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arXiv:1112.1154 · Europhysics Letters (EPL)

Pairing properties of cold fermions in a honeycomb lattice

Benoît Grémaud

Published May 1, 2012• 4 citations
arXivHTMLPDF

Abstract

The pairing properties of ultracold fermions, with an attractive interaction, loaded in a honeycomb (graphene-like) optical lattice are studied in a mean-field approach. We emphasize, in the presence of a harmonic trap, the unambiguous signatures of the band structure around half-filling ( i.e. the conical intersections) in the local order parameter, in particular in the situations of either imbalanced hopping parameters or imbalanced populations. It can also be observed in the system response to external perturbation, for instance by measuring the pair destruction rate when modulating the optical lattice depth. Going beyond the mean-field level, we estimate the critical temperature for the "condensation" of the preformed pairs.

DOI
10.1209/0295-5075/98/47003

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The pairing properties of ultracold fermions, with an attractive interaction, loaded in a honeycomb (graphene-like) optical lattice are studied in a mean-field approach. We emphasize, in the presence of a harmonic trap, the unambiguous signatures of the band structure around half-filling ( i.e. the conical intersections) in the local order parameter, in particular in the situations of either imbalanced hopping parameters or imbalanced populations. It can also be observed in the system response to external perturbation, for instance by measuring the pair destruction rate when modulating the optical lattice depth. Going beyond the mean-field level, we estimate the critical temperature for the "condensation" of the preformed pairs.
Pairing in a population-imbalanced Fermi system in a two-dimensional optical lattice is studied using determinant quantum Monte Carlo simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovchinnikov phase. Contrary to claims of fragility with increased dimensionality, we find that this phase is stable across a wide range of values for the polarization, temperature, and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center-of-mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold-atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels, which can be seen as the analog of the finite center-of-mass momentum pairing in the translationally invariant case. Finally, we perform mean-field calculations for the uniform and confined systems and show the results to be in good agreement with quantum Monte Carlo. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.
Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\ensuremath{\pi}/3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter t0{t}_{0}t0​ as a function of the optical lattice parameters. Our semiclassical instanton method proves 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. 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. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\ensuremath{\pi}/3$.
We study the pairing in an attractively interacting two-component Fermi gas in an optical lattice with a mixed geometry, where up-spin component is loaded on a honeycomb lattice while the down-spin component can occupy only the triangular sub-lattice of the honeycomb lattice. This system realizes a new type of the Fermi- Hubbard model, and we draw the phase diagram of the system within mean field theory. Our system differs from typical systems described by the usual BCS theory: First, it has three quasi particle energy bands. Second, the interaction is spatially inhomogeneous. Third, our system has natural mass-imbalance. We find that the ratio of the gap at zero temperature and the critical temperature does not agree with the value obtained from the BCS theory. We construct the phase diagram of the system by minimizing the grand potential to solve the superfluid order parameter. We find two qualitatively very different phase diagrams, one near the half-filling of the honeycomb lattice and the other at lower densities. In the near-half-filled systems, we find an exotic superfluid phase which resembles the breached pair phase. In this new phase, however, the minority component is not completely depleted in the momentum space breach. The state has two pairing channels. We find polarization even at zero temperature in this phase. We find out that the order of the superfluid phase transition depends also on the density. At low densities, we find tricritical points, at which the order of the transition changes. Near half-filling, we find no tricritical points and that the transition is always of second order. Our system has a nonuniform coupling, arising from the spatially inhomogeneous interaction. We find that this results in a chirally p-wave symmetric pairing, which is different from the usual isotropic (s-wave) pairing.
Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak coupling, we find that the maximum mean-field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean-field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence for a sharp sound mode, together with a well-defined Leggett mode over a wide region of the phase diagram. We also calculate the superfluid order parameter and collective modes in the presence of nonzero superfluid flow. The flow-induced softening of these collective modes leads to dynamical instabilities involving stripelike density modulations as well as a Leggett-mode instability associated with the natural sublattice symmetry-breaking charge-ordered state on the honeycomb lattice. The latter provides a nontrivial test for the experimental realization of the one-band Hubbard model. We delineate regimes of the phase diagram where the critical current is limited by depairing or by such collective instabilities, and discuss experimental implications of our results.
Using mean-field theory, we investigate the ground-state properties of ultracold bosons loaded in a honeycomb lattice with on-site repulsive interactions and imbalanced nearest-neighbor hopping amplitudes. Taking into account correlations between strongly coupled neighboring sites through an improved Gutzwiller ansatz, we predict the existence of half-integer Mott-insulator phases, i.e., states with half-integer filling and vanishing compressibility. These insulating phases result from the interplay between quantum correlations and the topology of the honeycomb lattice, and could be easily addressed experimentally because they have clear signatures in momentum space.
Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal repulsive on-site interactions U>0U>0U>0. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., they should be accessible to experiments. In addition, we present spectral functions and discuss the properties of a ``semicompressible'' state observed for large UUU near half filling.