The key role of a smooth impuritypotential in formation of the hole spectrum for p-Ge/Ge1-xSix heterostructures in the quantum Hallregime

Abstract

We have measured the temperature (0.1⩽T⩽15 K) and magnetic field (0⩽B⩽12 T) dependencesof longitudinal and Hall resistivities for p-Ge0.93Si0.07/Ge multilayers with different Ge layerwidths 10⩽dw⩽38 nm and hole densitiesps = (1-5)×1015 m-2. Two models forthe long-range random impurity potential (the model withrandomly distributed charged centres located outside theconducting layer and the model of the system with a spacer) areused for evaluation of the impurity potential fluctuationcharacteristics: the random potential amplitude, nonlinearscreening length in the vicinity of integer filling factors (FFs) ν = 1and 2 and the background density of states (DOS). Thedescribed models are suitable for an explanation of the unusuallyhigh value of DOS at ν = 1 and 2, in contrast to theshort-range impurity potential models. For half-integer FFs the linear temperature dependence of the effectivequantum Hall effect (QHE) plateau-to-plateau transition width ν0(T) is observed incontrast to scaling behaviour for systems with short-rangedisorder. The finite T→0 width of QHE transitions maybe due to an effective low-temperature screening of smoothrandom potential owing to Coulomb repulsion of electrons.