Resonant optical second harmonic generation in graphene-based heterostructures

An optical Second-Harmonic Generation (SHG) allows to probe various structural and symmetry-related properties of materials, since it is sensitive to the inversion symmetry breaking in the system. Here, we investigate the SHG response from a single layer of graphene disposed on an insulating hexagonal Boron Nitride (hBN) and Silicon Carbide (SiC) substrates. The considered systems are described by a non-interacting tight-binding model with a mass term, which describes a non-equivalence of two sublattices of graphene when the latter is placed on a substrate. The resulting SHG signal linearly depends on the degree of the inversion symmetry breaking (value of the mass term) and reveals several resonances associated with the band gap, van Hove singularity, and band width. The difficulty in distinguishing between SHG signals coming from the considered heterostrusture and environment (insulating substrate) can be avoided applying a homogeneous magnetic field. The latter creates Landau levels in the energy spectrum and leads to multiple resonances in the SHG spectrum. Position of these resonances explicitly depends on the value of the mass term. We show that at energies below the band-gap of the substrate the SHG signal from the massive graphene becomes resonant at physically relevant values of the applied magnetic field, while the SHG response from the environment stays off-resonant.