Study of Wigner crystal in n-GaAs/AlGaAs by surface acoustic waves

The surface acoustic wave (SAW) technique was used for studying a 65 nm wide GaAs quantum well containing a two dimensional electron system (2DES) with the density of 5·10¹⁰ cm^-2 and the mobility of 8·10⁶ cm²/V·s. A SAW propagated in proximity of the quantum well. Both SAW attenuation α and SAW velocity V were measured in perpendicular magnetic field of up to 18 T in the frequency f range 28.5–306 MHz at temperatures 40–380 mK. Then, both real and imaginary parts of the ac conductance σ(f) = σ₁(f) + i·σ₂(f) of the 2DES were calculated from α and V. Dependencies of α, V, σ₁, and σ₂ on magnetic fields showed a rich oscillation pattern, in particular, the fractional quantum Hall effect (FQHE). Thus, at low temperature, the FQHE state was observed at the filling factor ν = 0.20, whereas, in vicinity of this value, at ν = 0.19 and 0.21, the 2DES behaved as a 2D Wigner crystal weakly pinned by a disorder random potential. The calculated pinning frequencies at high and zero magnetic fields were 193 MHz and 12.4 GHz, respectively, and the correlation length of the random potential was 10^-2 cm. [Work supported by RFBR 14-02-00232, NSF DMR-1157490, the State of Florida, the Gordon and Betty Moore Foundation GBMF2719, and NSF MRSEC-DMR-0819860.]