The key role of a smooth impurity potential in formation of the hole spectrum for p-Ge/Ge1-xSix heterostructures in the quantum Hall regime

We have measured the temperature (0.1≤T≤15 K) and magnetic field (0≤B≤12 T) dependences of longitudinal and Hall resistivities for p-Ge0.93Si0.07/Ge multilayers with different Ge layer widths 10≤dw≤38 nm and hole densities ps = (1-5)×1015 m-2. Two models for the long-range random impurity potential (the model with randomly distributed charged centres located outside the conducting layer and the model of the system with a spacer) are used for evaluation of the impurity potential fluctuation characteristics: the random potential amplitude, nonlinear screening length in the vicinity of integer filling factors (FFs) ν = 1 and 2 and the background density of states (DOS). The described models are suitable for an explanation of the unusually high value of DOS at ν = 1 and 2, in contrast to the short-range impurity potential models. For half-integer FFs the linear temperature dependence of the effective quantum Hall effect (QHE) plateau-to-plateau transition width ν0(T) is observed in contrast to scaling behaviour for systems with short-range disorder. The finite T→0 width of QHE transitions may be due to an effective low-temperature screening of smooth random potential owing to Coulomb repulsion of electrons.

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