Open Access Nano Express

Theory of confined states of positronium in spherical and circular quantum dots with Kane’s dispersion law

Karen G Dvoyan*, Sergey G Matinyan and Branislav Vlahovic

Author affiliations

Department of Mathematics and Physics, North Carolina Central University, 1801 Fayetteville St., Durham, NC 27707, USA

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Citation and License

Nanoscale Research Letters 2013, 8:311  doi:10.1186/1556-276X-8-311

Published: 4 July 2013

Abstract

Confined states of a positronium (Ps) in the spherical and circular quantum dots (QDs) are theoretically investigated in two size quantization regimes: strong and weak. Two-band approximation of Kane’s dispersion law and parabolic dispersion law of charge carriers are considered. It is shown that electron-positron pair instability is a consequence of dimensionality reduction, not of the size quantization. The binding energies for the Ps in circular and spherical QDs are calculated. The Ps formation dependence on the QD radius is studied.

Keywords:
Quantum dot; Positron; Positronium; Narrow-gap semiconductors; Klein-Gordon equation; Kane’s dispersion law; Size quantization; Binding energy