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Resonant Magneto-phonon Emission by Supersonic Electrons in Ultra-high Mobility Two-dimensional System

We investigate resonant acoustic phonon scattering in the magneto-resistivity of an ultra-high mobility two-dimensional electron gas system subject to DC current in the temperature range 10 mK to 3.9 K. For a DC current density of $\sim$1.1 A/m, the induced carrier drift velocity $v_{drift}$ becomes equal to the speed of sound $s \sim$ 3 km/s. When $v_{drift} \gtrsim s$ very strong resonant features with only weak temperature dependence are observed and identified as phonon-induced resistance oscillations at and above the "sound barrier". Their behavior contrasts with that in the subsonic regime ($v_{drift} < s$) where resonant acoustic phonon scattering is strongly suppressed when the temperature is reduced unless amplified with quasi-elastic inter-Landau-level scattering. Our observations are compared to recent theoretical predictions from which we can extract a dimensionless electron-phonon coupling constant of $g^{2}$=0.0016 for the strong non-linear transport regime. We find evidence for a predicted oscillation phase change ' effect on traversing the "sound barrier". Crossing the "sound barrier" fundamentally alters the resulting phonon emission processes, and the applied magnetic field results in pronounced and sharp resonant phonon emission due to Landau level quantization.