Electric-field tuned second harmonic generation in twisted bilayer graphene

We report our theoretical investigation into both the twist angle-dependent and the electric field-controlled second harmonic generation (SHG) effect in twisted bilayer graphene (tBLG) based on the four-band continuum model and independent-particle approximation. This analytical theory provides a quantitative explanation for the twist angle-dependent SHG effect observed in noncentrosymmetric tBLG, as reported in [Matter3, 1361 (2020)10.1016/j.matt.2020.08.018], which represents a groundbreaking exploration introducing the twisting degree of freedom into nonlinear optics. Due to the one-photon and two-photon resonant transitions as well as the strong interlayer coupling, the SHG susceptibility of tBLG, which primarily stemmed from interband transitions, can reach up to 10³ pm²/V and increases as the twist angle decreases. Additionally, the application of an external electric field can boost the SHG susceptibility by at least one order of magnitude and effectively tune both the magnitude and the positions of the absorption peak with wider range by manipulating the movement of Dirac cones and van Hove singularities. These findings provide valuable insights for the design and implementation of optoelectronic devices with wide-band tunability and high-performance.