Polaron binding energy and 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 c
alculated using the Hubbards local field factor. It is found that the effective mass and the binding energy both decrease with increase in doping.
The polaron binding energy and effective mass in a degenerate polar gas is calculated in the fractional-dimensional approach under plasmon pole approximation.The effect of carrier densities on the static and dynamic screening correction of the electr
on-phonon interaction and electron-electron interaction to the polaronic propertis is calculated from electron self-energies within the second-order perturbation method. The Hubbard local field factor has been used for the static screening correction in the polaronic properties. We found that polaronic properties decrease with increase with carrier density and dimensionality of the system.
The dielectric function for electron gas with parabolic energy bands is derived in a fractional dimensional space. The static response function shows a good dimensional dependance. The plasma frequencies are obtained from the roots of the dielectric
functions. The plasma dispersion shows strong dimensional dependence. It is found that the plasma frequencies in the low dimensional systems are strongly dependent on the wave vector. It is weakly dependent in the three dimensional system and has a finite value at zero wave vector.
