DEVICE MOBILITY MEASUREMENTSThe device is first characterized in the dark state by applying a constant drainsource voltage V ds = 100 mV and sweeping the back-gate voltage V bg . The effective field-effect mobility of the device with 90 nm Au contacts and KOH/O 2 plasma surface pretreatment is estimated from the back gate sweep using the equation � = !" !" !" !" × ! !! ! ! !" where L=1 µm is the channel length, W = 2 µm channel width C i = 1.3×10 -4 Fm -2 the back gate capacitance (C i = ε 0 ε r /d; ε r = 3.9, d = 270 nm). For the device shown in Figure 1a in the manuscript, we obtain the fieldeffect mobility µ = 4 cm 2 /Vs, typical of monolayer MoS 2 devices.

*Semiconductor quantum dots have emerged as promising candidates for the implementation of quantum information processing, because they allow for a quantum interface between stationary spin qubits and propagating single photons [1][2][3] . In the meantime, transition-metal dichalcogenide monolayers have moved to the forefront of solid-state research due to their unique band structure featuring a large bandgap with degenerate valleys and non-zero Berry curvature 4 . Here, we report the observation of zero-dimensional anharmonic quantum emitters, which we refer to as quantum dots, in monolayer tungsten diselenide, with an energy that is 20-100 meV lower than that of two-dimensional excitons. Photon antibunching in second-order photon correlations unequivocally demonstrates the zero-dimensional anharmonic nature of these quantum emitters. The strong anisotropic magnetic response of the spatially localized emission peaks strongly indicates that radiative recombination stems from localized excitons that inherit their electronic properties from the host transition-metal dichalcogenide. The large ∼1 meV zero-field splitting shows that the quantum dots have singlet ground states and an anisotropic confinement that is most probably induced by impurities or defects. The possibility of achieving electrical control in van der Waals heterostructures 5 and to exploit the spin-valley degree of freedom 6 renders transitionmetal-dichalcogenide quantum dots interesting for quantum information processing.Advances in semiconductor-based quantum information processing have been made on two disjoint fronts. While optically active self-assembled quantum dots with deep electron and hole confinement allow for the realization of highly efficient single-photon sources 7 , all-optical manipulation of confined spins 8,9 and a spinphoton quantum interface 3,10 , the random nature of their growth seems to be the biggest hindrance to their use in scalable quantum information processing. In contrast, electrically defined single 11 or double quantum dots 12 hosting one or two excess electrons have been shown to exhibit long spin coherence times together with a clear path towards integrated scalable devices. However, weaker confinement has precluded the possibility to reliably transfer quantum information from spins to photons in these systems. Quantum dots in monolayer transition-metal dichalcogenides (TMDs) have the potential to combine the desirable features of both optically active and electrically defined quantum dots. Although we report tungsten diselenide (WSe 2 ) quantum dots that appear due to uncontrolled impurity-or defect-induced traps, the two-dimensional nature of these materials makes it easier to electrically control the local potentials on a scale of a few tens of nanometres. More importantly, strong electron-hole binding in TMDs suggests that it would be possible to obtain a quantized optical excitation spectrum due to trapping of excitons or trions in large electric field gradients induced by external gates 13 .The samples we s...

A monolayer of a transition metal dichalcogenide such as WSe 2 is a two-dimensional direct-bandgap valley-semiconductor 1,2 having an e ective honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly polarized light fields 3-5 , suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom 6-8 . Here we report such experiments that demonstrate the valley Zeeman e ect-strongly anisotropic lifting of the degeneracy of the valley pseudospin degree of freedom using an external magnetic field. The valley-splitting measured using the exciton transition deviates appreciably from values calculated using a three-band tight-binding model 9 for an independent electron-hole pair at ±K valleys. We show, on the other hand, that a theoretical model taking into account the strongly bound nature of the exciton yields an excellent agreement with the experimentally observed splitting. In contrast to the exciton, the trion transition exhibits an unexpectedly large valley Zeeman e ect that cannot be understood within the same framework, hinting at a di erent contribution to the trion magnetic moment. Our results raise the possibility of controlling the valley degree of freedom using magnetic fields in monolayer transition metal dichalcogenides or observing topological states of photons strongly coupled to elementary optical excitations in a microcavity 10 .Charge carriers in two-dimensional (2D) layered materials with a honeycomb lattice, such as graphene and transition metal dichalcogenides (TMDs), have a twofold valley degree of freedom labelled by ±K-points of the Brillouin zone, which are related to each other by time-reversal symmetry 7 . In TMDs, the low-energy physics takes place in the vicinity of ±K-points of the conduction and valence bands with Bloch states that are formed primarily from d z 2 and d x 2 −y 2 , d xy orbitals of the transition metal, respectively 9 . The magnetic moment of charged particles in a monolayer TMD arises from two distinct contributions: the intracellular component stems from the hybridization of the d x 2 −y 2 and d xy orbitals as d x 2 −y 2 ± id xy , which provide the Bloch electrons at ±K in the valence band an azimuthal angular momentum along z of l z = ±2h (Fig. 1a). The second-intercellular-contribution originates from the phase winding of the Bloch functions at ±K-points 11-14 . This latter contribution to orbital magnetic moment is different for conduction and valence bands owing to breakdown of electronhole symmetry. Both contributions yield magnetic-field-induced splitting with an opposite sign in the two valleys.In a 2D material such as a monolayer TMD, the current circulation from the orbitals can only be within the plane; as a consequence, the corresponding orbital magnetic moment can only point out-of-plane. A magnetic field (B) along z distinguishes the sense of circulation in 2D, causing opposite energy shifts (− µ· B) in ±K val...

