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

TL;DR

This paper investigates how 3-periodic grain boundaries in graphene induce intervalley scattering of massless Dirac fermions, providing a theoretical framework to compute boundary conditions and scattering effects.

Contribution

It introduces a method to compute boundary conditions and scattering for Dirac fermions at 3-periodic graphene grain boundaries, specifically analyzing the pentagon-only defect.

Findings

Intervalley scattering occurs at 3-periodic grain boundaries.

Boundary conditions for Dirac fermions can be derived from tight-binding models.

Effective potentials at the grain boundary influence scattering behavior.

Abstract

We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac points into the same position, and thus allow for intervalley scattering to occur. Starting from graphene's first-neighbor tight-binding model we show how can we compute the boundary condition seen by graphene's massless Dirac fermions at such grain boundaries. We illustrate this procedure for the 3-periodic pentagon-only grain boundary, and then work out the low-energy electronic scattering off this linear defect. We also compute the effective generalized potential seen by the Dirac fermions at the grain boundary region.