A Simple Shell Model for Quantum Dots in a Tilted Magnetic Field

TL;DR

This paper introduces a simple theoretical model for quantum dots subjected to tilted magnetic fields, analyzing their energy spectrum, wave functions, and shape dependence on various parameters.

Contribution

It presents a novel shell model for quantum dots in arbitrary magnetic field directions, incorporating classical solutions to determine quantum properties.

Findings

Spectrum and wave functions derived analytically.

Quantum dot shape depends on electron number and magnetic field.

Model predicts equilibrium shape variations with magnetic field orientation.

Abstract

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.