A.M. Mandel1, V.B. Oshurko2, S.G. Veselko3, K.G. Solomakho4, A.A. Sharts5

1–5 Moscow State University of Technology «STANKIN» (Moscow, Russia)

2 Prokhorov General Physics Institute of the Russian Academy of Sciences (Moscow, Russia)

1 arkadimandel@mail.ru

The problem of calculating the energy spectrum of electrons localized on a thin quantum ring (more precisely, on a quantum puck) in a magnetic field was considered.  The solution of the problem depends fundamentally on the adequate choice of the confining radial potential. The vast majority of authors use a potential with confinement for electrons. This completely masks the unique selection properties of quantum rings. Based on these properties, it is possible to control the parameters of an persistent current and the states of individual electrons localized on the ring by a magnetic field.

The specificity and novelty of the problem is determined by the presence of two interfaces on the inner and outer radius of the ring. This leads to two different (and difficult to reconcile) conditions for the continuity of the logarithmic derivative of the wave function at these interfaces. It is desirable to obtain simple analytical expressions for the wave function, ring parameters and persistent currents for a clear qualitative picture.

It has been shown that a thin quantum ring (with an adequate choice of radial confinement potential) has unique selection properties. They are due to two conditions for the continuity of the logarithmic derivative of the radial wave function. The combination of these properties with the geometry of the ring reduces its energy spectrum to a single electron energy level. This is con-firmed both by exact solutions of the Schrödinger equations and by simple analytical estimates that give a clear qualitative picture. For arbitrarily chosen radii of the ring, its spectrum is, as a rule, empty due to the inconsistency of the boundary conditions. Only a magnetic field of a strictly defined strength creates a stable electronic level in the ring, and all its quantum numbers are uniquely determined by the parameters of the ring and the external magnetic field. Thus, it becomes theoretically possible to create states of electrons (and the associated persistent current) with pre-planned quantum numbers using a magnetic field.

Mandel A.M., Oshurko V.B., Veselko S.G., Solomakho K.G., Sharts A.A. Quantum rings in a magnetic field: selection rules, quantization of persistent current and possibility to control the state of the electron. Achievements of modern radioelectronics. 2024. V. 78. № 10. P. 23–35. DOI: https://doi.org/10.18127/j20700784-202410-04 [in Russian]

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