Giant Enhancement of the Optical Second-Harmonic Emission of ${\mathrm{WSe}}_2$ Monolayers by Laser Excitation at Exciton Resonances

We show that the light-matter interaction in monolayer ${\mathrm{WSe}}_2$ is strongly enhanced when the incoming electromagnetic wave is in resonance with the energy of the exciton states of strongly Coulomb bound electron-hole pairs below the electronic band gap. We perform second harmonic generation (SHG) spectroscopy as a function of laser energy and polarization at $T=4\mathrm{K}$. At the exciton resonance energies we record an enhancement by up to 3 orders of magnitude of the SHG efficiency, due to the unusual combination of electric dipole and magnetic dipole transitions. The energy and parity of the exciton states showing the strong resonance effects are identified in 1- and 2-photon photoluminescence excitation experiments, corroborated by first principles calculations. Targeting the identified exciton states in resonant 2-photon excitation allows us to maximize $k$-valley coherence and polarization.

Figure 1

(a) Optical valley coherence generation following 1-photon absorption, linearly polarized (lin.X). The $1s$ state of the neutral $A$ exciton and the trion (T) transitions are marked. PL spectra copolarized (cross) with the laser are shown in blue (green). The onset of the localized state emission can be seen at low energy. (b) 1-photon optical valley selection rules in the exciton representation for ML ${\mathrm{WSe}}_2$. For simplicity, only the $A$-exciton series is shown. (c) Optical valley coherence generation following 2-photon absorption at $T=4\mathrm{K}$. Inset: SHG intensity (squares) and 2-photon PLE (circles) as a function of laser power.

Figure 2

(a) Schematic for SHG when 2 incident photons are resonant with the $2p$ state of the $A$ exciton (b) results of SHG spectroscopy at $T=4\mathrm{K}$ as a function of $2\hslash \omega$. Typical error bars are shown, based on the standard deviation of the measured laser pulse width (for each wavelength) as a direct measure of the fluctuation of the peak power during the experiment. (c) Schematic for 2-photon PLE, (d) 2-photon PLE intensity (left axis, black squares), and linear polarization (right axis, blue circles) as a function of $2\hslash \omega$. Typical error bar indicated (e) schematic for 1-photon PLE (f), 1-photon PLE intensity (left axis, black squares), and linear polarization (right axis, blue circles) as a function of $\hslash \omega$.

Figure 3

(a) Quasiparticle band structure of ${\mathrm{WSe}}_2$ monolayer at the ${\mathrm{GW}}_0$ level, including spin-orbit coupling perturbatively. (b) Frequency dependent imaginary part of the transverse dielectric function including excitonic effects and oscillator strengths of the optical transitions (bars), calculated at the $\mathrm{BSE}\text{−}{\mathrm{GW}}_0$ level without spin-orbit coupling. The corresponding ${\mathrm{GW}}_0$ gap ($E_g=2.4\pm 0.2\mathrm{eV}$) is also indicated.