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GaAs-type quantum wells (QWs) with p-type valence band embedded into theresonators. The Landau quantization of the electrons and heavy-holes (hh) wasinvestigated taking into account the Rashba spin-orbit coupling withthird-order chirality terms for hh and with nonparabolicity terms in theirdispersion low including the Zeeman splitting (ZS) effects. The exact solutionsfor the eigenfunctions and eigenenergies were obtained using the Rashba method[1]. We derive in the second quantization representation the Hamiltoniansdescribing the Coulomb electron-electron and the electron-radiationinteractions and determine the magnetoexciton energy branches and themagnetoexciton-photon interaction. The fifth order dispersion equationdescribing the energy spectrum of the cavity magnetoexciton-polariton isinvestigated. It takes into account the interaction of the cavity photons withtwo dipole-active and with two quadrupole-active 2D magnetoexciton energybranches. The cavity photons have the circular polarizations oriented alongtheir wave vectors, which has the quantized longitudinal component. Theselection rules of the exciton-photon interaction is expressed through thescalar products of the two-types circular polarizations and it is related withthe numbers of the LQ levels of electrons and heavy-holes. It is shown that theRabi frequency of the polariton branches and the magnetoexciton oscillatorstrength increase in dependence on the magnetic field strength. The opticalgyrotropy effects may be revealed if changing the sign of the photon circularpolarization at a given sign of the wave vector longitudinal projection orequivalently changing the sign of the longitudinal projection at the sameselected light circular polarization.

the european physical journal. b, condensed matter physics/european physical journal. b, condensed matter and complex systems

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