Two-dimensional materials such as graphene and transition metal dichalcogenides have attracted great attention because of their rich physics and potential applications in next-generation nanoelectronic devices. The family of two-dimensional materials was recently joined by atomically thin black phosphorus which possesses high theoretical mobility and tunable bandgap structure. However, degradation of properties under atmospheric conditions and high-density charge traps in black phosphorus have largely limited its actual mobility thus hindering its future applications. Here, we report the fabrication of stable sandwiched heterostructures by encapsulating atomically thin black phosphorus between hexagonal boron nitride layers to realize ultra-clean interfaces that allow a high field-effect mobility of ∼1,350 cm2V−1 s−1 at room temperature and on–off ratios exceeding 105. At low temperatures, the mobility even reaches ∼2,700 cm2V−1 s−1 and quantum oscillations in black phosphorus two-dimensional hole gas are observed at low magnetic fields. Importantly, the sandwiched heterostructures ensure that the quality of black phosphorus remains high under ambient conditions.

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.

In few-layer transition metal dichalcogenides (TMDCs), the conduction bands along the ΓK directions shift downward energetically in the presence of interlayer interactions, forming six Q valleys related by threefold rotational symmetry and time reversal symmetry. In even layers, the extra inversion symmetry requires all states to be Kramers degenerate; whereas in odd layers, the intrinsic inversion asymmetry dictates the Q valleys to be spin-valley coupled. Here we report the transport characterization of prominent Shubnikov-de Hass (SdH) oscillations and the observation of the onset of quantum Hall plateaus for the Q-valley electrons in few-layer TMDCs. Universally in the SdH oscillations, we observe a valley Zeeman effect in all odd-layer TMDC devices and a spin Zeeman effect in all even-layer TMDC devices, which provide a crucial information for understanding the unique properties of multi-valley band structures of few-layer TMDCs.