Realization of the Kohn’s Theorem in Ge/Si Quantum Dots with Hole Gas: Theory and Experiment

Abstract

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.

Long-wave Absorption of Few-Hole Gas in Prolate Ellipsoidal Ge/Si Quantum Dot: Implementation of Analytically Solvable Moshinsky Model

“…The specific geometry of the studied QD gives the conditions necessary for realization of the generalized Kohn’s theorem. In this point of view, we can note that in [ 36 ], the fulfillment of Kohn’s theorem for hole gas in a lens-shape Ge/Si QD was shown experimentally as well as theoretically. The necessary criterion for the fulfillment of this theorem is the pair-interaction model, which depends only on the interparticle distance.…”

“…This problem for the case of an electron gas localized in strongly oblate or prolate ellipsoidal QDs has been discussed [ 31 , 32 , 33 , 34 ]. Alternatively, in papers [ 35 , 36 ], results on absorption from a hole gas localized in a strongly flattened Ge/Si lens-shaped QD have been presented. Theoretically defined values of resonant frequencies gave a good match with the experimental result.…”

Effects of an External Magnetic Field on the Interband and Intraband Optical Properties of an Asymmetric Biconvex Lens-Shaped Quantum Dot

“…Along the axial direction, the particle is localized in the one-dimensional quantum well with following boundaries [ 5 , 34 ] …”

“…Recent papers [ 5 , 6 , 7 ] reported the realization of GeSi quantum dots (QDs) with a strongly oblate lens-shaped geometry. In particular, the morphology of the structures was determined, and the specific optical characteristics of such QDs were revealed.…”

Исследование Изменения Линейного И Нелинейного Показателей Преломления В Эллипсоидальной Квантовой Точке, Обусловленное Биэкситоном

“…Такие КТ имеют широкое применение в тех случаях, когда необходимо управлять энергией в широком диапазоне, а это возможно сделать с помощью двух геометрических параметров эллипсоида (малая и большая полуоси). Стоит особо подчеркнуть тот факт, что теорема Кона реализуется в эллипсоидальных КТ как теоретически, так и экспериментально [26,27]. Таким образом, теоретическое исследование нелинейных свойств биэкситонных комплексов в основном и возбужденном состояниях в эллипсоидальных КТ является актуальной задачей.…”