Non-Ohmic hopping transport in a-YSi: From isotropic to directed percolation

Electrical transport has been investigated in amorphous Y0.19Si0.81, from 3 0 mK to room temperature. Below 2 K, the conductance G exhibits Shklovskii- Efros behavior G similar to exp[-(T-0/T)(1/2)] at zero electric field, wher e conduction is expected to occur along a very sinuous path (isotropic perc olation). The nonlinear I-V characteristics are systematically studied up t o very high fields, far which the conductance no longer depends on T and fo r which the current paths are expected to be almost straight (directed perc olation). We show that the contributions of electronic and sample heating t o those nonlinearities are negligible. Then, we show that the conductance d ependence as a function of low electric fields (F/T<5000 V m(-1) K-1) is gi ven by G(F,T) = G(0,T)exp(-eFL/k(B)T). The order of magnitude (5-10 nm) and the T dependence (similar to T-1/2) of L agree with theoretical prediction s. From the T-0 value and the length characterizing the intermediate field regime, we extract an estimate of the dielectric constant of our system. Th e very high electric field data do not agree with the prediction I(F)simila r to exp[-(F-0/F)(gamma')] with gamma' = 1/2: we find a F dependence of gam ma' that could he partly due to tunneling across the mobility edge. In the intermediate electric field domain, we claim that our data show both the en hancement of the hopping probability with the field and the influence of th e straightening of the paths. The latter effect is due to the gradual trans ition from isotropic to directed percolation and depends essentially on the statistical properties of the ''returns,'' i.e., of the segments of the pa ths where the current flows against the electrical force. The critical expo nent of this returns contribution, which up to now was unknown both theoret ically and experimentally, is found to be beta = 1.15+/-0.10. An estimation of the length of the returns is also given.