Electron-phonon relaxation in disordered two-dimensional electron gas with dynamically screened deformation potential

We study the effect of a dynamically screened deformation potential on the electron longitudinal phonon relaxation in a disordered two-dimensional electron gas. On consideration of the dynamic dielectric function and polarization operator, and the frequency ω dependence, we find a significant change in the temperature exponent as well as the pre-factor α from the earlier reported approximate temperature power law dependence αT(4) obtained under static strong screening and impurity limit. More strikingly, a reversal in the character of the dependence of scattering rate on the mean free path takes place on the incorporation of dynamic screening, where the behaviour changes from the static 1/l to the dynamic l(2) at T = 1.0 K and l = 10 nm.