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Electrons hopping in two-dimensional honeycomb lattices possess a valleydegree of freedom in addition to charge and spin. In the absence of inversionsymmetry, these systems were predicted to exhibit opposite Hall effects forelectrons from different valleys. Such valley Hall effects have been achievedonly by extrinsic means, such as substrate coupling, dual gating, and lightilluminating. Here, we report the first observation of intrinsic valley Halltransport without any extrinsic symmetry breaking in the non-centrosymmetricmonolayer and trilayer MoS2, evidenced by considerable nonlocal resistance thatscales cubically with local resistance. Such a hallmark survives even at roomtemperature with a valley diffusion length at micron scale. By contrast, novalley Hall signal is observed in the centrosymmetric bilayer MoS2. Our workelucidates the topological quantum origin of valley Hall effects and marks asignificant step towards the purely electrical control of valley degree offreedom in topological valleytronics.

Intrinsic valley Hall transport in atomically thin MoS2