Fermions with attractive interactions on optical lattices and implications for correlated systems

Abstract

In this paper we address the behavior of the superfluid transition temperature $T_c$ in the attractive Hubbard model. We study systematically the effects of pairing fluctuations and address all filling fractions over the entire range of attractive interaction strength. While the attractive Hubbard model can be regarded as the generalization of BCS to Bose Einstein condensation (BEC) crossover to a lattice, we find that the BEC limit of this Hubbard model is very different from that of jellium, owing to the strong inter-site repulsion between pairs, which becomes important near half filling when the on-site attraction is strong. A central conclusion of our work is that in a lattice, around half filling, the smooth evolution from the BCS to the BEC limits is interrupted. For the attractive Hubbard model, $T_c$ vanishes when the system approaches the bosonic regime with increasing interaction strength. We suggest that the vanishing of $T_c$ at strong coupling strength may signal a quantum critical transition to another form of superfluid not continuously connected to a BCS-like phase. We present a simple variational ansatz for the ground state in this more strongly coupled superfluid. We further generalize the (s-wave) Hubbard model to d-wave pairing and address issues of potential relevance to high temperature superconductors. For the d-wave case, we present a phase diagram and show that here too, one observes a vanishing of $T_c$ when the pairing onset temperature $T^{\ast }$ becomes sufficiently large. We suggest that future experiments on ultracold fermions in optical lattices should not be exclusively limited to the repulsive Hubbard model, but should address the attractive model in order to elucidate features of high temperature superconductivity.

10 pages, 5 figures

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• Fragmentation of Bose-Einstein Condensates
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• Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
• BEC-BCS crossover in an optical lattice
• Popov approximation for composite bosons in the BCS-BEC crossover
• Stability of Superflow for Ultracold Fermions in Optical Lattices
• Superfuid-insulator transitions at non-integer filling in optical lattices of fermionic atoms
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• Perfect Fluids and Bad Metals: Transport Analogies Between Ultracold Fermi Gases and High $T_c$ Superconductors
• Collective modes and superflow instabilities of strongly correlated Fermi superfluids
• s-wave Cooper pair insulators and theory of correlated superconductors
• Repulsive vs. attractive Hubbard model: transport properties and spin-lattice relaxation rate
• Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points
• Anisotropic Ginzburg-Landau and Lawrence-Doniach Models for Layered Ultracold Fermi Gases
• Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices, Part I: Balanced case
• Theory of THz Conductivity in the Pseudogap Phase of the Cuprates: A Pre-Formed Pair Perspective
• Ground states of atomic Fermi gases in a two-dimensional optical lattice with and without population imbalance
• Flat band effects on the ground-state BCS-BEC crossover in atomic Fermi gases in a quasi-two-dimensional Lieb lattice
• Anomalous pseudogap in population imbalanced Fermi superfluids
• Electron pairing and evidence of a BCS-BEC crossover in d-wave superconductors
• Topological phase transition based on the attractive Hubbard model