Effective numerical algorithm for calculating binding energies of 2D quantum dots in external fields

Koval E.A.1, Koval O.A.

Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, 141980, Russia,,

1Department of Fundamental Problems of Microworld Physics, University “Dubna”, Dubna, 141980, Russia

The main aim of this work was developing of the effective algorithm for numerical calculation of the binding energies and corresponding electron densities of a two-dimensional (2D) Quantum Dots (QD) in tilted magnetic and electric fields. The special expansion of the 2D wave function is based on the idea of the paper [1].

Most of the papers of other authors (see the review [2]) are devoted to the external field that are perpendicular to the electron motion plane. Tilt of the magnetic field direction lead to the strong anisotropy of the effective interaction. We study the model of 2D QD in the presence of the hydrogenic impurity in the arbitrarily oriented magnetic and electric field.

Investigations of the properties of quantum dots in external fields have been performing for a long time and stay highly relevant nowadays due to numerous technological applications, such as possible applications in quantum computation [3], quantum cryptography [4], in room-temperature quantum-dot lasers, and so on [5].

As the result of the verification of the developed algorithm we have calculated the energy spectrum, dipole moments and mean radius of the 2D Hydrogen atom and 2D exciton without confinement potential. We also reproduce some results of the paper [7] for the 2D QD in the presence of hydrogenic impurity in the magnetic field, perpendicular to the XY plane of electron motion.

The advantages of the numerical algorithm are also discussed.

This work was supported by the Russian Foundation for Basic Research, Grant No.16-32-00865.


1. V. S. Melezhik, Journal of Computational Physics 92, 67 (1991).

2. R. Nazmitdinov, Physics of Particles and Nuclei 40, 71 (2009).

3. D. Loss, Phys. Rev. A 57, 120 (1998).

4. S. Molotkov, S. Nazin, Journal of Experimental and Theoretical Physics Letters 63, 687 (1996).

5. T. Chakraborty, Quantum Dots: A survey of the properties of artificial atoms (Elsevier, 1999).

6. E. A. Koval, O. A. Koval, Physica E 93, 160 (2017).

7. G. Rezaei, S. S. Kish, Physica E: Low-dimensional Systems and Nanostructures 45, 56 (2012).

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