Properties of many-polaron in fractional dimensional space

Polaron properties such as the binding energy and the effective mass are calculated in the fractional dimensional space approach using the second-order perturbation theory. The effect of carrier density on the static screening correction of the electron-phonon interaction is included in the Hubbard's local field factor. It is found that the polaron properties decrease with increase in dimension due to quantum confinement. Since the screening of the electron-phonon interaction is enhanced with increase in doping, the polaron properties decrease with increasing density.