Hopping conductivity beyond the percolation regime probed by shot-noise measurements

We have observed suppression of shot noise in the variable-range hopping regime for a two-dimensional electron gas whose localization length xi 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 xi/L-0(*), where L-0(*) is the characteristic length. In the case xi/L-0(*)<1, we have identified L-0(*) with the distance L-0 between the hard hops along the sample length. On the other hand, when xi is of the order of L-0(*), we have observed that L-0(*) does not agree with L-0 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.