Phonon confinement effect on the polaron states in a double quantum ring structure in the presence of electric and magnetic fields

In the framework of effective mass approximation the polaron problem in double quantum ring structures in the presence of perpendicular electric and magnetic fields with taken into account the effect of phonon confinement is considered. We derived general expressions for the normalized eigenfunctions of the confined optical and interface optical phonon modes and the dispersion relation for interface optical phonons as well as electron–confined optical phonon and electron–interface optical phonon Fröhlich interaction Hamiltonians in the double quantum ring system. Results reveal that the electron–optical phonon coupling leads to the decrease of the electron ground state energy. We have shown that the polaron energy exhibits a pronounced local maximum (minimuum) in dependence on an electric (magnetic) field which corresponds to the sharp decrease (increase) of the polaronic contributions due to confined optical and interface optical phonon modes.