DFT studies of 2D materials inspired by Lie algebras

Abstract

Inspired by the root systems of Lie algebras of rank 2, we propose a mathematical method to engineer new 2D materials with double periodic structures tessellating the plane. Concretely, we investigate two geometries relaying on squares and hexagons exhibiting the D 4 × D 4 and D 6 × D 6 dihedral group invariances, respectively. Due to lack of empirical verifications of such double configurations, we provide a numerical investigation by help of the open source quantum espresso. Motivated by hybrid structures of the graphene, the silicene, and the germanene, we investigate two models involving the D 4 × D 4 and D 6 × D 6 dihedral symmetries which we refer to as Si4Ge4 and Si6C6 compounds, respectively. For simplicities, we study only the opto-electronic physical properties by applying an electromagnetic source propagating in linear and isotropic mediums. Among others, we find that such 2D materials exhibit metallic behaviors with certain optical features. Precisely, we compute and discuss the relavant optical quantities including the dielectric function, the absorption spectra, the refractive index, and the reflectivity. We believe that the Lie algebra inspiration of such 2D material studies, via density functional theory techniques, could open new roads to think about higher dimensional cases.