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=L0*/L) for a broad range of values of xi/L_0*, where L0* is the characteristic length. In the case xi/L0*<<1, we have identified L0* with the distance L0 between the hard hops along the sample length. On the other hand, when xi is of the order of L0*, we have observed that L0* 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.