Scattering by linear defects in graphene: A continuum approach

Abstract

We study the low-energy electronic transport across periodic extended defects in graphene. In the continuum low-energy limit, such defects act as infinitessimally thin stripes separating two regions where the Dirac Hamiltonian governs the low-energy phenomena. The behavior of these systems is defined by the boundary condition imposed by the defect on the massless Dirac fermions. We demonstrate how this low-energy boundary condition can be computed from the tight-binding model of the defect line. For simplicity we consider defect lines oriented along the zigzag direction, which requires the consideration of only one copy of the Dirac equation. Three defect lines of this kind are studied and shown to be mappable between them: the pentagon-only, the $zz(558)$, and the $zz(5757)$ defect lines. In addition, in this same limit, we calculate the conductance across such defect lines with size $L$ and find it to be proportional to ${k}_{F}L$ at low temperatures.