Gapped Dirac materials and quantum valley currents in dual-gated hBN/bilayer-graphene heterostructures

In gapped Dirac materials, the topological current associated with each valley can flow in opposite directions creating long-range charge-neutral valley currents. We report valley currents in hexagonal boron nitride (hBN)/bilayer-graphene heterostructures with an energy gap, which is tunable by a perpendicular electric (displacement) field in a dual-gated structure. We observed significant nonlocal resistance, consistent with the scaling theory of the valley Hall effect. In the low-temperature limit, the nonlocal resistance approaches a saturated value near the ``quantum limit,'' indicating the emergence of quantum valley currents.