SNS junction in small angle twisted bilayer graphene

Due to the competition between van der Waals interaction and the elastic energy of the interface of a minimally twisted bilayer graphene system undergoes a smooth atomic reconstruction and forms domains of AB and BA stacked regions that are separated by solitonic boundaries. The difference in valley Chern number between the two sides of the boundary results in two ballistic modes propagating on boundaries, which are further connected via AA-stacked regions. Such a system is best described by network models of the Chalker-Coddington type, where each propagating channel forms the network's edges, and the AA stacked regions, in this case, serve as the scattering nodes. The form of the scattering matrices in each node and the corresponding link matrices are constrained by the microscopic symmetries of the system. Based on such a scattering network approach, we study transport characteristics of a superconductor-normal-superconductor (SNS) junction, where a small twist angle twisted graphene bilayer is the normal region.