Energy relaxation in disordered two-dimensional electron gas with dynamic deformation potential

We investigated the electron energy loss rate through the emission of acoustic phonons in disordered two-dimensional electron gas in the deformation coupling limit. The energy loss rate has been determined by considering dynamic screening of electrons as various earlier studies have shown that static screening underestimates the energy loss rate. We find a change in the temperature exponent as well as the pre-factor β from the earlier reported approximate temperature power law dependence βT6 obtained under static and dynamic strong screening and impurity limit. The difference in magnitude between the approximate analytic and numerical results mounts at decreasing sub-Kelvin temperatures with the pre-factor being enhanced about three times at a temperature 100 mK and mean free path length 8 nm, and the power dependency decreasing from the analytically derived T6 to numerically observed T5.2.