13-11U

The band spectrum of boson atoms in two-dimensional optical lattices with the graphene type structure is investigated. Dispersion laws in the bands and single-particle spectral densities for normal phase are calculated in the random phase approximation. The gapless spectrum with Dirac points placed on the border of Brillouin zone is obtained in the case if absence of crystal separation into two sublattices. It is shown that even at small differences between particle on site energies in sublattices, there appears a gap in the spectrum. The frequency dependences of the single-particle spectral density for both sublattices (as function of the chemical potential level, the magnitude of gap in the band spectrum as well as temperature) are determined.