Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0606470 · Physical Review Letters

BCS-BEC Crossover on the Two-Dimensional Honeycomb Lattice

Erhai Zhao, Arun Paramekanti

Published Dec 7, 2006• 133 citations
arXivHTMLPDF

Abstract

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.

DOI
10.1103/physrevlett.97.230404

Related papers

Attractive Hubbard model on a honeycomb lattice: Quantum Monte Carlo study

Kean Loon Lee, Karim Bouadim, G. G. Batrouni +4 more

We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. 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 $5.0<{U}_{c}/t<5.1$ from a semimetal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half filling, and increasing the interaction strength at finite but low temperature $T$, the system always 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.

arXiv:0909.2987•Physical Review B•Dec 23, 2009•24 citations

BCS-BEC crossover and effects of density fluctuations in a two-component Fermi gas described by the three-dimensional attractive Hubbard model

Hiromasa Tamaki, Yoji Ohashi, K. Miyake

We investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature ${T}_{\mathrm{c}}$, including both superfluid and (spin and charge) density fluctuations within the self-consistent $t$-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS--Bose-Einstein-condensation (BEC) crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of ${T}_{\mathrm{c}}$. As a result, the maximum ${T}_{\mathrm{c}}$ is obtained away from the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half-filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.

Physical Review A•Jun 18, 2008•19 citations

Two-dimensional attractive Hubbard model and the BCS-BEC crossover

Rodrigo A. Fontenele, Natanael C. Costa, Raimundo R. dos Santos +1 more

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 ${T}_{c}$ 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 ${T}_{p}$ and degeneracy ${T}_{d}$ 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.

Physical review. B./Physical review. B•May 2, 2022•34 citations

BCS-BEC crossover and effects of density fluctuations in a two-component Fermi gas loaded on an optical lattice

Hiromasa Tamaki, Yoji Ohashi, Miyake, K.

We investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature Tc, including both superfluid and (spin and charge) density fluctuations within the self-consistent t-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS-BEC crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of Tc. As a result, the maximum Tc is obtained away the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.

arXiv:0803.2084•Mar 14, 2008•1 citation

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

Chih-Chun Chien, Qijin Chen, Kathryn Levin

In this paper we address the behavior of the superfluid transition temperature ${T}_{c}$ in the attractive Hubbard model. The attractive Hubbard model can be regarded as the generalization of the BCS to Bose-Einstein condensation (BEC) crossover to a lattice and, as such, may have implications for future optical lattice studies. Nevertheless, the BEC limit of the Hubbard model is very different from that of the better-studied Fermi gases, owing to the strong intersite repulsion between pairs. Here we address systematically the effects of pairing fluctuations for all filling fractions over the entire range of attractive interaction strength. 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: ${T}_{c}$ vanishes when the system approaches the bosonic regime with increasing interaction strength. We suggest that this interruption of crossover may signal a quantum critical transition to another form of superfluid not continuously connected to a BCS-like phase. A simple variational ansatz for an alternate ground state in this more strongly coupled superfluid is presented. A generalization of the ($s$-wave) Hubbard model to $d$-wave pairing allows us to address issues of relevance to high-${T}_{c}$ superconductivity. The phase diagram (representing the pairing or pseudogap onset temperature ${T}^{*}$ and ${T}_{c}$) shows that here too one observes a vanishing of ${T}_{c}$ when ${T}^{*}$ becomes sufficiently large. Given this predicted breakdown of the crossover, and given the striking similarity to features of the cuprate phase diagram, 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.

arXiv:0808.1900•Physical Review A•Oct 23, 2008•19 citations

Topological superfluids and the BEC-BCS crossover in the attractive Haldane-Hubbard model

