Interband Transitions in a Spherical Quantum Layer in the Presence of an Electric Field: Spherical Rotator Model E. M. Kazaryan a , A. A. Kostanyan a , and H. A. Sarkisyan a,b a Russian-Armenian State University, Yerevan, Armenia b Yerevan State University, Yerevan, Armenia Received Febuary 28, 2007 Abstract⎯The interband transitions in a spherical GaAs quantum layer in the presence of an arbitrarily directed electric field are studied theoretically within the framework of the rigid spherical rotator model. The problem is solved under the assumption that the external field is a perturbation. Within the framework of the dipole approximation an expression for the interband absorption coefficient is obtained, and the absorption threshold frequency is determined. The corresponding selection rules are derived. A comparison with the case of quantum transitions in a spherical quantum layer in the presence of a radial electric field is performed. PACS numbers: 78.67. –n DOI: 10.3103/S1068337207040042 Key words: spherical quantum layer, interband transitions 1. INTRODUCTION Theoretical studies of physical properties of nanostructures remain a central preoccupation of physicists because the results of these investigations can find direct applications in semiconductor devices of a new generation. A distinguishing property of semiconductor nanostructures is the possibility to control the energy spectrum of charge carriers contained in them [1]. From the point of view of the size- quantization effects, the most interesting objects are quantum dots (QDs), in which, due to the size quantization in all three directions, the low-dimensional effects are most clearly expressed. By now QDs of different geometrical forms and sizes have been realized and studied theoretically: spherical, cylindrical, pyramidal, lens-shaped, ellipsoidal, etc. (see, e.g., [2–7]). In theoretical description of processes in QDs, a need arises for the correct modeling of the confining potential of a QD. On the one hand, it is necessary to take into account the geometry of a sample under investigation, and on the other hand, to consider the physical–chemical properties of both the QD and surrounding medium. These two factors are of great importance in construction of the corresponding Hamiltonian for the system considered. In this case the QD geometry determines the symmetry of the Hamiltonian, while the physical–chemical characteristics of the QD and surrounding medium form the profile and height of the confining potential. Widely held models of the confining potential of QDs are rectangular wells of finite or infinite height, a parabolic well, the Wood–Saxon potential, etc. [8–10]. As was mentioned above, by varying the form and sizes of QDs, one can control the energy spectrum of one-electron, impurity, exciton, and multielectron states formed in them. For example, considering one-electron states in a spherical QD with a confining potential of finite height, one can show that one- electron levels in such a system are formed, beginning with some threshold value of the QD radius [11]. A more interesting result arises in consideration of impurity states in spherical QDs. So, in [12] it was shown that, if an impurity is in the center of an opaque spherical QD, then the energy of this system may be both negative and positive depending on the QD radius. In other words, a bound Coulomb system in a QD may have also positive values of the energy. Another interesting manifestation of influence of the size quantization on multielectron states is the realization of the Kohn effect in nanostructures with a parabolic confining potential [13], when under certain conditions in multiparticle low-dimensional structures the one-particle transitions are realized. Recently, in connection with the investigation of physical processes in layered structures of different symmetry, a need arose to study the properties of a single layered structure. In particular, optical ISSN 1068-3372, Journal of Contemporary Physics (Armenian Academy of Sciences), 2007, Vol. 42, No. 4, pp. 145–150. © Allerton Press, Inc., 2007. Original Russian Text © E.M. Kazaryan, A.A. Kostanyan, H.A. Sarkisyan, 2007, published in Izvestiya NAN Armenii, Fizika, 2007, Vol. 42, No. 4, pp. 218–226. 145