Molybdenum disulphide is a novel two-dimensional semiconductor with potential applications in electronic and optoelectronic devices. However, the nature of charge transport in back-gated devices still remains elusive as they show much lower mobility than theoretical calculations and native n-type doping. Here we report a study of transport in few-layer molybdenum disulphide, together with transmission electron microscopy and density functional theory. We provide direct evidence that sulphur vacancies exist in molybdenum disulphide, introducing localized donor states inside the bandgap. Under low carrier densities, the transport exhibits nearest-neighbour hopping at high temperatures and variable-range hopping at low temperatures, which can be well explained under Mott formalism. We suggest that the low-carrier-density transport is dominated by hopping via these localized gap states. Our study reveals the important role of short-range surface defects in tailoring the properties and device applications of molybdenum disulphide.

Abstract:We demonstrate that a field effect transistor ( Main Text:Few-layer black phosphorus (BP) has received in recent years much attention due to its unique properties making this layered material attractive for technological applications(1-3). This twodimensional crystal has an anisotropic structure (Fig.1a) and is characterized by a BP thickness dependent direct band gap(4). In contrast to graphene, the presence of a band gap in BP permits for a selective depletion of charge carriers by electrostatic gating, which is an essential feature in field effect transistors (FETs). A high charge carrier mobility reaching 1000 cm 2 /Vs at room temperature accentuates this material for applications at room temperature(5). However, the exposure of BP crystals to ambient conditions causes the oxidation of BP and significantly degrades the quality of BP channels. Nevertheless, the encapsulation of BP layers by hexagonal boron nitride (h-BN) sheets in air or in an inert gas environment is found to be very effective for preventing BP oxidation(6-8). Surface impurity effects are largely reduced, and high charge carrier mobility up to several 10 3 cm 2 /Vs has been obtained in BP FETs at cryogenic temperature(6-8). The charge carrier scattering at the impurities encapsulated along with the BP layers hinders further mobility increase. Figure 1a shows Fig.1c). The mobility values are more than four times larger compared with that in previous studies, which indicates the improved quality of h-BN/BP interfaces(7). In spite of using the advanced fabrication technique,  FET and  H saturate at T<20 K, which implies that the disorder scattering dominates over the phonon scattering in this temperature regime, which limits the hole mobility at cryogenic temperature(9). The increase of  H with the carrier density p (Fig. 1c) suggests that the disorder potential is likely created by residual impurities and can be screened by the mobile carriers (7,10,11). The scattering behavior changes at high temperatures (T>100 K).  FET and  H decrease with increasing T and follow the dependence T    , where  =1.9 and 2.0 characterize the dependence for  H and  FET , respectively (black line in Fig. 1c). The large  values imply that the acoustic phonon rather than the optical phonon scattering dominates over the scattering by the residual impurities in this temperature regime. It is very noticeable that the room temperature hole mobility  H = 5200 cm 2 /Vs closely approaches the theoretically predicted hole mobility for a clean five-layer BP sheets, which lies in the range between 4,800 cm 2 V -1 s -1 and 6,400 cm 2 V -1 s -1 (9). The realization 4 of the predicated mobility value, which is solely limited by the phonon scattering at room temperature, is another demonstration of the improved BP heterostructure quality. Quantum Hall Effect (QHE) in BP 2DHGFigure 2a shows Hall resistance R yx and magnetoresistance R xx as a function of the magnetic field, which is measured in a clean heterostructure at the base temperature of the experim...

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.