Yi‐Cai Zhang, Zhihao Xu, Shizhong Zhang

Motivated by the recent realization of the Haldane model in a shaking optical lattice, we investigate the effects of attractive interaction and the BEC-BCS crossover in this model at and away from half-filling. We show that, contrary to the usual $s$-wave BEC-BCS crossover in the lattice, a topological superfluid with Chern number $C=2$ appears in an extended region of the phase space for intermediate strength of the attractive interaction on the interaction-density plane. When inversion symmetry is broken, a gapless weak topological state is realized. We also investigate the fluctuations in these superfluid phases and show that the Anderson-Bogoliubov mode is quadratic due to time-reversal symmetry breaking and the existence of an undamped Leggett mode in the strong-coupling limit. Near the topological phase transition, the damping of the Leggett mode reaches its maximum.

arXiv:1511.03833•Physical Review A•Apr 28, 2017•15 citations
The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength UUU (relative to the hopping parameter ttt) at half filling and zero temperature, the system undergoes a quantum phase transition at 5.0<Uc/t<5.15.0<{U}_{c}/t<5.15.0<Uc​/t<5.1 from a semimetal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half filling, and increasing the interaction strength at finite but low temperature TTT, the system always 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 UUU is increased and TTT is lowered.
We investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, including both superfluid and (spin and charge) density fluctuations within the self-consistent ttt-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS--Bose-Einstein-condensation (BEC) crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of Tc{T}_{\mathrm{c}}Tc​. As a result, the maximum Tc{T}_{\mathrm{c}}Tc​ is obtained away from the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half-filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.
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{T}_{c}Tc​ in terms of the band filling $\ensuremath{\langle}n\ensuremath{\rangle}$ and interaction strength UUU from which we pinpoint a somewhat wide region $|U|/t\ensuremath{\approx}5\ifmmode\pm\else\textpm\fi{}1$ (ttt 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{T}_{p}Tp​ and degeneracy Td{T}_{d}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 investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature Tc, including both superfluid and (spin and charge) density fluctuations within the self-consistent t-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS-BEC crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of Tc. As a result, the maximum Tc is obtained away the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.
In this paper we address the behavior of the superfluid transition temperature Tc{T}_{c}Tc​ in the attractive Hubbard model. The attractive Hubbard model can be regarded as the generalization of the BCS to Bose-Einstein condensation (BEC) crossover to a lattice and, as such, may have implications for future optical lattice studies. Nevertheless, the BEC limit of the Hubbard model is very different from that of the better-studied Fermi gases, owing to the strong intersite repulsion between pairs. Here we address systematically the effects of pairing fluctuations for all filling fractions over the entire range of attractive interaction strength. 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: Tc{T}_{c}Tc​ vanishes when the system approaches the bosonic regime with increasing interaction strength. We suggest that this interruption of crossover may signal a quantum critical transition to another form of superfluid not continuously connected to a BCS-like phase. A simple variational ansatz for an alternate ground state in this more strongly coupled superfluid is presented. A generalization of the (sss-wave) Hubbard model to ddd-wave pairing allows us to address issues of relevance to high-Tc{T}_{c}Tc​ superconductivity. The phase diagram (representing the pairing or pseudogap onset temperature T∗{T}^{*}T∗ and Tc{T}_{c}Tc​) shows that here too one observes a vanishing of Tc{T}_{c}Tc​ when T∗{T}^{*}T∗ becomes sufficiently large. Given this predicted breakdown of the crossover, and given the striking similarity to features of the cuprate phase diagram, 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.
Motivated by the recent realization of the Haldane model in a shaking optical lattice, we investigate the effects of attractive interaction and the BEC-BCS crossover in this model at and away from half-filling. We show that, contrary to the usual sss-wave BEC-BCS crossover in the lattice, a topological superfluid with Chern number C=2C=2C=2 appears in an extended region of the phase space for intermediate strength of the attractive interaction on the interaction-density plane. When inversion symmetry is broken, a gapless weak topological state is realized. We also investigate the fluctuations in these superfluid phases and show that the Anderson-Bogoliubov mode is quadratic due to time-reversal symmetry breaking and the existence of an undamped Leggett mode in the strong-coupling limit. Near the topological phase transition, the damping of the Leggett mode reaches its maximum.