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Monolayer transition metal dichalcogenides (TMDs) exhibit high nonlinear optical (NLO) susceptibilities. Experiments on MoS$_2$ have indeed revealed very large second-order ($\chi^{(2)}$) and third-order ($\chi^{(3)}$) optical susceptibilities. However, third harmonic generation results of other layered TMDs has not been reported. Furthermore, the reported $\chi^{(2)}$ and $\chi^{(3)}$ of MoS$_2$ vary by several orders of magnitude, and a reliable quantitative comparison of optical nonlinearities across different TMDs has remained elusive. Here, we investigate second- and third-harmonic generation, and three-photon photoluminescence in TMDs. Specifically, we present an experimental study of $\chi^{(2)}$, and $\chi^{(3)}$ of four common TMD materials (\ce{MoS2}, \ce{MoSe2}, \ce{WS2} and \ce{WSe2}) by placing different TMD flakes in close proximity to each other on a common substrate, allowing their NLO properties to be accurately obtained from a single measurement. $\chi^{(2)}$ and $\chi^{(3)}$ of the four monolayer TMDs have been compared, indicating that they exhibit distinct NLO responses. We further present theoretical simulations of these susceptibilities in qualitative agreement with the measurements. Our comparative studies of the NLO responses of different two-dimensional layered materials allow us to select the best candidates for atomic-scale nonlinear photonic applications, such as frequency conversion and all-optical signal processing., Comment: 7 pages, 5 figures, To be appeared in Physical Review B

Similar to electron waves, the phonon states in semiconductors can undergo changes induced by external boundaries. Modification of acoustic phonon spectrum in structures with periodically modulated elastic constant or mass density - referred to as phononic crystals - has been proven experimentally and utilized in practical applications. A possibility of modifying acoustic phonon spectrum in individual nanostructures via spatial confinement would bring tremendous benefits for controlling phonon-electron interaction and thermal conduction at nanoscale. However, despite strong scientific and practical importance, conclusive experimental evidence of acoustic phonon confinement in individual free-standing nanostructures, e.g. nanowires, is still missing. The length scale, at which phonon dispersion undergoes changes and a possibility of the phonon group velocity reduction, are debated. Here, we utilize specially designed high-quality GaAs nanowires (NWs) with different diameters, D, and large inter-nanowire distances to directly demonstrate acoustic phonon confinement. The measurements conducted with Brillouin - Mandelstam spectroscopy reveal confined phonon polarization branches with frequencies from 4 GHz to 40 GHz in NWs with D as large as ~128 nm, i.e. at length scale, which exceeds the "grey" phonon mean-free path in GaAs by an almost an order of magnitude. The phonon dispersion modification and phonon energy scaling with D in individual nanowires are in excellent agreement with theory. The obtained results can lead to more efficient nanoscale control of acoustic phonons, with benefits for nanoelectronics, thermoelectric energy conversion, thermal management, and novel spintronic technologies., Comment: 20 pages; 3 figures