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

Dvoyan KG, Matinyan SG, Vlahovic B - Nanoscale Res Lett (2013)

Bottom Line: 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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Mathematics and Physics, North Carolina Central University, 1801 Fayetteville St,, Durham, NC 27707, USA. kdvoyan@nccu.edu.

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.

No MeSH data available.


Related in: MedlinePlus

Dependences of ground-state energies on a QD radius. They are for the Ps in weak SQ regime and for separately quantized electron and positron in strong SQ regime.
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Figure 5: Dependences of ground-state energies on a QD radius. They are for the Ps in weak SQ regime and for separately quantized electron and positron in strong SQ regime.

Mentions: Finally, Figure 5 represents the comparative dependences of ground-state energies on the QD radius in two QS regimes simultaneously: for Ps in weak SQ regime and for separately quantized electron and positron in strong SQ regime. As shown in the figure, the obtained energy of the coupled electron-positron pair - a positronium - is much smaller than the energy of separately quantized particles. Note that the jump between the energy curves corresponding to strong and weak SQ regimes is precisely conditioned by the formation of Ps atom. This is the criterion of the formation of a Ps as a whole at the particular value of the QD radius. It is seen from the figure that in the case of Kane’s dispersion law, the jump of the energy is significantly greater than that in the parabolic case. In other words, more energy is emitted at the formation of a Ps in a QD. Consequently, the binding energy of the Ps is much higher than in the case of parabolic dispersion law. As it was noted above, this is a consequence of the Coulomb quantization enhancement due to the interaction of bands.


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

Dvoyan KG, Matinyan SG, Vlahovic B - Nanoscale Res Lett (2013)

Dependences of ground-state energies on a QD radius. They are for the Ps in weak SQ regime and for separately quantized electron and positron in strong SQ regime.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3716990&req=5

Figure 5: Dependences of ground-state energies on a QD radius. They are for the Ps in weak SQ regime and for separately quantized electron and positron in strong SQ regime.
Mentions: Finally, Figure 5 represents the comparative dependences of ground-state energies on the QD radius in two QS regimes simultaneously: for Ps in weak SQ regime and for separately quantized electron and positron in strong SQ regime. As shown in the figure, the obtained energy of the coupled electron-positron pair - a positronium - is much smaller than the energy of separately quantized particles. Note that the jump between the energy curves corresponding to strong and weak SQ regimes is precisely conditioned by the formation of Ps atom. This is the criterion of the formation of a Ps as a whole at the particular value of the QD radius. It is seen from the figure that in the case of Kane’s dispersion law, the jump of the energy is significantly greater than that in the parabolic case. In other words, more energy is emitted at the formation of a Ps in a QD. Consequently, the binding energy of the Ps is much higher than in the case of parabolic dispersion law. As it was noted above, this is a consequence of the Coulomb quantization enhancement due to the interaction of bands.

Bottom Line: 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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Mathematics and Physics, North Carolina Central University, 1801 Fayetteville St,, Durham, NC 27707, USA. kdvoyan@nccu.edu.

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.

No MeSH data available.


Related in: MedlinePlus