Conductivity of weakly and strongly localized electrons in a n ‐type Si/SiGe heterostructure

We have investigated the temperature dependence of the longitudinal conductivity σxx and Hall resistance Rxy of n-type Si/SiGe heterostructures in the quantum Hall effect regime in magnetic fields up to 23 T. It is shown that for odd integer filling factors i = 3,5,7,9, when the Fermi level EF is situated between the valley-split Landau levels, Δσxx(T) ∝ lnT, which is typical for weakly localized electrons. In the case of even i, when EF lies between spin-split or cyclotron-split levels, σxx(T) is characteristic of strong localization: activation of localized electrons from EF to the nearest mobility edge: σxx ∝ exp[−Δi/T] for i = 6, 10, 12 or variable-range-hopping via localized states in the vicinity of EF: σxx ∝ exp[−(T0i/T)]1/2 for i = 4, 8. For i = 3, 6, 8, 10, 12, the Hall resistance Rxy first overshoots the quantized plateau values h/ie2 and then returns. The explanatory model involves the temporary parallel contribution of the delocalized and weakly localized electrons with different mobilities in the measurement of the Hall voltage Vxy.