Molecular dipoles in designer honeycomb lattices

Recent advances in ultracold atoms optical lattices and developments surface science have allowed for the creation of artificial as well control many-body interactions. Such systems provide new settings to investigate interaction-driven instabilities non-trivial topology. In this paper, we explore interplay between molecular electric dipoles on a two-dimensional triangular lattice with fermions hopping dual decorated honeycomb which hosts Dirac flat band states. We show that short-range dipole-dipole interaction can lead ordering into various stripe vortex crystal ground study these ordered states their thermal transitions function range using simulated annealing Monte Carlo methods. For special case zero wave vector ferrodipolar order, incorporating dipole-electron interactions integrating out electrons leads six-state clock model dipole ordering. Finally, discuss impact orders electronic structure local tunneling density Our work may be relevant studies "molecular graphene" -- CO molecules arranged Cu(111) been explored scanning spectroscopy, molecule-fermion mixtures lattices.