EFFECT OF DISORDER ON PHONON EMISSIONS FROM A TWO-DIMENSIONAL ELECTRON GASIN GAAS/ALXGA1-XAS HETEROSTRUCTURES

We report heating measurements in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures with tunable mobilities in the temperature range 100--710 mK. We find a power-law dependence on temperature for the phonon emission power ${P=dT}^{b}.$ With decreasing mobility, the exponent $b$ changes systematically from 5.15\ifmmode\pm\else\textpm\fi{}0.10 to 3.80\ifmmode\pm\else\textpm\fi{}0.02; the prefactor $d$ increases by more than an order of magnitude. These results explicitly corroborate the prediction by Girvin [in Phys. Rev. Lett. 77, 1143 (1996)] that the phonon emission changes character due to a disorder induced change in the screening from static to dynamic.