Resonances of piezoelectric plate with embedded 2D electron system

Abstract

A thin GaAs/AlGaAs plate was studied by the resonant ultrasound spectroscopy (RUS) in the temperature range 0.3–10 K and in magnetic fields of up to 18 T. The resonance frequencies and linewidths were measured. Quantum oscillations of both these values were observed and were associated with the quantum Hall effect occurred in the 2D electron system. For an analysis the sample was treated as a dielectric piezoelectric plate covered on one side by a film with a field dependent conductivity. Screening of the strain-driven electric field was changed due to the variation of the electron relaxation time in the vicinity of the metal-dielectric transitions caused by the magnetic field in the 2D system. The dielectric film does not affect properties of GaAs and thus the resonance frequencies are defined only by the elastic, piezoelectric and dielectric constants of GaAs. A metallic 2D sheet effectively screens the parallel electric field, so the ultrasound wave velocities and resonance frequencies decrease when the sheet conductivity increases. Oscillations of the resonance linewidth reflect the influence of the 2D system on the ultrasound attenuation, which is proportional to the linewidth. A metallic film as well as a dielectric one does not affect this attenuation but at some finite nonzero value of the conductivity the linewidth approaches a maximum. In high magnetic field each oscillation of the conductivity produces one oscillation of a resonance frequency and two linewidth peaks. The observed phenomena can be described by the relaxation type equations and the resonant ultrasound spectroscopy opens another opportunity for contactless studies on 2D electron systems.