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.

van der Waals layered structures, notably the transitional metal dichalcogenides (TMDs) and TMD-based heterostructures, have recently attracted immense interest due to their unique physical properties and potential applications in electronics, optoelectronics, and energy harvesting. Despite the recent progress, it is still a challenge to perform comprehensive characterizations of critical properties of these layered structures, including crystal structures, chemical dynamics, and interlayer coupling, using a single characterization platform. In this study, we successfully developed a multimodal nonlinear optical imaging method to characterize these critical properties of molybdenum disulfide (MoS2) and MoS2-based heterostructures. Our results demonstrate that MoS2 layers exhibit strong four-wave mixing (FWM), sum-frequency generation (SFG), and second-harmonic generation (SHG) nonlinear optical characteristics. We believe this is the first observation of FWM and SFG from TMD layers. All three kinds of optical nonlinearities are sensitive to layer numbers, crystal orientation, and interlayer coupling. The combined and simultaneous SHG/SFG-FWM imaging not only is capable of rapid evaluation of crystal quality and precise determination of odd-even layers but also provides in situ monitoring of the chemical dynamics of thermal oxidation in MoS2 and interlayer coupling in MoS2-graphene heterostructures. This method has the advantages of versatility, high fidelity, easy operation, and fast imaging, enabling comprehensive characterization of van der Waals layered structures for fundamental research and practical applications.