Construction of the trial wave function of the X--trion in the retarding potential of a quantum dot in a constant magnetic field

Abstract

In this article we consider one of the types of quasiparticles in electron-hole plasma that takes place in semiconductors, bound state of two electrons and hole - it is a negatively charged X^--trion. It is hypothesized that two-dimensional trions formed in semiconductor heterolayers are more stable formations than three-dimensional trions, that's why the two-dimensional trions are investigated in the article. For such trions a Hamiltonian is drawn that describes a system of two electrons and hole captured by the oscillator potential of quantum dot. The oscillatory potential that captures quasiparticles is a stabilizing factor that keeps trions from decay, which makes it possible to observe the trions at sufficiently high temperatures. As additional stabilizing factor we took constant uniform magnetic field directed perpendicular to heterolayer that contains the quantum dot. It is shown that the presence of magnetic field results to change in parameters of the oscillator potential. The interaction of electrons and holes is described with the help of the Coulomb potential. A trial wave function of the X^--trion is obtained in neglecting of spin-orbit interaction for all quasiparticles and exchange interaction between electrons (the Hartree approximation). Quantum numbers characterizing the orbital motion of individual quasiparticles constituting the trion are introduced. The energies of individual quasiparticles constituting the trion are calculated. A method for calculating the binding energy of trion is discussed. The proposed method of calculation can be used to calculate the energy characteristics of positively charged X⁺-trion. The formation of quasiparticles complexes like trions during capture of electrons and holes by quantum dots must also take place for impurity ions, which will affect the spectrum of absorption and luminescence of semiconductors which contain impurity ions. As a result of this, we postulate that in calculation of spectroscopic properties of impurity ions, it is not enough to take into account only the effects of covalent bonding between atoms in semiconductor structures, it is also necessary to take into account the effects of capture of trions and other more complex quasiparticles formations.