Electric-field switchable second-harmonic generation in bilayer MoS$_{2}$ by inversion symmetry breaking

We demonstrate pronounced electric-field-induced second-harmonic generation in naturally inversion symmetric 2H stacked bilayer MoS$_{2}$ embedded into microcapacitor devices. By applying strong external electric field perturbations ($|F| = \pm 2.6 MVcm^{-1}$) perpendicular to the basal plane of the crystal we control the inversion symmetry breaking and, hereby, tune the nonlinear conversion efficiency. Strong tunability of the nonlinear response is observed throughout the energy range ($E_{\omega} \sim 1.25 eV - 1.47 eV$) probed by measuring the second-harmonic response at $E_{2\omega}$, spectrally detuned from both the A- and B-exciton resonances. A 60-fold enhancement of the second-order nonlinear signal is obtained for emission at $E_{2\omega} = 2.49 eV$, energetically detuned by $\Delta E = E_{2\omega} - E_C = -0.26 eV$ from the C-resonance ($E_{C} = 2.75 eV$). The pronounced spectral dependence of the electric-field-induced second-harmonic generation signal reflects the bandstructure and wave function admixture and exhibits particularly strong tunability below the C-resonance, in good agreement with Density Functional Theory calculations. Moreover, we show that the field-induced second-harmonic generation relies on the interlayer coupling in the bilayer. Our findings strongly suggest that the strong tunability of the electric-field-induced second-harmonic generation signal in bilayer transition metal dichalcogenides may find applications in miniaturized electrically switchable nonlinear devices.