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We consider the transmission of massless Dirac fermions through an array ofshort range scatterers which are modeled as randomly positioned $\delta$-function like potentials along the x-axis. We particularly discuss theinterplay between disorder-induced localization that is the hallmark of anon-relativistic system and two important properties of such massless Diracfermions, namely, complete transmission at normal incidence and periodicdependence of transmission coefficient on the strength of the barrier thatleads to a periodic resonant transmission. This leads to two different types ofconductance behavior as a function of the system size at the resonant and theoff-resonance strengths of the delta function potential. We explain thisbehavior of the conductance in terms of the transmission through a pair of suchbarriers using a Green's function based approach. The method helps tounderstand such disordered transport in terms of well known optical phenomenasuch as Fabry Perot resonances.

A Green's function approach to transmission of massless Dirac fermions in graphene through an array of random scatterers