interactions in quantum dots, highlighting symmetry breaking and state hierarchy variations with size.

Findings

Symmetry breaking observed via level splitting due to Rashba spin-orbit coupling.

Hierarchy of multiplet states depends on quantum dot size.

Spin texture results from combined Rashba effect and electron interactions.

Abstract

We describe the simultaneous effects of the spin-orbit (SO) perturbation and a magnetic field $B$ on a disk shaped quantum dot (QD). {As it is known the} combination of electrostatic forces among the $N$ electrons confined in the QD and the Pauli principle can induce a spin polarization when $B$ (applied in the direction orthogonal to the QD) is above a threshold value. In the presence of an electric field parallel to $B$, coupled to the spin $ S $ by a Rashba term, we demonstrate that a symmetry breaking takes place: we can observe it by analyzing the splitting of the levels belonging to an unperturbed multiplet. We also discuss the competitive effects of the magnetic field, the SO perturbation and the electron electron interaction, in order to define the hierarchy of the states belonging to a multiplet. We demonstrate how this hierarchy depends on the QD's size. We show the spin texture due to the combined effects of the Rashba effect and the interaction responsible for the polarization.