Crossover between localized states and pinned Wigner crystal in high-mobility n-GaAs/AlGaAs heterostructures near filling factor $ u=1$

We have measured magnetic field dependences of the attenuation and velocity of surface acoustic waves in a high-mobility $n$-GaAs/AlGaAs structure with a wide quantum well. The results allowed us to find the complex conductance, $sigma(omega)$, of the heterostructure for different frequencies, temperatures and magnetic fields near filling factors $ u=1, 2$. Observed behavior of $sigma(omega)$ versus magnetic field outside close vicinities of integer fillings reveals an oscillation pattern indicative of the rich fractional quantum Hall effect. Our result is that in very close vicinities of integer filling factors the AC response of a high-mobility two-dimensional structures behaves as that of a two-dimensional system of localized electrons. Namely, both real and imaginary parts of the complex AC conductance at low temperatures agree with the predictions for the two-site model for a two-dimensional hopping system. Another result is the specific temperature dependences of $sigma(omega)$, which are extremely sensitive to the filling factor value. These dependences indicate a sharp crossover between the localized modes and a pinned Wigner crystal.