We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, d(x(2)-y(2)) and extended-s (s()), in the Bardeen-Cooper-Schrieffer-Bose-Einstein Condensation crossover region. We find that the fermion momentum distribution function, v(k)(2), the ratio of the Bogoliubov coefficients, v(k)/u(k), and the Fourier transform of v(k)(2) are strikingly different for d and s() symmetries in the crossover region. The chemical potential and the gap functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.
We study superfluid properties of fermions on a 2D lattice using a finite-range pairing interaction derivable from an extended Hubbard model. We obtain signatures of unconventional pair-symmetry states,
dx2−y2 and extended-s (
s∗), in the BCS-BEC crossover region. The fermion momentum distribution function,
vk2, the ratio of the Bogoliubov coefficients,
vk/uk, and the Fourier transform of
vk2 are among the properties that are strikingly different for d- and
s∗ symmetries in the crossover region. Fermionic atoms in 2D optical lattices may provide a way to observe these signatures. We discuss possible experimental ramifications of our results.
Recent experiments with ultracold fermionic atoms in optical lattices have provided a tuneable and clean realization of the attractive Hubbard model (AHM). In view of this, several physical properties may be thoroughly studied across the crossover between weak (Bardeen-Cooper-Schrieffer, BCS) and strong (Bose-Einstein condensation, BEC) couplings. Here we report on extensive determinant Quantum Monte Carlo (DQMC) studies of the AHM on a square lattice, from which several different quantities have been calculated and should be useful as a roadmap to experiments. We have obtained a detailed phase diagram for the critical superconducting temperature,
Tc, in terms of the band filling, $\ave{n}$, and interaction strength,
U, from which we pinpoint a somewhat wide region
∣U∣/t≈5±1 (
t is the hopping amplitude) and $\ave{n} \approx 0.79 \pm 0.09$ leading to a maximum
Tc≈0.16t. Two additional temperature scales, namely pairing,
Tp, and degeneracy,
Td, have been highlighted: the former sets the scale for pair formation (believed to be closely related to the scale for the gap of spin excitations in cuprates), while the latter sets the scale for dominant quantum effects. Our DQMC data for the distribution of doubly occupied sites, for the momentum distribution function, and for the quasiparticle weight show distinctive features on both sides of the BCS-BEC crossover, being also suggestive of an underlying crossover between Fermi- and non-Fermi liquid behaviors.
We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly bound Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal long-range order for fermions we calculate analytically and numerically the pair binding energy, the energy gap, and the condensate fraction of Cooper pairs as a function of interaction strength and filling factor of atoms in the lattice at zero temperature.
Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.
Recent experiments with ultracold fermionic atoms in optical lattices have provided a tuneable and clean realization of the attractive Hubbard model (AHM). In view of this, several physical properties may be thoroughly studied across the crossover between weak [Bardeen-Cooper-Schrieffer, (BCS)] and strong [Bose-Einstein condensation (BEC)] couplings. Here we report on extensive determinant Quantum Monte Carlo (DQMC) studies of the AHM on a square lattice from which several different quantities have been calculated and should be useful as a road map to experiments. We have obtained a detailed phase diagram for the critical superconducting temperature
Tc in terms of the band filling $\ensuremath{\langle}n\ensuremath{\rangle}$ and interaction strength
U from which we pinpoint a somewhat wide region $|U|/t\ensuremath{\approx}5\ifmmode\pm\else\textpm\fi{}1$ (
t is the hopping amplitude) and $\ensuremath{\langle}n\ensuremath{\rangle}\ensuremath{\approx}0.79\ifmmode\pm\else\textpm\fi{}0.09$ leading to a maximum ${T}_{c}\ensuremath{\approx}0.16t$. Two additional temperature scales, namely, pairing
Tp and degeneracy
Td have been highlighted: The former sets the scale for pair formation (believed to be closely related to the scale for the gap of spin excitations in cuprates), whereas the latter sets the scale for dominant quantum effects. Our DQMC data for the distribution of doubly occupied sites for the momentum distribution function, and for the quasiparticle weight show distinctive features on both sides of the BCS-BEC crossover, being also suggestive of an underlying crossover between Fermi- and non-Fermi liquid behaviors.
We study the finite size effects within the 2D Bose-Einstein-Condensate (BEC) Bardeen-Cooper-Schrieffer(BCS) crossover by varying particle number from small to large to determine the effect on the pairing gap via ground state Diffusion-Monte- Carlo (DMC) calculations. Progress is made in the determination of a 2D mean field gap calculation and the 2D gap expression as well as a potential V(k, k') is derived. Using a two body attractive Poschl-Teller potential and 10 optimization parameters we determine optimized wavefunctions with energy minimization. We then vary the number of particle around closed shell values N=10,18,26,42,50,58 and use prescribed methods to determine the pairing gap through out the crossover region with coupling eta = 0.5 to eta = 3.0. We see predicted energy pairing gap suppression from the mean field line in the BCS limit not seen in previous DMC calculations. These results provide a detailed look at the finite size effects present within the BEC-BCS crossover region and show the sensitivity of the gap to finite size effects.