Electronic transport across linear defects in graphene

Abstract

We investigate the low-energy electronic transport across grain boundaries in graphene ribbons and infinite flakes. Using the recursive Green's function method, we calculate the electronic transmission across different types of grain boundaries in graphene ribbons. We show results for the charge density distribution and the current flow along the ribbon. We study linear defects at various angles with the ribbon direction, as well as overlaps of two monolayer ribbon domains forming a bilayer region. For a class of extended defect lines with periodicity 3, an analytic approach is developed to study transport in infinite flakes. This class of extended grain boundaries is particularly interesting, since the K and K Dirac points are superposed.

Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

“…The calculations below closely follow what was done in Ref. 37. In sub-Section A 1 we concentrate on the calculations leading to the bulk transfer matrix, while in sub-Section A 2 we focus on the calculations giving rise to the tight-binding boundary condition that originates from the presence of the 3-periodic pentagon-only grain boundary.…”

“…Finally, we must note that, as we can quickly infer from the above results (where we have considered different sets of values for the hopping renormalizations ξ i ), the scattering properties of the grain boundary are strongly dependent on the microscopic details at the grain boundary, as previously remarked by other studies. 34,35,37 Such behaviour points towards the possibility of making use of this kind of nanostructures to control and explore the valley degree of freedom of graphene. Chemical decoration of the grain boundary region, application of strains, of electric and of magnetic fields, all likely modify the electronic scattering off these grain boundaries, thus suggesting their usage as sensors and current switchers.…”

“…As was shown in Ref. 37, we can employ a basis transformation L(n) = Λ(k x )L(n) that makes the transfer matrix block diagonal, T = diag[T h , T l− , T l+ ]. We will use the notation L(n) = {A h , B h , A l− , B l− , A l+ , B l+ } to identify the elements of a vector in this basis.…”

“…Similarly, when we set ξ 1 = ξ 2 = ξ and ξ 3 = 0, we recover the case of the zz(558) grain boundary, which owing to its periodicity of 2u 1 also maps the projected Dirac points into distinct values of k x , which ends up blocking intervalley scattering. [31][32][33][34][35][36][37] Moreover, there are a few cases where, despite the 3periodicity of the grain boundary, intervalley scattering is suppressed. In these cases, the microscopic details of the grain boundary, i.e.…”

Scaling properties of polycrystalline graphene: a review

“…Therefore, because of its promise for large-area electronic applications, a detailed understanding of the electrical transport properties of polycrystalline graphene is crucial. To this end, a great deal of experimental [13,[18][19][20][21][22][23][24][25][26][27] and theoretical [7,[28][29][30][31][32][33][34][35][36][37][38] effort has has been devoted to studying charge transport across individual graphene GBs, and several reviews have already discussed this topic in great detail [5,26,39]. Therefore, here we briefly summarize the main features of electrical transport across individual graphene GBs before shifting our focus to a more global perspective of charge transport in polycrystalline graphene.…”