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Semiclassical analysis of a two-electron quantum dot in a magnetic field: Dimensional phenomena

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Nazmitdinov,  R. G.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Rost,  J. M.
Division Prof. Dr. Joachim H. Ullrich, MPI for Nuclear Physics, Max Planck Society;
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Nazmitdinov, R. G., Simonovič, N. S., & Rost, J. M. (2002). Semiclassical analysis of a two-electron quantum dot in a magnetic field: Dimensional phenomena. Physical Review B, 65(15): 155307. Retrieved from http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRBMDO000065000015155307000001&idtype=cvips&gifs=yes.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-37AE-B
Abstract
It is shown that with the inclusion of the vertical extension of a quantum dot the experimental findings of Ashoori [Phys. Rev. Lett. 71, 613 (1993)] can be modeled consistently with a parabolic confinement. Furthermore, the magnetic properties such as the magnetic moment and the susceptibility are sensitive to the presence and strength of a vertical confinement. Using a semiclassical approach the calculation of the eigenvalues reduces to simple quadratures providing a transparent and almost analytical quantization of the three- dimensional quantum dot energy levels that differ from the exact energies only by a few percent. While the dynamics for three-dimensional axially symmetric two-electron quantum dot with parabolic confinement potentials is in general nonseparable due to the Coulomb interaction we have found an exact separability for specific values of the magnetic field.