Optical second-harmonic generation from two-dimensional hexagonal crystals with broken space inversion symmetry

Abstract

We propose a microscopic theory of the optical second-harmonic generation (SHG) from π electrons in two-dimensional (2D) honeycomb lattice structures with broken space inversion symmetry, such as graphene epitaxially grown on a SiC substrate and boronitrene (a single sheet of hexagonal boron nitride (h-BN)). The approach developed is based on a simple two-band π-electron tight-binding model combined with the original Genkin-Mednis formalism of the second-order nonlinear optical response theory, detailed in our recent paper (2010 Phys. Rev. B 82 235426). Within the framework of the approach, we derive an explicit expression for the SHG susceptibility χ2(SHG(ω), which involves two distinct contributions originating from a mixture of interband and intraband motion of π electrons. Both the contributions, and, hence, the χ2(SHG(ω) on the whole, are found to tend to zero when the π-electron energy bands involved are treated at the simplest level of approximation, neglecting the effect of their trigonal warping around the corners of the Brillouin zone of the 2D hexagonal lattice. Through numerical calculations, it is shown that this effect, though rather small, leads to a fairly large magnitude of the SHG susceptibility, reaching the order of 10(-4) esu for the graphene/SiC overlayer system and 10(-7) esu for monolayer h-BN, when the pump photon energy ħω approaches half the bandgap energy Eg of those structures. These theoretical findings suggest that SHG can be used as a sensitive optical probe of the electronic structure of the examined 2D hexagonal crystals and simultaneously demonstrate that those crystals may be an appropriate material for practical uses in future optoelectronic nano-devices.

Resonant optical second harmonic generation in graphene-based heterostructures

“…Indeed, we find that, contrary to the result of the Ref. 6, the SHG response is proportional to the band-gap, which in the case of graphene disposed on the substrate is small compared to the band-gap of the clean substrate. Therefore, the SHG signal from graphene can hardly be seen on top of the large SHG signal from the band insulator.…”

Second harmonic generation inh-BN and MoS2monolayers: Role of electron-hole interaction

“…With few isolated exceptions [13][14][15], a large number of calculations of nonlinear optical properties, and specifically of SHG in 2D crystals [16][17][18], employ the independent-particle approximation (IPA), which is inadequate for low-dimensional systems, where it is expected that the strongly bound excitons significantly modify the SHG.…”

Gauge invariance of excitonic linear and nonlinear optical response

“…Nowadays, perturbative calculations of linear and nonlinear optical response functions are routinely performed in the independent-particle approximation (IPA), in which the electron-hole interaction is simply ignored, e.g., see Refs. [3][4][5][6][7][8][9][10][11] (and references therein). However, it is well known that including the electron-hole interaction, i.e., excitonic effects, can have a significant influence on the optical response of solids [12][13][14][15][16].…”