We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N = 1, 2, ... 6 S-Mo-S monolayers have been investigated by optical spectroscopy. Through characterization by absorption, photoluminescence, and photoconductivity spectroscopy, we trace the effect of quantum confinement on the material's electronic structure. With decreasing thickness, the indirect band gap, which lies below the direct gap in the bulk material, shifts upwards in energy by more than 0.6 eV. This leads to a crossover to a direct-gap material in the limit of the single monolayer. Unlike the bulk material, the MoS 2 monolayer emits light strongly. The freestanding monolayer exhibits an increase in luminescence quantum efficiency by more than a factor of 1000 compared with the bulk material.

Molybdenum disulfide (MoS(2)) of single- and few-layer thickness was exfoliated on SiO(2)/Si substrate and characterized by Raman spectroscopy. The number of S-Mo-S layers of the samples was independently determined by contact-mode atomic force microscopy. Two Raman modes, E(1)(2g) and A(1g), exhibited sensitive thickness dependence, with the frequency of the former decreasing and that of the latter increasing with thickness. The results provide a convenient and reliable means for determining layer thickness with atomic-level precision. The opposite direction of the frequency shifts, which cannot be explained solely by van der Waals interlayer coupling, is attributed to Coulombic interactions and possible stacking-induced changes of the intralayer bonding. This work exemplifies the evolution of structural parameters in layered materials in changing from the three-dimensional to the two-dimensional regime.

Two-dimensional (2D) atomic crystals, such as graphene and transition-metal dichalcogenides, have emerged as a new class of materials with remarkable physical properties 1 . In contrast to graphene, monolayer MoS 2 is a non-centrosymmetric material with a direct energy gap 2-5 . Strong photoluminescence 2,3 , a current on-off ratio exceeding 10 8 in field-effect transistors 6 , and efficient valley and spin control by optical helicity 7-9 have recently been demonstrated in this material. Here we report the spectroscopic identification in doped monolayer MoS 2 of tightly bound negative trions, a quasi-particle composed of two electrons and a hole. These quasiparticles, which can be created with valley and spin polarized holes, have no analogue in other materials. They also possess a large binding energy (~ 20 meV), rendering them significant even at room temperature. Our results open up new avenues both for fundamental studies of many-body interactions and for optoelectronic and valleytronic applications in 2D atomic crystals.The trion binding energy that we observe in monolayer MoS 2 is nearly an order of magnitude larger than that found in conventional quasi-2D systems, such as semiconductor quantum wells (QWs) [10][11][12][13] . This is a consequence of the greatly enhanced Coulomb interactions in monolayer MoS 2 , arising from reduced dielectric screening in gapped 2D crystals and the relatively heavy carrier band masses associated with the Mo d-manifolds 4,5,14 . For an electron density as high as n = 10 11 cm -2 , for instance, the dimensionless interaction parameter r s is ~60 in monolayer MoS 2 (Supplementary Information S1). This value is significantly larger than that for carriers in QWs even at very low doping levels 15 . Monolayer MoS 2 is a strongly interacting system even in the presence of relatively high carrier densities; it thus presents an ideal laboratory for exploring many-body phenomena, such as carrier multiplication and Wigner crystallization 16 .The atomic structure of MoS 2 consists of hexagonal planes of S and Mo atoms in a trigonal prismatic structure (Fig. 1a) 17 . The two sublattices of the hexagonal MoS 2 structure are occupied, respectively, by one Mo and two S atoms (Fig. 1b). Monolayer MoS 2 is a direct gap semiconductor with energy gaps located at the K and K' points of the Brillouin zone (Fig. 1c). Both the highest valence bands and the lowest conduction bands are formed primarily from the Mo d-orbitals 4,17 . The large spin-orbit interaction 2 splits the highest valence bands at the K (K') point by ~ 160 meV 2,3,7,14,18 . The valley and spin (VS) degrees are coupled because of the lack of inversion symmetry in monolayer MoS 2 . As has been recently shown experimentally, this allows optical pumping of a single valley (and spin) with circularly polarized light 7-9 .Here we investigate the optical response of monolayer MoS 2 as a function of carrier density by means of absorption and photoluminescence (PL) spectroscopy. In our investigations we have made use of MoS 2 monolayers p...

Using friction force microscopy, we compared the nanoscale frictional characteristics of atomically thin sheets of graphene, molybdenum disulfide (MoS2), niobium diselenide, and hexagonal boron nitride exfoliated onto a weakly adherent substrate (silicon oxide) to those of their bulk counterparts. Measurements down to single atomic sheets revealed that friction monotonically increased as the number of layers decreased for all four materials. Suspended graphene membranes showed the same trend, but binding the graphene strongly to a mica surface suppressed the trend. Tip-sample adhesion forces were indistinguishable for all thicknesses and substrate arrangements. Both graphene and MoS2 exhibited atomic lattice stick-slip friction, with the thinnest sheets possessing a sliding-length-dependent increase in static friction. These observations, coupled with finite element modeling, suggest that the trend arises from the thinner sheets' increased susceptibility to out-of-plane elastic deformation. The generality of the results indicates that this may be a universal characteristic of nanoscale friction for atomically thin materials weakly bound to substrates.

Atomically thin forms of layered materials, such as conducting graphene, insulating hexagonal boron nitride (hBN), and semiconducting molybdenum disulfide (MoS2), have generated great interests recently due to the possibility of combining diverse atomic layers by mechanical "stacking" to create novel materials and devices. In this work, we demonstrate field-effect transistors (FETs) with MoS2 channels, hBN dielectric, and graphene gate electrodes. These devices show field-effect mobilities of up to 45 cm(2)/Vs and operating gate voltage below 10 V, with greatly reduced hysteresis. Taking advantage of the mechanical strength and flexibility of these materials, we demonstrate integration onto a polymer substrate to create flexible and transparent FETs that show unchanged performance up to 1.5% strain. These heterostructure devices consisting of ultrathin two-dimensional (2D) materials open up a new route toward high-performance flexible and transparent electronics.

Pristine graphene is the strongest material ever measured. However, large-area graphene films produced by means of chemical vapor deposition (CVD) are polycrystalline and thus contain grain boundaries that can potentially weaken the material. We combined structural characterization by means of transmission electron microscopy with nanoindentation in order to study the mechanical properties of CVD-graphene films with different grain sizes. We show that the elastic stiffness of CVD-graphene is identical to that of pristine graphene if postprocessing steps avoid damage or rippling. Its strength is only slightly reduced despite the existence of grain boundaries. Indentation tests directly on grain boundaries confirm that they are almost as strong as pristine. Graphene films consisting entirely of well-stitched grain boundaries can retain ultrahigh strength, which is critical for a large variety of applications, such as flexible electronics and strengthening components.

Electron tunneling through atomically flat and ultrathin hexagonal boron nitride (h-BN) on gold-coated mica was investigated using conductive atomic force microscopy. Low-bias direct tunneling was observed in mono-, bi-, and tri-layer h-BN. For all thicknesses, Fowler-Nordheim tunneling (FNT) occurred at high bias, showing an increase of breakdown voltage with thickness. Based on the FNT model, the barrier height for tunneling (3.07 eV) and dielectric strength (7.94 MV/cm) of h-BN are obtained; these values are comparable to those of SiO2.