  Electrons hopping in two-dimensional honeycomb lattices possess a valley
degree of freedom in addition to charge and spin. In the absence of inversion
symmetry, these systems were predicted to exhibit opposite Hall effects for
electrons from different valleys. Such valley Hall effects have been achieved
only by extrinsic means, such as substrate coupling, dual gating, and light
illuminating. Here, we report the first observation of intrinsic valley Hall
transport without any extrinsic symmetry breaking in the non-centrosymmetric
monolayer and trilayer MoS2, evidenced by considerable nonlocal resistance that
scales cubically with local resistance. Such a hallmark survives even at room
temperature with a valley diffusion length at micron scale. By contrast, no
valley Hall signal is observed in the centrosymmetric bilayer MoS2. Our work
elucidates the topological quantum origin of valley Hall effects and marks a
significant step towards the purely electrical control of valley degree of
freedom in topological valleytronics.
