Effect of coupling to the leads on the conductance fluctuations in one-dimensional disordered, mesoscopic systems

We study the electronic transport in a one-dimensional disordered chain with both site-diagonal and off-diagonal (hopping) disorder, the latter being perfectly correlated to the diagonal disorder at the nearest neighbor sites in a linear fashion. Since we allow the hopping in the perfect leads to be different from the average hopping in the sample, the average two-probe conductance ($$) and the conductivity ($\sigma$) decay non-monotonically with length. Because the peak regions of conductivity represent nearly constant $\sigma^{\prime}$s, these domains are quasi-Ohmic with their “effective" mean free paths equal to the stationary values of $\sigma$ in these domains. Indeed, when $$ passes through these quasi-Ohmic regions, the standard deviation of $g$ latches on to almost constant values of about $0.3e^{2}/h$, appropriate for 1D (as observed by us in a recent paper). The evolution of the probability distribution $P(g)$ with length demonstrates that it is unusually broad (nearly uniform) around the first quasi-diffusive regime and that for larger lengths, $P(g)$ narrows down in general, but becomes non-monotonically broader whenever $\sigma$ peaks up again, i.e., around the other (than the first) quasi-diffusive regimes