Scattering by linear defects in graphene: a continuum approach

TL;DR

This paper models electronic transport across periodic defects in graphene using a continuum Dirac approach, deriving boundary conditions from tight-binding models, and analyzing conductance behavior for different defect types.

Contribution

It introduces a method to compute boundary conditions for Dirac fermions from tight-binding models and applies it to various defect lines in graphene.

Findings

Conductance across defect lines scales with size L and Fermi wavevector k_F.

Different defect lines can be mapped onto each other in the low-energy limit.

Boundary conditions can be derived from tight-binding models for various defect geometries.

Abstract

We study the low-energy electronic transport across periodic extended defects in graphene. In the continuum low-energy limit, such defects act as infinitesimally thin stripes separating two regions where 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 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_FL at low temperatures.