Fig. 1: Second-harmonic generation (SHG) spectroscopy in bilayer MoS₂ with 2H stacking in different dielectric environments.

a Schematics of SHG in MoS₂ bilayers with 2H stacking. b SHG spectra plotted as a function of twice the laser energy 2E_L. Each spectrum is a separate measurement and we plot all the SHG spectra for the different laser energies as in ref. ³⁶. SHG experiments are performed on nonencapsulated 2H MoS₂ bilayers (laser power 4 mW) and hBN-encapsulated samples (10 mW), see (e). The main excitonic transitions are marked: intralayer A, B and interlayer (IE). c Differential reflectivity spectrum of the same sample as a function of photon energy. d Polarization-resolved SHG intensity³³ for 2 × E_L = 2.01 eV in resonance with the interlayer exciton IE (black squares) energy of 2H MoS₂ bilayers. For comparison we show the laser reflection (red circles) which remains constant for each angle. (e, f) same as (b, c), but for bilayer samples encapsulated in hBN. Note that in (e) we have multiplied the SHG signal in the orange shaded region by 10, and in the yellow shaded region by 50 to discern all transitions on a linear scale. In addition to previously identified exciton transitions a new transition at 2.05 eV emerges in SHG spectroscopy, that we tentatively attribute to the A:2s state of the intralayer excitons. High field magneto-optics is needed to confirm this assignment⁷¹ through measuring the diamagnetic shift.