We present low-temperature uanspon measurements on the two-dimensional electron gas in 8-doped GaAs which undergoes an insulatorquantum Hall-insulator vansition as the magnetic field is increased. Both low-and high-field vansitions are marked by pe& in ox, and Lhe temperahlre-independent critical value of oxy of 0.5ez/h per spin. We map out the phase diagram versus disorder and magnetic field and study the t e m p e m dependence of ox* throughout. In the quantum Hall region we observe Molt variable range hopping and, around the high-field transitions, s d i g via a single parameter: z = (S -B')T-"'. The functional dependence on L above this transition is fitted by recent network percolation calculations.

Variable-range hopping ͑VRH͒ conductance fluctuations in the gate-voltage characteristics of mesoscopic gallium arsenide and silicon transistors are analyzed by means of their full distribution functions ͑DF's͒. The forms of the DF predicted by the theory of Raikh and Ruzin have been verified under controlled conditions for both the long, narrow wire and the short, wide channel geometries. The variation of the mean square fluctuation size with temperature in wires fabricated from both materials is found to be described quantitatively by Lee's model of VRH along a one-dimensional chain. Armed with this quantitative validation of the VRH model, the DF method is applied to the problem of magnetoconductance in the insulating regime. Here a nonmonotonic variation of the magnetoconductance is observed in silicon metal-oxide-semiconductor fieldeffect transistors whose sign at low magnetic fields is dependent on the channel geometry. The origin of this effect is discussed within the framework of the interference model of VRH magnetoconductance in terms of a narrowing of the DF in a magnetic field. ͓S0163-1829͑96͒10227-7͔

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