Microscopic quantum description of second-order nonlinearities in two-dimensional hexagonal nanostructures beyond the Dirac cone approximation

Abstract

Single layers of hexagonal two-dimensional nanostructures such as graphene, silicene, and germanene exhibit large carrier Fermi velocities and, consequently, large light-matter coupling strength making these materials promising elements for nano-optoelectronics. Although these materials are centrosymmetric, the spatial dispersion turns out to be quite large allowing the second-order noninear response of such materials to be comparable to the noncentrosymmetric 2D ones. The second-order response of massless Dirac fermions has been extensively studied, however, a general approach correct over the full Brillouin zone is lacking so far. To complete this gap, in the current paper, we develop a general quantum-mechanical theory of the in-plane second-order nonlinear response beyond the Dirac cone approximation and applicable to the full Brillouin zone of the hexagonal tight-binding nanostructures. We present explicit calculation of the nonlinear susceptibility tensor of 2D hexagonal nanostructures applicable to arbitrary three-wave mixing processes.