Semiconductor p-n junctions are essential building blocks for electronic and optoelectronic devices. In conventional p-n junctions, regions depleted of free charge carriers form on either side of the junction, generating built-in potentials associated with uncompensated dopant atoms. Carrier transport across the junction occurs by diffusion and drift processes influenced by the spatial extent of this depletion region. With the advent of atomically thin van der Waals materials and their heterostructures, it is now possible to realize a p-n junction at the ultimate thickness limit. Van der Waals junctions composed of p- and n-type semiconductors--each just one unit cell thick--are predicted to exhibit completely different charge transport characteristics than bulk heterojunctions. Here, we report the characterization of the electronic and optoelectronic properties of atomically thin p-n heterojunctions fabricated using van der Waals assembly of transition-metal dichalcogenides. We observe gate-tunable diode-like current rectification and a photovoltaic response across the p-n interface. We find that the tunnelling-assisted interlayer recombination of the majority carriers is responsible for the tunability of the electronic and optoelectronic processes. Sandwiching an atomic p-n junction between graphene layers enhances the collection of the photoexcited carriers. The atomically scaled van der Waals p-n heterostructures presented here constitute the ultimate functional unit for nanoscale electronic and optoelectronic devices.

We have experimentally determined the energies of the ground and first four excited excitonic states of the fundamental optical transition in monolayer WS2, a model system for the growing class of atomically thin two-dimensional semiconductor crystals. From the spectra, we establish a large exciton binding energy of 0.32 eV and a pronounced deviation from the usual hydrogenic Rydberg series of energy levels of the excitonic states. We explain both of these results using a microscopic theory in which the non-local nature of the effective dielectric screening modifies the functional form of the Coulomb interaction. These strong but unconventional electron-hole interactions are expected to be ubiquitous in atomically thin materials.

The piezoelectric characteristics of nanowires, thin films and bulk crystals have been closely studied for potential applications in sensors, transducers, energy conversion and electronics. With their high crystallinity and ability to withstand enormous strain, two-dimensional materials are of great interest as high-performance piezoelectric materials. Monolayer MoS2 is predicted to be strongly piezoelectric, an effect that disappears in the bulk owing to the opposite orientations of adjacent atomic layers. Here we report the first experimental study of the piezoelectric properties of two-dimensional MoS2 and show that cyclic stretching and releasing of thin MoS2 flakes with an odd number of atomic layers produces oscillating piezoelectric voltage and current outputs, whereas no output is observed for flakes with an even number of layers. A single monolayer flake strained by 0.53% generates a peak output of 15 mV and 20 pA, corresponding to a power density of 2 mW m(-2) and a 5.08% mechanical-to-electrical energy conversion efficiency. In agreement with theoretical predictions, the output increases with decreasing thickness and reverses sign when the strain direction is rotated by 90°. Transport measurements show a strong piezotronic effect in single-layer MoS2, but not in bilayer and bulk MoS2. The coupling between piezoelectricity and semiconducting properties in two-dimensional nanomaterials may enable the development of applications in powering nanodevices, adaptive bioprobes and tunable/stretchable electronics/optoelectronics.

We have measured optical second-harmonic generation (SHG) from atomically thin samples of MoS2 and h-BN with one to five layers. We observe strong SHG from materials with odd layer thickness, for which a noncentrosymmetric structure is expected, while the centrosymmetric materials with even layer thickness do not yield appreciable SHG. SHG for materials with odd layer thickness was measured as a function of crystal orientation. This dependence reveals the rotational symmetry of the lattice and is shown to provide a purely optical method of determining the orientation of crystallographic axes. We report values for the nonlinearity of monolayers and odd-layers of MoS2 and h-BN and compare the variation as a function of layer thickness with a model that accounts for wave propagation effects.

We report a determination of the complex in-plane dielectric function of monolayers of four transition metal dichalcogenides: MoS 2 , MoSe 2 , WS 2 and WSe 2 , for photon energies from 1.5-3 eV. The results were obtained from reflection spectra using a Kramers-Kronig constrained variational analysis. From the dielectric functions, we obtain the absolute absorbance of the monolayers. We also provide a comparison of the dielectric function for the monolayers with the corresponding bulk materials.

High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales [1][2][3][4][5][6] . The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands [7][8][9][10][11][12][13][14] . Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process The recent observation of HHG in bulk solids provides a new approach to attosecond photonics and has opened up exciting opportunities for the study of strong-field and ultrafast electron dynamics in the condensed phase [1][2][3][4][5][6]

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We have measured circularly polarized photoluminescence in monolayer MoSe2 under perpendicular magnetic fields up to 10 T. At low doping densities, the neutral and charged excitons shift linearly with field strength at a rate of ∓0.12  meV/T for emission arising, respectively, from the K and K' valleys. The opposite sign for emission from different valleys demonstrates lifting of the valley degeneracy. The magnitude of the Zeeman shift agrees with predicted magnetic moments for carriers in the conduction and valence bands. The relative intensity of neutral and charged exciton emission is modified by the magnetic field, reflecting the creation of field-induced valley polarization. At high doping levels, the Zeeman shift of the charged exciton increases to ∓0.18  meV/T. This enhancement is attributed to many-body effects on the binding energy of the charged excitons.