Line defects and quantum Hall plateaus in graphene

Line defects in graphene can be either tailored-growth or arise naturally and are at the center of many discussions. Here we study the multiterminal conductance of graphene with an extended line defect in the quantum Hall regime analyzing the effects of the geometry of the setup, disorder and strain on the quantum Hall plateaus. We show that the defect turns out to affect the local and non-local conductance in very different ways depending on the geometrical configuration. When the defect is parallel to the sample edges one gets an equivalent circuit formed by parallel resistors. In contrast, when the defect bridges opposite edges, the Hall conductance may remain unaltered depending on the geometry of the voltage/current probes. The role of disorder, strain and the microscopic details of the defect in our results is also discussed. We show that the defect provides a realization of the electrical analog of an optical beam splitter. Its peculiar energy dependent inter-edge transmission allows it to be turned on or off at will and it may be used for routing the chiral edge states.