A spatially indirect exciton in vertically coupled quantum dots: 1/Q-expansion

• Published in: Laser physics letters 2004-03, Vol.1 (3), p.154-160
• Main Authors: Lozovik, Yu. E., Mur, V. D., Narozhny, N. B., Petrosyan, A. N.
• Format: Article
• Language: English
• Subjects: 1/Q-expansion; exciton; Padé approximation; quantum dot
• ISSN: 1612-2011; 1612-202X
• DOI: 10.1002/lapl.200310040

A spatially indirect exciton in vertically coupled quantum dots is considered with the use of 1/Q‐expansion, where Q is the dimensionless quantum parameter determined by the ratio of characteristic Coulomb energy of electron‐hole interaction to the energy of one‐particle transition in a confining potential. Analytical expressions for the energies and the wave functions are derived. They are asymptotically exact when Q ≫ 1 and the parameter of separation of quantum dots d is much larger than the size of a direct exciton a*B. It is shown, however, that even the first four terms in the 1/Q‐expansion provide one percent accuracy for the energies of relative motion in the ground and the first excited states of the exciton for Q ≳ 2 and d ≳ a*B. It is also shown that the Padé summation of the first four terms in the 1/Q‐expansion provides accuracy no worse than 5% even for Q ∼ 0.2. We use the perturbation theory with respect to Coulomb interaction to calculate the energies for smaller values of Q and thus obtain analytical expressions for them in the whole range of variation of the parameter Q. (© 2004 by HMS Consultants. Inc. Published exclusively by WILEY‐VCH Verlag GmbH & Co.KGaA)