Magnetic properties of a two-electron quantum dot

TL;DR

This paper investigates the magnetic properties of a two-electron quantum dot, revealing Aharonov-Bohm oscillations in low-energy states and demonstrating that an extended Hubbard model accurately reproduces these effects.

Contribution

The study introduces an extended Hubbard model incorporating Coulomb interactions and Hartree states to accurately describe magnetic oscillations in a two-electron quantum dot.

Findings

Aharonov-Bohm oscillations decrease with increasing magnetic field.

Extended Hubbard model reproduces exact numerical results.

Hopping matrix element's phase and magnitude are crucial for oscillation behavior.

Abstract

The low-energy eigenstates of two interacting electrons in a square quantum dot in a magnetic field are determined by numerical diagonalization. In the strong correlation regime, the low-energy eigenstates show Aharonov-Bohm type oscillations, which decrease in amplitude as the field increases. These oscillations, including the decrease in amplitude, may be reproduced to good accuracy by an extended Hubbard model in a basis of localized one-electron Hartree states. The hopping matrix element, $t$, comprises the usual kinetic energy term plus a term derived from the Coulomb interaction. The latter is essential to get good agreement with exact results. The phase of $t$ gives rise to the usual Peierls factor, related to the flux through a square defined by the peaks of the Hartree wavefunctions. The magnitude of $t$ decreases slowly with magnetic field as the Hartree functions become more localized, giving rise to the decreasing amplitude of the Aharonov-Bohm oscillations.