The metal-insulator transition is one of the remarkable electrical properties of atomically thin molybdenum disulphide. Although the theory of electron–electron interactions has been used in modelling the metal-insulator transition in molybdenum disulphide, the underlying mechanism and detailed transition process still remain largely unexplored. Here we demonstrate that the vertical metal-insulator-semiconductor heterostructures built from atomically thin molybdenum disulphide are ideal capacitor structures for probing the electron states. The vertical configuration offers the added advantage of eliminating the influence of large impedance at the band tails and allows the observation of fully excited electron states near the surface of molybdenum disulphide over a wide excitation frequency and temperature range. By combining capacitance and transport measurements, we have observed a percolation-type metal-insulator transition, driven by density inhomogeneities of electron states, in monolayer and multilayer molybdenum disulphide. In addition, the valence band of thin molybdenum disulphide layers and their intrinsic properties are accessed.

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 origin of valley Hall effects and marks a significant step towards the purely electrical control of valley degree of freedom in topological valleytronics.

Low carrier mobility and high electrical contact resistance are two major obstacles prohibiting explorations of quantum transport in TMDCs. Here, we demonstrate an effective method to establish low-temperature Ohmic contacts in boron nitride encapsulated TMDC devices based on selective etching and conventional electron-beam evaporation of metal electrodes. This method works for most extensively studied TMDCs in recent years, including MoS2, MoSe2, WSe2, WS2, and 2H-MoTe2. Low electrical contact resistance is achieved at 2 K. All of the few-layerTMDCdevices studied show excellent performance with remarkably improved field-effect mobilities ranging from 2300 to 16 000 cm 2 V-1 s(-1), as verified by the high carrier mobilities extracted from Hall effect measurements. Moreover, both high-mobility n-type and p-typeTMDCchannels can be realized by simply using appropriate contact metals. Prominent Shubnikov-de Haas oscillations have been observed and investigated in these high-quality TMDC devices.