Two-dimensional electrons, holes, magnetoexcitons, and cavity polaritons under the action of strong perpendicular magnetic and electric fields

Abstract

The review is focused on the energy spectrum of two-dimensional electrons, holes, magnetoexcitons, and cavity polaritons under the action of strong magnetic and electric fields perpendicular to the surface of GaAs-type quantum wells (QWs) with a p-type valence band embedded into resonators. As the first step in this direction, the Landau quantization (LQ) of electrons and heavy holes (hhs) has been studied taking into account the Rashba spin-orbit coupling (RSOC) with third-order chirality terms for hhs and nonparabolicity terms in their dispersion law, including the Zeeman splitting (ZS) effects. The nonparabolicity terms proportional to the electric field strength have been introduced to avoid the collapse of the semiconductor energy gap under the action of the third-order chirality terms. Exact solutions for the eigenfunctions and eigenenergies for the LQ task have been obtained on the basis of the Rashba method [1]. In the next steps of our review paper, we have deduced Hamiltonians describing the Coulomb electron–electron and electron–radiation interactions in the second quantization representation. They make it possible to determine the magnetoexciton energy branches and deduce the Hamiltonian of the magnetoexciton–photon interaction. The fifth-order dispersion equation describing the energy spectrum of the cavity magnetoexciton–polaritons has been studied. It takes into account the interaction of the cavity photons with two dipole-active and two quadrupole-active 2D magnetoexciton energy branches. The cavity photons have circular polarizations k s ± oriented along their wave vectors k with quantized longitudinal components kz = ±p Lc , where c L is the resonator length, and with small transverse components || k oriented in the plane of the QW. The 2D magnetoexcitons are characterized by in-plane wave vectors || k and circular polarizations M s arising in the p-type valence band with magnetic momentum projection M = ±1 in the direction of the magnetic field. The selection rules of the exciton– photon interaction have two origins. One of them, of geometrical type, is expressed in terms of the scalar products of the two types of circular polarizations. They depend on in-plane wave vectors || k even in the case of dipole-active transitions, because the cavity photons have an oblique incidence to the surface of the QW. The other origin is related with numbers e n and h n of the LQ levels of electrons and hhs involved in the magnetoexciton formation. Thus, the dipole-active transitions take place under condition , e h n = n whereas in the quadrupole-active transitions the relationship is as follows: 1. e h n = n ± The optical gyrotropy effects appear changing the sign of the photon circular polarization at a given sign of wave vector longitudinal projection z k or equivalently changing the sign of longitudinal projection z k at the same selected circular polarization of light.