This article discusses specific quantum transitions in a few-particle hole gas, localized in a strongly oblate lens-shaped quantum dot. Based on the adiabatic method, the possibility of realizing the generalized Kohn theorem in such a system is shown. The criteria for the implementation of this theorem in a lens-shaped quantum dot, fulfilled in the experiment, is presented. An analytical expression is obtained for the frequencies of resonant absorption of far-infrared radiation by a gas of heavy holes, which depends on the geometric parameters of the quantum dot. The results of experiments on far-infrared absorption in the arrays of p-doped Ge/Si quantum dots grown by molecular beam epitaxy (MBE) with gradually increasing average number of holes in dot are presented. Experimental results show that the Coulomb interaction between the holes does not affect the resonant frequency of the transitions. A good agreement between the theoretical and experimental results is shown.

Interband transitions in a narrow-gap InSb cylindrical quantum dot (QD) have been theoretically studied in the regime of strong dimensional quantization with allowance for a nonparabolic dispersion of electrons and light holes. The corresponding absorption coefficients and threshold frequencies for a QD array are calculated within the framework of a two-band Kane model for electrons and light holes and a parabolic dispersion law for heavy holes. These threshold frequencies fall in the IR range. Quantitative calculations are performed using the recent data of Moiseev et al. [1] on the growth of InSb quantum dots by liquid phase epitaxy.