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Magnetic properties of a two-electron quantum dot

C. E. Creffield·J. H. Jefferson·S. Sarkar·D. L. Tipton
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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.

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C. E. Creffield, J. H. Jefferson, S. Sarkar, D. L. Tipton. 1999-12-23. Magnetic properties of a two-electron quantum dot. https://arxiv.org/abs/cond-mat/9912428

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