Atomically thin two-dimensional semiconductors such as MoS 2 hold great promise in electrical, optical, and mechanical devices and display novel physical phenomena. However, the electron mobility of mono-and few-layer MoS 2 has so far been substantially below theoretically predicted limits, which has hampered efforts to observe its intrinsic quantum transport behaviours. Potential sources of disorder and scattering include both defects such as sulfur vacancies in the MoS 2 itself, and extrinsic sources such as charged impurities and remote optical phonons from oxide dielectrics. To reduce extrinsic scattering, here we developed a van der Waals heterostructure device platform where MoS 2 layers are fully encapsulated within hexagonal boron nitride, and electrically contacted in a multi-terminal geometry using gate-tunable graphene electrodes. Magneto-transport measurements show dramatic improvements in performance, including a record-high Hall mobility reaching 34,000 cm 2 /Vs for 6-layer MoS 2 at low temperature, confirming that low-temperature performance in previous studies was limited by extrinsic interfacial impurities rather than bulk defects in the MoS 2 . We also observed Shubnikov-de Haas oscillations for the first time in high-mobility monolayer and few-layer MoS 2 . Modeling of potential scattering sources and quantum lifetime analysis indicate that a combination of short-ranged and long-ranged interfacial scattering limits low-temperature mobility of MoS 2 . 3Following the many advances in basic science and applications of graphene, other twodimensional (2D) materials, especially transition metal dichalcogenides (TMDCs), have attracted significant interest for their fascinating electrical, optical, and mechanical properties [1][2][3][4][5][6][7][8] . Among the TMDCs, semiconducting MoS 2 has been the mostly widely studied: it shows a thicknessdependent electronic band structure 3,5 , reasonably high carrier mobility 1,2,6-9 , and novel phenomena such as coupled spin-valley physics and the valley Hall effect 10-14 , leading to various applications, such as transistors 1,7,15 , memories 16 , logic circuits 17,18 , light-emitters 19 , and photo-detectors 20 with flexibility and transparency 2,21 . However, as for any 2D material, the electrical and optical properties of MoS 2 are strongly affected by impurities and its dielectric environment 1,2,9,22 , hindering the study of intrinsic physics and limiting the design of 2D-material-based devices. In particular, the theoretical upper bound of the electron mobility of monolayer (1L) MoS 2 is predicted to be from several tens to a few thousands at room temperature (T) and exceed 10 5 cm 2 /Vs at low T depending on the dielectric environment, impurity density and charge carrier density [23][24][25] . In contrast, experimentally measured 1L MoS 2 devices on SiO 2 substrates have exhibited room-T two-terminal field-effect mobility that ranges from 0.1 -55 cm 2 /Vs 1,26,27 . This value increases to 15 -60 cm 2 /Vs with encapsulation by highdielectric materials 1...

The assembly of individual two-dimensional materials into van der Waals heterostructures enables the construction of layered three-dimensional materials with desirable electronic and optical properties. A core problem in the fabrication of these structures is the formation of clean interfaces between the individual two-dimensional materials which would affect device performance. We present here a technique for the rapid batch fabrication of van der Waals heterostructures, demonstrated by the controlled production of 22 mono-, bi- and trilayer graphene stacks encapsulated in hexagonal boron nitride with close to 100% yield. For the monolayer devices, we found semiclassical mean-free paths up to 0.9 μm, with the narrowest samples showing clear indications of the transport being affected by boundary scattering. The presented method readily lends itself to fabrication of van der Waals heterostructures in both ambient and controlled atmospheres, while the ability to assemble pre-patterned layers paves the way for complex three-dimensional architectures.

The electrical performance of graphene synthesized by chemical vapor deposition and transferred to insulating surfaces may be compromised by extended defects, including for instance grain boundaries, cracks, wrinkles, and tears. In this study, we experimentally investigate and compare the nano- and microscale electrical continuity of single layer graphene grown on centimeter-sized single crystal copper with that of previously studied graphene films, grown on commercially available copper foil, after transfer to SiO2 surfaces. The electrical continuity of the graphene films is analyzed using two noninvasive conductance characterization methods: ultrabroadband terahertz time-domain spectroscopy and micro four-point probe, which probe the electrical properties of the graphene film on different length scales, 100 nm and 10 μm, respectively. Ultrabroadband terahertz time-domain spectroscopy allows for measurement of the complex conductance response in the frequency range 1-15 terahertz, covering the entire intraband conductance spectrum, and reveals that the conductance response for the graphene grown on single crystalline copper intimately follows the Drude model for a barrier-free conductor. In contrast, the graphene grown on commercial copper foil shows a distinctly non-Drude conductance spectrum that is better described by the Drude-Smith model, which incorporates the effect of preferential carrier backscattering associated with extended, electronic barriers with a typical separation on the order of 100 nm. Micro four-point probe resistance values measured on graphene grown on single crystalline copper in two different voltage-current configurations show close agreement with the expected distributions for a continuous 2D conductor, in contrast with previous observations on graphene grown on commercial copper foil. The terahertz and micro four-point probe conductance values of the graphene grown on single crystalline copper shows a close to unity correlation, in contrast with those of the graphene grown on commercial copper foil, which we explain by the absence of extended defects on the microscale in CVD graphene grown on single crystalline copper. The presented results demonstrate that the graphene grown on single crystal copper is electrically continuous on the nanoscopic, microscopic, as well as intermediate length scales.