Eur. Phys. J. B 86 (2013) 86: 317
https://doi.org/10.1140/epjb/e2013-40278-9

Regular Article

Transmission of massless Dirac fermions through an array of random scatterers in terms of Fabry-Perot resonances: a Green’s function approach

¹ Centre for Applied Research in Electronics, Indian Institute of Technology Delhi, 110016 New Delhi, India
² Department of Physics, Indian Institute of Technology Delhi, 110016 New Delhi, India

^a e-mail: sankalpa@physics.iitd.ac.in

Received: 3 April 2013
Received in final form: 17 May 2013
Published online: 10 July 2013

Abstract

Transmission properties of massless Dirac fermions that are charge carriers in graphene through a double potential barrier can be completely understood in terms of resonances in Fabry-Perrot cavity. Using a Green’s function based approach we generalize this analysis to the case of transmission through an array of short range random scatterers modeled as delta function. The method helps to understand such disordered transport in terms of well-known optical phenomena such as Fabry-Perot resonances. Using this optical analogy we particularly provide a microscopic understanding of the interplay between disorder-induced localisation 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. Within this framework we show that this leads to two different types of conductance behaviour as a function of the system size at the resonant and the off-resonance strengths of the delta function potential.