DFT Studies of 2D Materials Inspired by Lie Algebras

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 D4 D4 and D6 D6 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 graphene, silicene, germanene, we investigate two models involving D4 D4 and D6 D6 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. 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 by implementing generalized Cartan matrices.