Topological Aspects of Charge-Carrier Transmission across Grain Boundaries in Graphene

We systematically investigate the transmission of charge carriers across the grain-boundary defects in polycrystalline graphene by means of the Landauer-B\"uttiker formalism within the tight-binding approximation. Calculations reveal a strong suppression of transmission at low energies upon decreasing the density of dislocations with the smallest Burger's vector ${\mathbf b}=(1,0)$. The observed transport anomaly is explained from the point of view of back-scattering due to localized states of topological origin. These states are related to the gauge field associated with all dislocations characterized by ${\mathbf b}=(n,m)$ with $n-m \neq 3q$ ($q \in \mathbb{Z}$). Our work identifies an important source of charge-carrier scattering caused by topological defects present in large-area graphene samples produced by chemical vapor deposition.