Two-electron quantum dot in a magnetic field: Analytic solution for finite potential model

TL;DR

This paper derives an analytical solution for the energy spectrum of two interacting electrons in a finite Gaussian potential quantum dot under a magnetic field, providing insights into state transitions and matching experimental data.

Contribution

It presents an analytic solution for the two-electron energy spectrum in a finite potential quantum dot under magnetic field, extending previous models with infinite potentials.

Findings

Calculated magnetic field for spin-state transition matches experimental data

Derived energy levels for two-electron system in finite potential

Compared ground state energies with experimental results

Abstract

The energy levels of two interacting electrons in a 2D quantum dot confined by a finite Gaussian potential and subjected to a uniform magnetic field perpendicular to the plane of the dot are studied. Analytic results are obtained for the energy spectrum of the two-electron system as well as for a single electron. The magnetic field at which the ground state transitions from the spin-singlet to the spin-triplet state for the two-electron system is calculated and compared with the experimental data and previous theoretical results for the infinite harmonic confining potential. The ground state energy of the two-electron system as a function of the magnetic field is calculated and compared with the experimental data.