Highly Anisotropic Parallel Conduction in the Stepped Substrate of Epitaxial Graphene Grown on Vicinal SiC

We report highly anisotropic appearance of the quantum Hall effect (QHE) in epitaxial single-layer graphene grown on a vicinal SiC(0001) substrate. Well-developed QHE with zero resistance manifests itself for the current along the steps, whereas the QHE is obscured by pronounced positive magnetoresistance with quadratic magnetic-field dependence for the current across the steps. The latter, as well as the small slope of the Hall resistance, implies the presence of parallel conduction due to remnant carriers in the SiC substrate, albeit with seeming inconsistency with the zero resistance observed for the former current direction. We interpret the anisotropic behavior by assuming that the parallel conduction is sizable along the steps but is virtually prohibited across the steps.