Dependence of pinning modes of 2D electron system on short-ranged alloy disorder

A 2D electron system (2DES) in a low Landau filling ($\nu )$ pinned Wigner solid state exhibits a striking resonance in its rf or microwave spectrum. The resonance is understood as a pinning mode, in which the electrons oscillate about their pinned positions, and the frequency (f$_{pk})$ increases for larger disorder. We report on microwave spectroscopy of the low-$\nu $ Wigner solids in Al$_{x}$Ga$_{1-x}$As-Al$_{0.1}$Ga$_{0.9}$As heterojunctions with x=0.4 and 0.8{\%}. The 2DES resides mainly in the dilute Al$_{x}$Ga$_{1-x}$As, and the alloy disorder has been shown to be randomly distributed [1]. We compare the pinning modes of the samples as density ($n$, controlled by backgates) and magnetic field are varied. For example, with densities around $n\sim $6.5$\times $10$^{10 }$cm$^{-2}$ (in sample state with no indication of a 1/5 fractional quantum Hall effect) f$_{pk} \approx $ 5.93 and 8.55 GHz at $\nu \sim $0.2 for x=0.4 and 0.8{\%} respectively.\\[4pt] [1] W. Li \textit{et al}., Appl. Phys. Lett., 83, 2832 (2003).