In graphene superlattices, bulk topological currents can lead to long-range charge-neutral flow and non-local resistance near Dirac points. A ballistic version of these phenomena has never been explored. Here, we report transport properties of ballistic graphene superlattices. This allows us to study and exploit giant non-local resistances with a large valley Hall angle without a magnetic field. In the 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 non-local resistance plateau, implying rigidity of the qVHS, emerges as a function of magnetic field, and the collapse of this plateau is observed, which is considered as a manifestation of valley/pseudospin magnetism.
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