Two-dimensional (2D) materials such as monolayer molybdenum disulfide (MoS(2)) are extremely interesting for integration in nanoelectronic devices where they represent the ultimate limit of miniaturization in the vertical direction. Thanks to the presence of a band gap and subnanometer thickness, monolayer MoS(2) can be used for the fabrication of transistors exhibiting extremely high on/off ratios and very low power dissipation. Here, we report on the development of 2D MoS(2) transistors with improved performance due to enhanced electrostatic control. Our devices show currents in the 100 μA/μm range and transconductance exceeding 20 μS/μm as well as current saturation. We also record electrical breakdown of our devices and find that MoS(2) can support very high current densities, exceeding the current-carrying capacity of copper by a factor of 50. Our results push the performance limit of MoS(2) and open the way to their use in low-power and low-cost analog and radio frequency circuits.

CONSPECTUS: Atomic crystals of two-dimensional materials consisting of single sheets extracted from layered materials are gaining increasing attention. The most well-known material from this group is graphene, a single layer of graphite that can be extracted from the bulk material or grown on a suitable substrate. Its discovery has given rise to intense research effort culminating in the 2010 Nobel Prize in physics awarded to Andre Geim and Konstantin Novoselov. Graphene however represents only the proverbial tip of the iceberg, and increasing attention of researchers is now turning towards the veritable zoo of so-called "other 2D materials". They have properties complementary to graphene, which in its pristine form lacks a bandgap: MoS 2 , for example, is a semiconductor, while NbSe 2 is a superconductor. They could hold the key to important practical applications and new scientific discoveries in the two-dimensional limit. This family of materials has been studied since the 1960s, but most of the research focused on their tribological applications: MoS 2 is best known today as a high-performance dry lubricant for ultrahigh-vacuum applications and in car engines. The realization that single layers of MoS 2 and related materials could also be used in functional electronic devices where they could offer advantages compared with silicon or graphene created a renewed interest in these materials. MoS 2 is currently gaining the most attention because the material is easily available in the form of a mineral, molybdenite, but other 2D transition metal dichalcogenide (TMD) semiconductors are expected to have qualitatively similar properties. In this Account, we describe recent progress in the area of single-layer MoS 2 -based devices for electronic circuits. We will start with MoS 2 transistors, which showed for the first time that devices based on MoS 2 and related TMDs could have electrical properties on the same level as other, more established semiconducting materials. This allowed rapid progress in this area and was followed by demonstrations of basic digital circuits and transistors operating in the technologically relevant gigahertz range of frequencies, showing that the mobility of MoS 2 and TMD materials is sufficiently high to allow device operation at such high frequencies. Monolayer MoS 2 and other TMDs are also direct band gap semiconductors making them interesting for realizing optoelectronic devices. These range from simple phototransistors showing high sensitivity and low noise, to light emitting diodes and solar cells. All the electronic and optoelectronic properties of MoS 2 and TMDs are accompanied by interesting mechanical properties with monolayer MoS 2 being as stiff as steel and 30× stronger. This makes it especially interesting in the context of flexible electronics where it could combine the high degree of mechanical flexibility commonly associated with organic semiconductors with high levels of electrical performance. All these results show that MoS 2 and TMDs are promising materials for elect...