Defects usually play an important role in tailoring various properties of two-dimensional materials. Defects in two-dimensional monolayer molybdenum disulphide may be responsible for large variation of electric and optical properties. Here we present a comprehensive joint experiment–theory investigation of point defects in monolayer molybdenum disulphide prepared by mechanical exfoliation, physical and chemical vapour deposition. Defect species are systematically identified and their concentrations determined by aberration-corrected scanning transmission electron microscopy, and also studied by ab-initio calculation. Defect density up to 3.5 × 10¹³ cm⁻² is found and the dominant category of defects changes from sulphur vacancy in mechanical exfoliation and chemical vapour deposition samples to molybdenum antisite in physical vapour deposition samples. Influence of defects on electronic structure and charge-carrier mobility are predicted by calculation and observed by electric transport measurement. In light of these results, the growth of ultra-high-quality monolayer molybdenum disulphide appears a primary task for the community pursuing high-performance electronic devices.

Grazing-angle x-ray reflectivity (XRR) is described as an efficient, nondestructive, parameter-free means to measure the mass density of various types of amorphous carbon films down to the nanometer thickness range. It is shown how XRR can also detect layering if it is present in the films, in which case the reflectivity profile must be modeled to derive the density. The mass density can also be derived from the valence electron density via the plasmon energy, which is measured by electron energy-loss spectroscopy (EELS). We formally define an interband effective electron mass $m^{*},$ which accounts for the finite band gap. Comparison of XRR and EELS densities allows us to fit an average $m^{*}=0.87m$ for carbon systems, m being the free-electron mass. We show that, within the Drude-Lorentz model of the optical spectrum, $m^{*}=\left[1-{n\left(0\right)\mathrm{}}^{-2}\right]m,$ where $n\left(0\right)\mathrm{}$ is the refractive index at zero optical frequency. The fraction of ${\mathrm{sp}}^2$ bonding is derived from the carbon K-edge EELS spectrum, and it is shown how a choice of “magic” incidence and collection angles in the scanning transmission electron microscope can give ${\mathrm{sp}}^2$ fraction values that are independent of sample orientation or anisotropy. We thus give a general relationship between mass density and ${\mathrm{sp}}^3$ content for carbon films.

The recent prediction and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years had elapsed since the recognition of the physical significance and potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free-space propagation of optical beams and the time-independent Schrödinger equation governing freely propagating electron vortex beams. There are, however, key differences in the properties of the two kinds of vortex beams. This review is primarily concerned with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution, and the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analyzed, including nanoparticle manipulation and the mechanisms of orbital angular momentum transfer in the electron vortex interaction with matter.