Ultracold fermions in a honeycomb optical lattice

Abstract

A honeycomb lattice half-filled with fermions has its excitations described by massless Dirac fermions, e.g. graphene. We investigate the experimental feasibility of loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb structure and we go beyond graphene by addressing interactions between fermions in such a lattice. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles 2pi/3. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and the excitations obey Weyl-Dirac equations. In an ideal honeycomb lattice, the presence of Dirac cones is a consequence of the point group symmetry and it is independent of the optical potential depth. We obtain the important parameter that characterizes the tight-binding model, the nearest-neighbor hopping parameter t, as a function of the optical lattice parameters. Our semiclassical instanton method is in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. The presence of the Dirac cones can be understood in terms of geometrical configuration of hopping parameters. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. To study the interactions between fermions, we focus on attractive fermionic Hubbard model on a honeycomb lattice. The study is carried out using determinant quantum Monte Carlo algorithm and we extract the frequency-dependent spectral function using maximum entropy method. By increasing the interaction strength U (relative to the hopping parameter t) at half-filling and zero temperature, the system undergoes a quantum phase transition at U_c/t< 5 from a disordered phase to a phase displaying simultaneously superfluid behavior and density order. Meng et al. reported recently a lower critical strength and they showed that the system first enters a pseudo-spin liquid phase before becoming superfluid. We attributed the discrepancy in the numbers to the ?relatively high? temperature at which our simulations were performed. We were not able to identify the pseudo-spin liquid phase because computing the relevant time-displaced pair Green?s function is computationally too expensive for us. Doping away from half-filling, and increasing the interaction strength at finite but low temperature T, the system appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as U is increased and T is lowered.