  Second Harmonic Generation (SHG) of single-layer monochalcogenides, such as
GaSe and InSe, has been recently reported [2D Mater. 5 (2018) 025019; J. Am.
Chem. Soc. 2015, 137, 79947997] to be extremely strong with respect to bulk and
multilayer forms. To clarify the origin of this strong SHG signal, we perform
first-principles real-time simulations of linear and non-linear optical
properties of these two-dimensional semiconducting materials. The simulations,
based on ab-initio many-body theory, accurately treat the electron-hole
correlation and capture excitonic effects that are deemed important to
correctly predict the optical properties of such systems. We find indeed that,
as observed for other 2D systems, the SHG intensity is redistributed at
excitonic resonances. The obtained theoretical SHG intensity is an order of
magnitude smaller than that reported at the experimental level. This result is
in substantial agreement with previously published simulations which neglected
the electron-hole correlation, demonstrating that many-body interactions are
not at the origin of the strong SHG measured. We then show that the
experimental data can be reconciled with the theoretical prediction when a
single layer model, rather than a bulk one, is used to extract the SHG
coefficient from the experimental data.
