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Journal Electromagnetic Waves and Electronic Systems №6 for 2014 г.
Article in number:
Localization via magnetic field one-electron states near quantum dots of fractional dimension
Keywords: quantum dot &#948 well localized one-electron states
Authors:
A.M. Mandel - Ph. D. (Phys.-Math.), Professor, Department of Physics, MSTU «STANKIN» (Moscow). E-mail: arkadimandel@mail.ru
V.B. Oshurko - Dr. Sc. (Phys.-Math.), Head of Department of Physics, MSTU «STANKIN» (Moscow). E-mail: vbo08@yandex.ru
G.I. Solomakho - Ph. D. (Phys.-Math.), Professor, Department of Physics, MSTU «STANKIN» (Moscow). E-mail: solgeo@yandex.ru
Abstract:
The system of quantum dots on the surface of a solid has been considered. Quantum dot parameters (size and material) has been chosen in such a way that the internal energy levels and localized states were absent. However, the external magnetic field could create the localized electron states in the vicinity of the quantum dots. The typical size of the electron cloud in this state has been ~ 180−60 nm at the magnetic field B = (0.1−1.0) T. The energy of this state has been approximately equal to (0.00003−0.0003) eV. The usual depth of the potential well created by the quantum dot is a few eV. Therefore, when the size of the quantum dot is a few nm, we could consider it infinitely small and infinitely deep (δ well). Schrödinger equation has been solved with a 3D δ potential and potential of the magnetic field in the strong coupling limit, that is for non-interacting quantum dots. We have obtained the wave functions and energy of these states. Electron spin-variable has been taken into account. The wave functions have been expressed through the integrals on the dimensionless time. For them, the analytical approximation has been obtained to facilitate qualitative analysis of solution. The binding energy is proportional to the magnetic field. This allows to adjust the size of the electron cloud in a very wide range. The latter factor would give possibility to control the degree of overlap of the electron clouds of neighboring quantum dots and thus the degree of entanglement of their quantum states. The solution of the Schrödinger equation is generalized to the δ well of fractional dimension. It would allow us to explore the non-trivial fractal properties of quantum dots and created cluster structures in future. We have established that the described states always have an induced magnetic moment in the external magnetic field. It is produced by the probability current generating the electrical current on the surface of solid around the quantum dots. The analytic dependency of this current from the external magnetic field and the value of electron spin-variable have been detected on the base of the calculated electron wave functions. The magnetic moment interacts with the source of the external magnetic field. It could be, for example, the magnetic sensor of an atomic force microscope. As a result, the forces of interaction (attraction-repulsion) between the probe and the quantum dot depending on the electron spin orientation have been arisen. The measurement of these forces theoretically would allow us to detect the value of the spin-variable electronic state associated with a given quantum dot.
Pages: 67-73
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