Molecular dipoles in designer honeycomb lattices

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