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Two-dimensional cavity polaritons under the influence of the perpendicular strong magnetic and electric fields. The gyrotropy effects

The properties of the two-dimensional cavity polaritons subjected to the action of a strong perpendicular magnetic and electric fields, giving rise to the Landau quantization (LQ) of the 2D electrons and holes accompanied by the Rashba spin-orbit coupling, by the Zeeman splitting and by the nonparabolicity of the heavy-hole dispersion law are investigated. We use the method proposed by Rashba [1] and the obtained results are based on the exact solutions for the eigenfunctions and for the eigenvalues of the Pauli-type Hamilonians with third order chirality terms and nonparabolic dispersion law for heavy-holes and with the first order chirality terms for electrons. The selection rules of the band-to-band optical quantum transitions as well as of the quantum transitions from the ground state of the crystal to the magnetoexciton states depend essentially on the numbers $n_{e}$ and $n_{h}$ of the LQ levels of the (e-h) pair forming the magnetoexciton. It is shown that the Rabi frequency $Ω_{R}$ of the polariton branches and the magnetoexciton oscillator strength $f_{osc}$ increase with the magnetic field strength $B$ as $Ω_{R}\sim \sqrt{B}$, and $f_{osc}\sim B$. The optical gyrotropy effects may be revealed changing the sign of the photon circular polarization at a given sign of the wave vector longitudinal projection $k_{z}$ or eqivalently changing the sign of $k_{z}$ at the same selected circular polarization.