Double Resonant Tunable Second Harmonic Generation in Two-dimensional Layered Materials through Band Nesting

We proposed a mechanism to generate giant anisotropic second harmonic nonlinear response via double resonance effect, achieved through electronic bandstructure engineering. The ideal band setup would be a triplet of nested bands separated by the fundamental resonance energy, $\hbar\omega$. We demonstrate theoretically that the proposed phenomenon can be realized in bilayer SnS by band tuning with perpendicular electrical bias, which maximizes the second harmonic susceptibility by several orders of magnitude. Moreover, the tunability of the polarization anisotropy can be useful for realizing novel polarization-sensitive devices.