The effect of the electron–phonon interaction on the energy levelsand g-factor of electrons in nanowires

We analyze the effect of longitudinal optical phonons on the energy states of electrons in a nanowire in the presence of Rashba interaction and an in-plane magnetic field. Due to the electron–phonon interaction, an energy splitting appears at zero wave vector accompanied by a downward shift of the dispersion relation in the absence of external magnetic fields. The splitting increases linearly with the product of the Rashba parameter and the dimensionless constant characterizing the Fröhlich Hamiltonian. It also induces an enhancement in the [Formula: see text]-factor that is inversely proportional to the strength of the magnetic field. Moreover, we calculate the contribution of Rashba intersubband coupling (RIC) to the electron energy. This contribution does not influence the [Formula: see text]-factor for the case of parallel magnetic field to the nanowire, but it causes reduction in it by increasing the angle between the nanowire and the field.