Scattering Theory of Graphene Grain Boundaries

Abstract

The implementation of graphene-based electronics requires fabrication processes that are able to cover large device areas, since the exfoliation method is not compatible with industrial applications. The chemical vapor deposition of large-area graphene represents a suitable solution; however, it has an important drawback of producing polycrystalline graphene with the formation of grain boundaries, which are responsible for the limitation of the device’s performance. With these motivations, we formulate a theoretical model of a single-layer graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. The model only includes the long-wavelength regime of the charge carrier transport, which provides the main contribution to the device conductance. Using symmetry-based arguments deduced from the current conservation law, we derive unconventional boundary conditions characterizing the grain boundary physics and analyze their implications on the transport properties of the system. Angle resolved quantities, such as the transmission probability, are studied within the scattering matrix approach. The conditions for the existence of preferential transmission directions are studied in relation with the grain boundary properties. The proposed theory provides a phenomenological model to study grain boundary physics within the scattering approach, and represents per se an important enrichment of the scattering theory of polycrystalline graphene. Moreover, the outcomes of the theory can contribute to understanding and limiting the detrimental effects of graphene grain boundaries, while also providing a benchmark for more elaborate techniques.

Valley to charge current conversion in graphene grain boundaries

“…Scattering theory of graphene grain boundaries has been formulated in Ref. [13][14][15][16][17] . In particular, in Ref.…”

“…In particular, in Ref. 17 , it has been shown that, under appropriate circumstances, a grain boundary can be treated as a linear defect separating two regions with rotated crystallographic axes. The misorientation angle between the different sides of the junction has been taken into account by writing the Dirac equation within a rotated reference frame.…”

“…Here a different technique is used which is a direct generalization of the matching matrix approach developed in Ref. 17 . Within the mentioned framework, a richer set of boundary conditions for the scattering problem has been derived and the experimental implications of these findings have been carefully discussed.…”

Conduction properties of extended defect states in Dirac materials

“…In general, it is easy to show that Φ † + Φ − = 0 is a necessary requirement to get translational invariant solutions. Boundary conditions at x = 0 are implemented by using the matching matrix method in the form Ψ(0 + , y) = MΨ(0 − , y), with the matching matrix M directly derived from the interface potential according to the relation M = exp(−iσ x B + /( v)) [20]. Inspection of the boundary conditions shows that the quantum state we are talking about nucleates at the interface provided that M 11 = 0, i.e.…”

“…Moreover, following [20], it can be shown that the interface potential of a grain boundary junction with rotated crystallographic axes retains a dependence on the misorientation angle. According to this observation, we expect that in graphene grain boundaries the renormalized modes velocity v ef f can be controlled by the misorientation angle between the crystallographic axes of the two sides of the junction.…”