We have studied nonlinear effects in the resistance of a two-dimensional system with a large localization length on both sides of the crossover from weak to strong localization. It is shown that nonlinearity in the hopping regime is due to electron overheating rather than the field effects. This qualitatively new behavior is a signature of a two-dimensional hopping transport with a large localization length.

We have observed suppression of shot noise in the variable-range hopping regime for a twodimensional electron gas whose localization length, ξ, is controlled by a gate voltage. We have found that the suppression factor F (Fano factor) is approximately inversely proportional to the length of the system L (F = L * 0 /L) for a broad range of values of ξ/L * 0 , where L * 0 is the characteristic length. In the case ξ/L * 0 << 1, we have identified L * 0 with the distance L0 between the hard hops along the sample length. On the other hand, when ξ is of the order of L * 0 , we have observed that L * 0 does not agree with L0 calculated from the percolation model of hopping. We attribute this discrepancy to a breakdown of that model and to a reconstruction of the hopping paths.

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