Electronic transmission through a set of metallic clusters randomly attached to an adsorbed nanowire: Localization-delocalization transition

The electron transmission through a monatomic nanowire containing N attached quasiperiodically distributed nanoclusters is studied within the ballistic model. A decimation procedure is performed to renormalize the self-energy of the nanowire sites connected to the clusters and to transform the nanodevice into an effective disordered one-dimensional chain. The transmittance is determined using the transfer matrix formalism. It allows us to express each elementary reflection/transmission process per cluster in terms of a single parameter which accounts for the self-energy renormalization. It is shown that cluster antiresonances are responsible for the occurrence of a localization-delocalization transition which discriminates between insulating and conducting regimes for the electron transport. These results are interpreted in a general way on the basis of the scaling theory which involves the random phase approximation to characterize the behavior of the probability distribution connected to the transmittance. However, the scaling theory fails for particular values of the electron energy leading to singularities in the average transmittance called tips and dips. These singularities are related to the reminiscence of quantum interferences which the disorder is not sufficient to break.