Second Harmonic Generation in h-BN and MoS$_2$ monolayers: the role of electron-hole interaction

In this letter we show by means of first principle numerical simulations that electron-hole interaction significantly contributes to the second-harmonic generation spectrum of h-BN or MoS$_2$ monolayers. Specifically, it doubles the signal intensity at the excitonic resonances with respect to the contribution from independent electronic transitions. This result hints that the intensity of second-harmonic signal of those materials can be tuned by changing the dielectric screening, that controls the strength of the electron-hole interaction.