Coexistence of two hole-phases in the vicinity of filling factors 1 and 1/3 in p-GaAs/AlGaAs studied by acoustic method

We studied ac conductivity in a 17 nm wide single p-GaAs/AlGaAs quantum well with hole concentration ~1.2×10¹¹ cm⁻² and mobility ~1.8×10⁶ cm²/Vs. The ac conductivity σ_ac=σ₁ - iσ₂ was calculated from simultaneously measured absorption and velocity of surface acoustic waves (SAWs) propagating parallel to the well. Measurements, performed at SAW frequency 30  – 300 MHz and temperatures 20 – 300 mK, exhibited integer and fractional quantum Hall (QH) effects in magnetic fields. Analysis of the σ₁ and σ₂ shows that at the filling factor ν = 1 the carriers are localized in the minima of random potential with single-carrier hoppings between localized states, whereas at ν = 1/3 the carrier state corresponds to incompressible liquid. When ν deviates from 1 and 1/3, the temperature and frequency dependencies of σ_1, σ_2, and σ₁/σ₂ gradually change and become drastically modified. We link this evolution to the formation of domains of the Wigner solid which are most pronounced at the lowest temperature at ν equal to 1.2 and 0.78, as well as 0.375 and 0.3. When the temperature rises, the domains melt as concluded by studying the frequency dependencies of σ₂. We explain the lack of sharp transitions in the conductivity behaviors by the coexistence of the QH-related hole states and Wigner domains.