Abstract
In this paper, the behavior of a heavy hole gas in a strongly prolate ellipsoidal Ge/Si quantum dot has been investigated. Due to the specific geometry of the quantum dot, the interaction between holes is considered one-dimensional. Based on the adiabatic approximation, it is shown that in the z-direction, hole gas is localized in a one-dimensional parabolic well. By modeling the potential of pair interaction between holes in the framework of oscillatory law, the problem is reduced to a one-dimensional, analytically solvable Moshinsky model. The exact energy spectrum of the few-hole gas has been calculated. A detailed analysis of the energy spectrum is presented. The character of long-wave transitions between the center-of-mass levels of the system has been obtained when Kohn theorem is realized.
Highlights
The investigation of few-particle states in quantum dots (QDs) has academic and applied significances [1,2,3]
The realization of the Kohn theorem has been shown for the prolate ellipsoidal Ge/Si quantum dot
The long-wave absorption is considered by the few-hole gas
Summary
The investigation of few-particle states in quantum dots (QDs) has academic and applied significances [1,2,3]. Authors have considered a pair-interacting electron gas localized in two-dimensional symmetric parabolic QDs, in the presence of an axial magnetic field. It can be assumed that in such systems, the generalized Kohn theorem can be implemented This problem for the case of an electron gas localized in strongly oblate or prolate ellipsoidal QDs has been discussed [31,32,33,34]. The goal of this paper is analytical investigation of pair-interacting hole gas in a strongly prolate ellipsoidal QD, and demonstration of the realization of generalized Kohn’s theorem in such a Nsatnroumcattuerriaels.
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