Role of Rashba spin-orbit interaction on polaron Zeeman effect in a two-dimensional quantum dot with parabolic confinement

•Low-lying polaron energies are calculated in a quantum dot including Rashba effect.•LLPH method is used to get all-coupling results for arbitrary dot size.•Interplay between Rashba and polaronic effects is studied in presence of magnetic field.•Our results are applied to GaAs and CdS quantum dots.•Though polaronic effect suppresses Zeeman splitting, Rashba coupling enhances it. We calculate the energies of the ground and the first excited states of a free polaron and that of a polaron bound to a Coulomb impurity in a quantum dot with harmonic confinement in the presence of Rashba spin-orbit interaction by employing the variation theory of Lee, Low and Pines as modified by Huybrechts for an all-coupling range of the electron-phonon interaction and arbitrary confinement length. We show that in both cases, the Rashba interaction removes the two-fold spin-degeneracy of the first-excited states even in the absence of any applied magnetic field, though the ground state does not show any such spin splitting. The self-energy corrections due to the polaronic effect are however not affected by the Rashba interaction. We also investigate the combined effect of Rashba and polaronic interactions in the presence of an external magnetic field using the Rayleigh-Schrödinger perturbation theory. Application of our results to GaAs and CdS quantum dots shows that the suppression of the phonon-induced size-dependent Zeeman splitting in a quantum dot is reduced by the Rashba coupling.