On the Possibility of Implementation of Kohn’s Theorem in the Case of Ellipsoidal Quantum Dots D. B. Hayrapetyan a,b , E. M. Kazaryan a , and H. A. Sarkisyan a,c a Russian–Armenian (Slavonic) University, Yerevan, Armenia b State Engineering University of Armenia, Yerevan, Armenia c Yerevan State University, Yerevan, Armenia Received July 23, 2012 Abstract⎯An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional, coupled. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the dot in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system. DOI: 10.3103/S1068337213010052 Keywords: ellipsoidal quantum dots, Kohn’s theorem, geometrical adiabaticity 1. INTRODUCTION Quantum dots (QDs) are in many respects similar to atoms and often exhibit properties which are inherent in atoms. Therefore a unique possibility is created for adaptation of a number of quantum-mechanical problems of atomic physics to the case of semiconductor QDs of various sizes and geometrical shapes. A prominent example of transfer of phraseology, inherent in atomic physics, to the case of QDs in the classification of one-electron states in spherically symmetric QDs by the values of orbital numbers (s-states, p-states, etc.) [1]. This circumstance essentially simplifies a theoretical description of many physical properties of QDs beginning with optical and ending with current properties [2]. At the same time, theoretical study of many-particle and few-particle systems in QDs also is a subject of the keen interest of researchers, because the obtained results can be used in design of new-generation semiconductor devices. The simplest zero-dimensional complex, containing several particles, is a QD with two electrons – “artificial helium atom” [3–7]. As calculations show, known description method of helium-like atoms may be well applied to describe the properties of two-electron systems in QDs. The latters possess important advantages: in “artificial helium atoms” electron states can be manipulated by means of variation of both sizes and geometrical shapes of QDs [8, 9]. In the case of many electrons one can successfully employ, from the one hand, the Hartry–Fock method and, from the other hand, the Thomas–Fermi approximation [10–12]. One of the most interesting many-particle effects in QDs is a realization of quantum transitions characteristic for one-particle systems (Kohn’s theorem) in pairwise interacting electron gas [13, 14]. This theorem was initially formulated for electron gas in a magnetic field [15]. Due to the presence of the field the electron gas is localized in a parabolic well. Further, after realization of QDs with the parabolic confining potential it was succeeded to localize the electron gas without use of the magnetic field, owing to the oscillatory potential of QD wells (generalized Kohn’s theorem). In the case of electron gas with the pair interaction the parabolic shape of confining potential allows one to separate the center-of-mass motion from a relative one and, thus, to realize the conditions for fulfillment of Kohn’s theorem. Formation of the parabolic profile of the confining potential of QD can be caused, for instance, by interdiffusion of QD’s components and its environment [16–18]. At the same time, in a number of works it was shown [19, 20] that the condition for arising the parabolic potential of confinement of QD walls can be also realized in QDs with strongly oblated and strongly prolated ellipsoidal symmetries. ISSN 1068–3372, Journal of Contemporary Physics (Armenian Academy of Sciences), 2013, Vol. 48, No. 1, pp. 32–36. © Allerton Press, Inc., 2013. Original Russian Text © D.B. Hayrapetyan, E.M. Kazaryan, H.A. Sarkisyan, 2013, published in Izvestiya NAN Armenii, Fizika, 2013, Vol. 48, No. 1, pp. 48–54. 32