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

Abstract

We consider the transmission of massless Dirac fermions through an array of short range scatterers which are modelled as randomly positioned δ-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.

Electron scattering in a superlattice of line defects on the surface of topological insulators

“…Also, for any value of k y (i.e., fixed angle of incidence), T changes alternatively in terms of U . These are single barrier features found in single barrier structures on graphene [31,32] and are seen here as well.…”

“…3 can be attributed to constructive interferences due to multiple reflection of electron waves between the line defects. The position and the number of resonant peaks, as already seen in double-barrier structures on graphene [31,32], depend not only on the strength of U , but also on the acquired phase (k x d) of propagating waves between two line defects, i.e., d and the wave vector component k x , which is E and θ dependent. It is clear that at incident energy E = 100 meV, only electrons with k y < 0.04 Å−1 can propagate through the superlattice (see Fig.…”

“…For instance, Fig. 6 for U = 1 eV• Å shows that by increasing the number N of line defects, the number of maxima (Fabry-Perot resonances) increases, due to the multiple reflections, which can be understood from double barrier structures on graphene [32].…”

“…Nevertheless, by tuning the parameters and changing one of them, regular features can be observed. For instance, figure 6 for U = 1 eV Å shows that by increasing the number N of line defects, the number of maxima (Fabry-Perot resonances) increases, due to the multiple reflections, which can be understood from double barrier structures on graphene [32]. To examine the transmission probabilities of electrons at different incident angles, θ, we have shown T versus θ in figures 8(a), (b) and (c), (d) for a series of line defects extending along y and x directions, respectively.…”