Mean Field Study of a New Nanotube Structure from a Double Hexagonal Symmetry

Abstract

Borrowing ideas from Lie algebras, we propose a new nanotube model based on a double hexagonal geometry appearing in the G 2 Lie symmetry. This structure involves two hexagons of unequal side length at angle 30 ∘ producing $(\sqrt {3}~\times ~\sqrt {3})R30~^{\circ }$ and (1 × 1) geometries. In this configuration system, the principal unit cell contains 12 sites instead of only 6 ones, arising in the single hexagonal structure on which the graphene-like models are based. More precisely, we engineer a superlattice model based on periodic bilayers consisting of particles with the spins $\sigma =\pm \frac {1}{2}$ having two possible states, placed at sites of the double hexagonal structure. Then, we investigate the phase diagrams and the magnetic properties using the mean field method. In particular, we find six stable phases required by a global Z 2 symmetry associated with the spin values placed at the site of the G 2 double hexagonal structure.