Superlight small pairs in face-centered-cubic extended Hubbard models

Ganiyu D. Adebanjo, P. E. Kornilovitch, J. P. Hague

Published Sep 7, 2021• 0 citations

Abstract

We exactly solve a two-particle $UV$ model to explore the behavior of pairs in a face-centered cubic (FCC) lattice within an extended Hubbard model. The conditions for pair formation, pair mass, pair size, and the Bose-Einstein condensation (BEC) temperature are examined. Our results show that strongly bound, superlight and small pairs can be generated in the FCC lattice, which are much lighter than pairs in other 3D lattices. We estimate that such pairs can Bose condense at high temperatures even if the lattice constant is large. Therefore, in the search for materials with high superconducting transition temperatures, three-dimensional materials with an underlying FCC structure should be investigated due to the possibility of superlight small pairs.

Related papers

Superlight pairs in face-centred-cubic extended Hubbard models with strong Coulomb repulsion

G D Adebanjo, P E Kornilovitch, J P Hague

arXiv:2109.03031Journal of Physics Condensed MatterJan 5, 20224 citations

Fermion pair formation and condensation in extended Hubbard models in body-centered-cubic optical lattices

Ganiyu D. Adebanjo, P. E. Kornilovitch, J. P. Hague

Feb 15, 20210 citations

Ubiquitous light real-space pairing from long-range hopping and interactions

Ganiyu D. Adebanjo, J. P. Hague, P. E. Kornilovitch

arXiv:2211.06498Physics Letters AApr 5, 202411 citations

Bose-Einstein condensation in tight-binding bands

R. Ramakumar, A. N. Das

arXiv:cond-mat/0505539Physical Review BSep 2, 20059 citations

From BCS-like superconductivity to condensation of local pairs: A numerical study of the attractive Hubbard model

Johannes Maria Singer, M. H. Pedersen, T. Schneider +2 more

Physical review. B, Condensed matterJul 1, 199697 citations

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

Chih-Chun Chien, Qijin Chen, Kathryn Levin

arXiv:0808.1900Physical Review AOct 23, 200819 citations

Superlight small pairs in face-centered-cubic extended Hubbard models

Ganiyu D. Adebanjo, P. E. Kornilovitch, J. P. Hague

Published Sep 7, 2021• 0 citations

OpenAlex

Abstract

We exactly solve a two-particle

UV

model to explore the behavior of pairs in a face-centered cubic (FCC) lattice within an extended Hubbard model. The conditions for pair formation, pair mass, pair size, and the Bose-Einstein condensation (BEC) temperature are examined. Our results show that strongly bound, superlight and small pairs can be generated in the FCC lattice, which are much lighter than pairs in other 3D lattices. We estimate that such pairs can Bose condense at high temperatures even if the lattice constant is large. Therefore, in the search for materials with high superconducting transition temperatures, three-dimensional materials with an underlying FCC structure should be investigated due to the possibility of superlight small pairs.

Related papers

Superlight pairs in face-centred-cubic extended Hubbard models with strong Coulomb repulsion

G D Adebanjo, P E Kornilovitch, J P Hague

The majority of fulleride superconductors with unusually high transition-temperature to kinetic-energy ratios have a face-centred-cubic (FCC) structure. We demonstrate that, within extended Hubbard models with strong Coulomb repulsion, paired fermions in FCC lattices have qualitatively different properties than pairs in other three-dimensional cubic lattices. Our results show that strongly bound, light, and small pairs can be generated in FCC lattices across a wide range of the parameter space. We estimate that such pairs can Bose condense at high temperatures even if the lattice constant is large (as in the fullerides).The majority of fulleride superconductors with unusually high transition-temperature to kinetic-energy ratios have a face-centred-cubic (FCC) structure. We demonstrate that, within extended Hubbard models with strong Coulomb repulsion, paired fermions in FCC lattices have qualitatively different properties than pairs in other three-dimensional cubic lattices. Our results show that strongly bound, light, and small pairs can be generated in FCC lattices across a wide range of the parameter space. We estimate that such pairs can Bose condense at high temperatures even if the lattice constant is large (as in the fullerides).

arXiv:2109.03031Journal of Physics Condensed MatterJan 5, 20224 citations

Fermion pair formation and condensation in extended Hubbard models in body-centered-cubic optical lattices

