Polaronic and bound polaronic effects in the energy states of an electron in a two-dimensional parabolic quantum dot in the presence of Rashba spin-orbit interaction

We perform a variational calculation to obtain the polaronic corrections to the ground state and first-excited state energies of an electron in a two-dimensional parabolic quantum dot of a polar semiconductor in the presence of Rashba spin-orbit interaction for the entire range of electron-phonon coupling constant and confinement length. We also present the results for the bound polaron problem. It is shown that for both the models in the absence of any external magnetic field, first-excited states with non-zero angular momentum get split into two branches for up and down spin of the electron due to Rashba spin-orbit interaction, whereas ground states with zero angular momentum show no spin splitting in both the cases. Application of our theory to GaAs quantum dot shows that polaronic corrections are reasonably large for quantum dots when their sizes are reduced to a few nanometres. But the polaronic corrections remain unaffected by Rashba spin-orbit interaction.