Hidden symmetry and excitonic transitions in the quantum well

✍ Scribed by E.M. Kazaryan; L.S. Petrosyan; H.A. Sarkisyan

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 184 KB
• Volume: 40
• Category: Article
• ISSN: 1386-9477
• DOI: 10.1016/j.physe.2007.08.013

✦ Synopsis

In this article it is shown that, Sommerfeld's coefficients for excitonic transitions in quantum wells are determined only with the principle quantum number within the framework of two-dimensional Coulomb potential. This is a consequence of hidden symmetry of two-dimensional Coulomb problem, conditioned by the existence of two-dimensional analog of the Runge-Lentz vector. For the narrow gap semiconductor quantum well with the non-parabolic dispersion law of electron and hole in the two-band Kane model it is shown that two-dimensional excitonic states are described in the frames of an analog of Klein-Gordon equation with the two-dimensional Coulomb potential. The non-stability of the ground state of the two-dimensional Kane's exciton is shown.