Quantum Hall effect in graphene with twisted bilayer stripe defects

We analyze the quantum Hall effect in single layer graphene with bilayer stripe defects. Such defects are often encountered at steps in the substrate of graphene grown on silicon carbide. We show that $\mathit{AB}$ or $\mathit{AA}$ stacked bilayer stripes result in large Hall conductivity fluctuations that destroy the quantum Hall plateaux. The fluctuations are a result of the coupling of edge states at opposite edges through currents traversing the stripe. Upon rotation of the second layer with respect to the continuous monolayer (a twisted-bilayer stripe defect), such currents decouple from the extended edge states and develop into long-lived discrete quasibound states circulating around the perimeter of the stripe. Backscattering of edge modes then occurs only at precise resonant energies, and hence the quantum Hall plateaux are recovered as twist angle grows.