Observation of the quantum valley Hall state in ballistic graphene superlattices

In graphene superlattices, bulk topological currents can lead to long-range charge-neutral flow and nonlocal resistance near Dirac points. A ballistic version of these phenomena has never been explored. We report transport properties of ballistic graphene superlattices. This allows us to study and exploit giant nonlocal resistances with a large valley Hall angle without a magnetic field. In a low-temperature regime, a crossover occurs toward a new state of matter, referred to as a quantum valley Hall state (qVHS), which is an analog of the quantum Hall state without a magnetic field. Furthermore, a nonlocal resistance plateau, implying rigidity of the qVHS, emerges as a function of magnetic field, and this plateau collapses, which is considered a manifestation of valley/pseudospin magnetism.