The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice

Abstract

We study the ground state properties of the interacting spinless fermions in the $p_{x,y}$-orbital bands in the two dimensional honeycomb optical lattice, which exhibit different novel features from those in the $p_z$-orbital system of graphene. In addition to two dispersive bands with Dirac cones, the tight-binding band structure exhibits another two completely flat bands over the entire Brillouin zone. With the realistic sinusoidal optical potential, the flat bands acquire a finite but much smaller band width compared to the dispersive bands. The band flatness dramatically enhanced interaction effects giving rise to various charge and bond ordered states at commensurate fillings of $n=\frac{i}{6} (i=1 \sim 6)$. At $n=1/6$, the many-body ground states can be exactly solved as the close packed hexagon states which can be stabilized even in the weak interacting regime. The dimerization of bonding strength occurs at both $n=1/2$ and 5/6, and the latter case is accompanied with the charge density wave of holes. The trimerization of bonding strength and charge inhomogeneity appear at $n={1/3},{2/3}$. These crystalline orders exhibit themselves in the noise correlations of the time of flight spectra.