▎ 摘　　要

In this paper, we study the electronic structure of monolayer materials based on a double hexagonal geometry with (1x1) and (root 3 x root 3)R30 degrees superstructures. Inspired from the two-dimensional root system of an exceptional Lie algebra called G(2), this hexagonal atomic configuration involves two hexagons of unequal side length at angle 30 degrees. The principal unit hexagonal cell contains twelve atoms instead of the usual configuration involving only six ones relying only on the (1 x 1) superstructure. Using ab initio calculations based on FPLO9.00-34 code, we investigate numerically the graphene and the germanene with the double hexagonal geometry. In particular, we find that the usual electronic properties and the lattice parameters of such materials are modified. More precisely, the lattice parameters are increased. It has been shown that, in the single hexagonal geometry, the grapheme and the germanene behave as a gapless semiconductor and a semi-metallic, respectively. In double hexagonal geometry however, both materials becomes metallic.