Transport through small world networks

Abstract

We numerically investigate the transport properties through a system where small world networks are added to a one-dimensional chain. One-electron Green's function method is applied to standard tight-binding Hamiltonians on networks, modeled as (i) adding connections between any two nonadjacent random sites in the chain, (ii) introducing finite one-dimensional chains between any pair of such connected sites, and (iii) attaching finite dangling chains at random sites in the chain. Due to the small world bonds and dangling conduction paths, the systems have irregular geometrical shapes, leading to quenched disordered systems. We consider the qualitative influence of the small world bonds and dangling bonds on the transmittance and find that the systems exhibit a strong energy dependence on the transmittance, with strong sample-to-sample fluctuations.