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

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.

Spontaneous Exciton Collapse in a Strongly Flattened Ellipsoidal InSb Quantum Dot

“…An important feature of the implementation of this regime is the ability to cover new energy areas for the purposes one pursues, in particular, negative energies. As can be seen from result (38), in the parabolic dispersion law case, the energy conditioned by quantum confinement of the QD walls is positive, and the Coulomb energy is negative. With a change in the geometric parameters of the QD, the total energy can change sign.…”

“…Moreover, the Coulomb energy in the Kane’s model case has an explicit dependence on the radial and orbital QNs. The interband interaction in the case of the two-band model violates the high order of hidden symmetry of the Coulomb interaction due to the imposition of lower order symmetry [ 38 ]. Obviously, this cannot be a consequence of the imposition of the ellipsoidal symmetry of the QD itself, since the hidden symmetry is not violated in the case of the parabolic dispersion law.…”