Ganiyu D. Adebanjo, P. E. Kornilovitch, J. P. Hague

We investigate the formation and condensation of fermion pairs in cold atom quantum simulators for extended Hubbard models (UV models) with body center cubic (BCC) optical lattices, predicting small and light pairs with Bose--Einstein condensation (BEC) temperatures up to the order of 100 nK. Pair mass, radius, and binding conditions are calculated, and then used to compute transition temperatures. We predict that: (a) local pairs can form in BCC optical lattices; (b) for particular cases where the onsite $U$ and intersite V are attractive with similar size, the pairs are both small and light; and (c) that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms in blue (red) BCC optical lattices. Beyond the application to pairs on BCC optical lattices, we expect our results to be relevant to strong-coupling BCC superconductors.We investigate the formation and condensation of fermion pairs in cold atom quantum simulators for extended Hubbard models (UV models) with body center cubic (BCC) optical lattices, predicting small and light pairs with Bose--Einstein condensation (BEC) temperatures up to the order of 100 nK. Pair mass, radius, and binding conditions are calculated, and then used to compute transition temperatures. We predict that: (a) local pairs can form in BCC optical lattices; (b) for particular cases where the onsite $U$ and intersite V are attractive with similar size, the pairs are both small and light; and (c) that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms in blue (red) BCC optical lattices. Beyond the application to pairs on BCC optical lattices, we expect our results to be relevant to strong-coupling BCC superconductors.

Feb 15, 20210 citations

Ubiquitous light real-space pairing from long-range hopping and interactions

Ganiyu D. Adebanjo, J. P. Hague, P. E. Kornilovitch

We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbour hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎ are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼t‾0.1, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbour hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎ are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼t‾0.1, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.

arXiv:2211.06498Physics Letters AApr 5, 202411 citations

Bose-Einstein condensation in tight-binding bands

R. Ramakumar, A. N. Das

We present a theoretical study of the condensation of bosons in tight-binding bands corresponding to simple cubic, body-centered cubic, and face-centered cubic lattices. We have analyzed noninteracting bosons, weakly interacting bosons using the Bogoliubov method, and strongly interacting bosons through a renormalized Hamiltonian approach valid for the number of bosons per site less than or equal to unity. In all the cases studied, we find that bosons in a body-centered cubic lattice have the highest Bose condensation temperature. The growth of the condensate fraction of noninteracting bosons is found to be very close to that of free bosons. The interaction partially depletes the condensate at zero temperature and close to it, while enhancing it beyond this range below the Bose-Einstein condensation temperature. Strong interaction enhances the boson effective mass as the band-filling is increased and eventually localizes the bosons to form a Bose-Mott-Hubbard insulator for integer filling.We present a theoretical study of the condensation of bosons in tight-binding bands corresponding to simple cubic, body-centered cubic, and face-centered cubic lattices. We have analyzed noninteracting bosons, weakly interacting bosons using the Bogoliubov method, and strongly interacting bosons through a renormalized Hamiltonian approach valid for the number of bosons per site less than or equal to unity. In all the cases studied, we find that bosons in a body-centered cubic lattice have the highest Bose condensation temperature. The growth of the condensate fraction of noninteracting bosons is found to be very close to that of free bosons. The interaction partially depletes the condensate at zero temperature and close to it, while enhancing it beyond this range below the Bose-Einstein condensation temperature. Strong interaction enhances the boson effective mass as the band-filling is increased and eventually localizes the bosons to form a Bose-Mott-Hubbard insulator for integer filling.

arXiv:cond-mat/0505539Physical Review BSep 2, 20059 citations

From BCS-like superconductivity to condensation of local pairs: A numerical study of the attractive Hubbard model

Johannes Maria Singer, M. H. Pedersen, T. Schneider +2 more

We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above ${\mathit{T}}_{\mathit{c}}$ . These features are also mirrored in the shape of the specific-heat peak around ${\mathit{T}}_{\mathit{c}}$ , the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak-coupling regime to a superconductivity properly described by a Bose-Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above ${\mathit{T}}_{\mathit{c}}$. These features are also mirrored in the shape of the specific-heat peak around ${\mathit{T}}_{\mathit{c}}$, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterJul 1, 199697 citations

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.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:0808.1900Physical Review AOct 23, 200819 citations

We exactly solve a two-particle

UV

U

and intersite V are attractive with similar size, the pairs are both small and light; and (c) that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms in blue (red) BCC optical lattices. Beyond the application to pairs on BCC optical lattices, we expect our results to be relevant to strong-coupling BCC superconductors.

{\mathit{T}}_{\mathit{c}}

. These features are also mirrored in the shape of the specific-heat peak around

{\mathit{T}}_{\mathit{c}}

, the separation of the temperature regimes where pair formation and their condensation occur, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state. \textcopyright{} 1996 The American Physical Society.

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.