Scattering by linear defects in graphene: a tight-binding approach

Abstract

We develop an analytical scattering formalism for computing the transmittance through periodic defect lines within the tight-binding model of graphene. We first illustrate the method with a relatively simple case, the pentagon-only defect line. Afterwards, more complex defect lines are treated, namely the zz(558) and the zz(5757) ones. The formalism developed uses only simple tight-binding concepts, reducing the problem to matrix manipulations which can be easily worked out by any computational algebraic calculator.

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

“…In calculating it, we will follow the methodology developed for the cases of the pentagon-only, zz(558) and zz(5757) grain boundaries. 34,35 Below, we show that the boundary condition obtained from the tight-binding gives rise, in the low-energy limit, to a boundary condition explicitly introducing intervalley scattering. Furthermore, we will show how, starting from the grain boundary's microscopic details, can we determine the generalized potential associated with viewing the grain boundary as a finite width strip with a potential constraining the Dirac fermions' dynamics.…”

“…33,34 In alternative, the grain boundary can also be thought of as a finite width strip containing a generalized potential that constrains the dynamics of the massless Dirac fermions. [34][35][36] The specific form of the boundary condition seen by the massless Dirac fermions at the 3-periodic pentagononly grain boundary is determined by the details of its microscopic tight-binding model. In calculating it, we will follow the methodology developed for the cases of the pentagon-only, zz(558) and zz(5757) grain boundaries.…”

Zero modes on zero-angle grain boundaries in graphene

“…The development of practical methods for the synthesis of large area single-and few-layer graphenes [1][2][3][4] is focusing attention on the influence of grain boundaries on their electronic behavior [3][4][5][6][7] . These extended defects have been studied theoretically to understand their reconstruction of the low energy Dirac spectra and their signatures in transport [7][8][9][10][11][12][13][14] . In this Rapid Communication we consider the family of "zero angle" grain boundaries (ZGB's) and study their electronic properties using a new quantum geometric formulation.…”

“…Our Hamiltonian describes nearest neighbor hopping on the links of the two dimensional networks shown in Figure 1 neglecting perturbations due to remote hopping amplitudes and out of plane structural relaxations. These networks have been used to examine the transmission and reflection of Bloch waves from extended one dimensional defects on the graphene lattice [11][12][13] and are a natural starting point for studying electronic physics in the grain boundary.…”

“…Our preliminary work indicates that this distinction is important and can determine the topological character of the boundary 20 . It will also be useful to augment this topological analysis to address the consequences of local symmetry breaking perturbations (presumed to be weak) that inevitably occur in atomistic models that suggest structure-specific spectral reconstruction near the neutrality point [7][8][9][10][11][12][13][14] . Finally the presence of flat or weakly dispersing bands near charge neutrality invites an investigation of its interaction-induced instabilities.…”