We study features of weakly-coupled BCS and strongly-coupled BE pair states for dx2-y2 and extended-s (s*) symmetries on a 2D lattice with on-site repulsion U, and nearest-neighbor attraction V. We explore the topological nature of the pair regimes. At arbitrary filling, we find that unlike the s* case, for dx2-y2 symmetry, the BE and BCS regimes are topologically distinct, suggesting a topological phase transition. This is manifested in the electron distribution function vk2 in νk/uk, and in their Fourier transforms. We discuss experimental ramifications of our findings.
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.
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.
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 have analyzed the doping and temperature dependencies of the physical properties of a square-lattice narrow-band superconductor with a relevant for systems with local Hubbard repulsion nematic pairing due to effective nearest-neighbor attraction. Our focus was a possible crossover of the system from the Bardeen–Cooper–Schrieffer (BCS) superconductivity to the Bose–Einstein condensation (BEC) regimes with increasing temperature. We have found that in the d-channel the crossover does not take place at realistic values of doping and temperature, and even at a large attraction, i.e., the system is always in the BCS regime, unlike the “usual” d-wave superconductor. Contrary to non-nematic d-wave superconductors, the chemical potential μ always grows with temperature increase that might indicate an unexpectedly large size of Cooper pairs. At the same time, in the s-channel, we have found a BCS–BEC crossover with temperature for a wide range of temperatures even at rather high dopings, nf ≈ 0.2. This result is different from the “usual” s-case, where a narrow-band (i.e., at strong coupling) system is always in the BEC state. We have found for a given large value of attraction that there is a value of doping when for a wide range of temperature the system is in a “pre-crossover” regime with μ ≈ 0, i.e., in a regime of coexistence of local and extended pairs. Thus, in narrow-band systems a “usual” s-superconductor is in a BEC state, but in the nematic case one can expect a BCS–to–BEC crossover with temperature growth at realistic system parameters, i.e., the crossover might be measured experimentally.
The work by Soares et al. [Phys. Rev. B 65, 174506 (2002)] investigates the BCS to Bose-Einstein crossover for d-wave pairing in the two-dimensional attractive Hubbard model. Contrary to their claims, we found that a nonpairing region does not exist in the density vs coupling phase diagram. The gap parameter at
T=0, as obtained by solving analytically as well as numerically the BCS equations, is in fact finite for any nonzero density and coupling, even in the weak-coupling regime.
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.