We report the observation of optical second harmonic generation (SHG) in single-layer indium selenide (InSe). We measure a second harmonic signal of $>10^3$ $textrm{cts/s}$ under nonresonant excitation using a home-built confocal microscope and a sta
ndard pulsed pico-second laser. We demonstrate that polarization-resolved SHG serves as a fast, non-invasive tool to determine the crystal axes in single-layer InSe and to relate the sharp edges of the flake to the armchair and zigzag edges of the crystal structure. Our experiment determines these angles to an accuracy better than $pm$ $0.2^{circ}$. Treating the two-dimensional material as a nonlinear polarizable sheet, we determine a second-order nonlinear sheet polarizability $| chi_{textrm{sheet}}^{(2)}|=(17.9 pm 11.0)times 10^{-20}$ $textrm{m}^2 textrm{V}^{-1}$ for single-layer InSe, corresponding to an effective nonlinear susceptibility value of $| chi_textrm{eff}^{(2)}| approx (223 pm 138) times 10^{-12}$ $textrm{m} textrm{V}^{-1}$ accounting for the sheet thickness ($textrm{d} approx 0.8$ $textrm{nm}$). We demonstrate that the SHG technique can also be applied to encapsulated samples to probe their crystal orientations. The method is therefore suitable for creating high quality van der Waals heterostructures with control over the crystal directions.
The optical susceptibility is a local, minimally-invasive and spin-selective probe of the ground state of a two-dimensional electron gas. We apply this probe to a gated monolayer of MoS$_2$. We demonstrate that the electrons are spin polarized. Of th
e four available bands, only two are occupied. These two bands have the same spin but different valley quantum numbers. We argue that strong Coulomb interactions are a key aspect of this spontaneous symmetry breaking. The Bohr radius is so small that even electrons located far apart in phase space interact, facilitating exchange couplings to align the spins.
The optics of dangling-bond-free van der Waals heterostructures containing transition metal dichalcogenides are dominated by excitons. A crucial property of a confined exciton is the quantum confined Stark effect (QCSE). Here, such a heterostructure
is used to probe the QCSE by applying a uniform vertical electric field across a molybdenum disulfide (MoS$_2$) monolayer. The photoluminescence emission energies of the neutral and charged excitons shift quadratically with the applied electric field provided the electron density remains constant, demonstrating that the exciton can be polarized. Stark shifts corresponding to about half the homogeneous linewidth were achieved. Neutral and charged exciton polarizabilities of $(7.8~pm~1.0)times 10^{-10}~tr{D~m~V}^{-1}$ and $(6.4~pm~0.9)times 10^{-10}~tr{D~m~V}^{-1}$ at relatively low electron density ($8 times 10^{11}~tr{cm}^{-2}$) have been extracted, respectively. These values are one order of magnitude lower than the previously reported values, but in line with theoretical calculations. The methodology presented here is versatile and can be applied to other semiconducting layered materials as well.
