壊れた空間反転対称性を備えた2次元六角結晶からの光学的性水準生成

2次元（2D）ハニカム格子構造のπ電子からの光学第二水調波生成（SHG）の顕微鏡理論を提案します。これは、SIC基質やボロニトレン（六角形のボロンニトリド（H-bn）の単一枚のシートでエピタキセンに増殖したグラフェン）などのグラフェンが壊れた壊れた反転対称性を備えています。開発されたアプローチは、最近の論文（2010年Phys。Rev.B82 235426）で詳述されている2次非線形光学応答理論の元のGenkin-Mednis形式と組み合わせた、単純な2バンドπ電子密着モデルに基づいています。アプローチのフレームワーク内で、SHG感受性χ2（SHG（ω）の明示的な式を導き出します。これには、間帯域とπ電子の混合物に由来する2つの異なる寄与が含まれます。数値計算により、2D六角形の格子のブリルアンゾーンの角を回る三角の反りの効果を無視します。これらの理論的所見EGの半分のバンドギャップエネルギーの半分に近づいています。

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.