Bound states of the two-dimensional magnetoexcitons taking into account the Rashba spin-orbit coupling

Molecular-type bound states of two-dimensional (2D) magnetoexcitons supplementarily subjected to the action of an external electric field perpendicular to the layer and parallel to a strong magnetic field are studied. The electron and hole wave functions have different numbers of the Landau quantization levels for different spin projections. The Rashba spin–orbit coupling (RSOC) is characterized by first-order chirality terms for electrons and third-order chirality terms for heavy holes in GaAs-type quantum wells. In this case, the external electric field gives rise to the nonparabolic dispersion law of heavy holes and a nonmonotonous dependence of their energy levels on the magnetic field strength. The lowest spinor-type wave functions of electrons and holes are used to construct the one- and two-magnetoexciton wave functions, determine their normalization conditions, and deduce the Hamiltonian of the Coulomb electron–electron interaction in the presence of the RSOC. It contains electron and hole imprint factors, the difference of which determines the affinities of the electron–hole pairs to interact between themselves. The average value of the Coulomb interaction Hamiltonian makes it possible to calculate the mean energy value per two pairs forming the molecule versus parameter a of the wave function, which determines the relative motion of two magnetoexcitons in the frame of the bound state. The next numerical calculations will show whether the stable bound state of the molecular type or the metastable bound state does exist