Orbital Magnetism in Three-Dimensional Quantum Dots

TL;DR

This paper investigates the orbital magnetism of 3D quantum dots with parabolic confinement, revealing distinct magnetic behaviors across temperature and magnetic field regimes, and highlighting differences from 2D quantum dots.

Contribution

It provides a comprehensive analysis of magnetic properties in 3D quantum dots, including numerical calculations and classification of magnetization behaviors, which were not previously detailed.

Findings

Identification of three magnetic regimes: Landau diamagnetism, de Haas-van Alphen oscillation, mesoscopic fluctuation.

Longer oscillation periods in 3D quantum dots compared to 2D counterparts.

Large paramagnetism at low temperatures and weak magnetic fields.

Abstract

We study orbital magnetism in a three-dimensional (3D) quantum dot with a parabolic confining potential. We calculate the free energy of the system as a function of the magnetic field and the temperature. By this, we show that the temperature-field plane can be classified into three regions in terms of the characteristic behavior of the magnetization: the Landau diamagnetism, de Haas-van Alphen oscillation and mesoscopic fluctuation of magnetization. We also calculate numerically the magnetization of the system and then the current density distribution. As for the oscillation of the magnetization when the field is varied, the 3D quantum dot shows a longer period than a 2D quantum dot which contains the same number of electrons. A large paramagnetism appears at low temperatures when the magnetic field is very weak.