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

TL;DR

This paper investigates how massless Dirac fermions in graphene transmit through random short-range scatterers, revealing unique resonant and localization behaviors explained via a Green's function approach and optical analogies.

Contribution

It introduces a Green's function method to analyze disordered Dirac fermion transport, highlighting the interplay of localization and resonant transmission phenomena.

Findings

Resonant transmission occurs periodically with barrier strength.

Conductance varies with system size at resonance and off-resonance.

Optical phenomena like Fabry Perot resonances explain transport behavior.

Abstract

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