Eur. Phys. J. B (2015) 88: 218
https://doi.org/10.1140/epjb/e2015-60335-7

Regular Article

Effects of Rashba spin-orbit coupling, Zeeman splitting and gyrotropy in two-dimensional cavity polaritons under the influence of the Landau quantization

¹ Institute of Applied Physics of the Academy of Sciences of Moldova, Academic Str. 5, Chisinau, MD2028, Republic of Moldova
² Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden

^a e-mail: dum@phys.asm.md

Received: 28 April 2015
Received in final form: 17 July 2015
Published online: 7 September 2015

Abstract

We consider the energy spectrum of the two-dimensional cavity polaritons under the influence of a strong magnetic and electric fields perpendicular to the surface of the GaAs-type quantum wells (QWs) with p-type valence band embedded into the resonators. As the first step in this direction the Landau quantization (LQ) of the electrons and heavy-holes (hh) was investigated taking into account the Rashba spin-orbit coupling (RSOC) with third-order chirality terms for hh and with nonparabolicity terms in their dispersion low including as well the Zeeman splitting (ZS) effects. The nonparabolicity term is proportional to the strength of the electric field and was introduced to avoid the collapse of the semiconductor energy gap under the influence of the third order chirality terms. The exact solutions for the eigenfunctions and eigenenergies were obtained using the Rashba method [E.I. Rashba, Fiz. Tverd. Tela 2, 1224 (1960) [Sov. Phys. Solid State 2, 1109 (1960)]]. On the second step we derive in the second quantization representation the Hamiltonians describing the Coulomb electron-electron and the electron-radiation interactions. This allow us to determine the magnetoexciton energy branches and to deduce the Hamiltonian of the magnetoexciton-photon interaction. On the third step the fifth order dispersion equation describing the energy spectrum of the cavity magnetoexciton-polariton is investigated. It takes into account the interaction of the cavity photons with two dipole-active and with two quadrupole-active 2D magnetoexciton energy branches. The cavity photons have the circular polarizations σ^±_k oriented along their wave vectors k, which has the quantized longitudinal component k_z = ± π/L_c, where L_c is the resonator length and another small transverse component k_∥ oriented in the plane of the QW. The 2D magnetoexcitons are characterized by the in-plane wave vectors k_∥ and by circular polarizations σ_M arising in the p-type valence band with magnetic momentum projection M = ± 1 on the direction of the magnetic field. The selection rules of the exciton-photon interaction have two origins. The first one, of geometrical-type, is expressed through the scalar products of the two-types circular polarizations. They depend on the 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. Another origin is related with the numbers n_e and n_h of the LQ levels of electrons and heavy-holes taking part in the magnetoexciton formation. So, the dipole-active transitions take place for the condition n_e = n_h, whereas in the quadrupole-active transitions the relation is n_e = n_h ± 1. It was shown that the Rabi frequency Ω_R of the polariton branches and the magnetoexciton oscillator strength f_osc increase in dependence on the magnetic field strength B as Ω_R ~ √B, and f_osc ~ B. The optical gyrotropy effects may be revealed if changing the sign of the photon circular polarization at a given sign of the wave vector longitudinal projection k_z or equivalently changing the sign of the longitudinal projection k_z at the same selected light circular polarization.