Surface acoustic waves as a probe of the Wigner crystal in n-GaAs/AlGaAs in vicinity of $\bf{^{\circ}\nu=1/5}$, 1, and 2

Both attenuation of a surface acoustic wave (SAW) and variation of its speed due to interaction with 2D electrons in n-GaAlAs/GaAs/GaAlAs structures are measured versus perpendicular magnetic field of up to 18 T in the frequency range of (28.5 -- 306) MHz and at temperatures (40 -- 380) mK. The study is performed on $\delta$-doped from both sides 65~nm wide GaAs quantum well with the carrier density of n = $5\cdot10^{10}$~cm$^{-2}$ and their mobility of $\mu$ = $8\cdot10^6$~cm$^2$/V·s. The complex AC conductance, $\sigma$ is calculated. Analysis of $\sigma$ shows that at low temperatures and at the filling factor of 2, 1, and 1/5 the electron system resides in the integer and fractional quantum Hall states, respectively. However, in vicinities to these values, namely at $\nu$ = 1.9, (1.1 and 0.9), (0.21 and 0.19), the electron states can be interpreted as so-called pinning modes of Wigner crystal (WC). Temperature dependences of $\sigma$ indicates a crossover between the localized modes (at $\nu$ = 1 and 2) and a pinned WC. When the temperature (or the SAW intensity) increases the behavior of the complex conductance can be understood as manifestation of WC melting.