arXiv:2108.12950 · Physical review. B./Physical review. B

Enhancing d -wave superconductivity with nearest-neighbor attraction in the extended Hubbard model

Mi Jiang

Published Jan 13, 2022• 30 citations

Abstract

Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the $d$-wave superconductivity based on dynamic cluster quantum Monte Carlo calculations of a doped two-dimensional extended Hubbard model with nearest-neighbor attraction $\ensuremath{-}V$. Focusing on the range of $0<\ensuremath{-}V/t\ensuremath{\le}2$, our simulations indicate that the dynamics of $d$-wave projected pairing interaction is attractive at all frequencies and increases with $|V|$. Moreover, turning on $\ensuremath{-}V$ attraction enhances the $(\ensuremath{\pi},\ensuremath{\pi})$ spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at $V/t=\ensuremath{-}1$ relevant to the ``holon folding branch'', the charge fluctuations are insufficient to compete with the $d$-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggests the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.

DOI: 10.1103/physrevb.105.024510

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arXiv:2108.12950 · Physical review. B./Physical review. B

Enhancing d -wave superconductivity with nearest-neighbor attraction in the extended Hubbard model

Mi Jiang

Published Jan 13, 2022• 30 citations

arXiv HTML PDF

Abstract

d

-wave superconductivity based on dynamic cluster quantum Monte Carlo calculations of a doped two-dimensional extended Hubbard model with nearest-neighbor attraction

\ensuremath{-}V

. Focusing on the range of

0<\ensuremath{-}V/t\ensuremath{\le}2

, our simulations indicate that the dynamics of

d

-wave projected pairing interaction is attractive at all frequencies and increases with

|V|

. Moreover, turning on

\ensuremath{-}V

attraction enhances the

(\ensuremath{\pi},\ensuremath{\pi})

spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at

V/t=\ensuremath{-}1

relevant to the ``holon folding branch'', the charge fluctuations are insufficient to compete with the

d

-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggests the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.

DOI: 10.1103/physrevb.105.024510

Related papers

Drastic enhancement of d -wave superconductivity in an extended checkerboard Hubbard model

Kai Cheng, Shi-Chao Fang, Zhongbing Huang

Motivated by the recent discovery of anomalously strong nearest-neighbor attraction in the one-dimensional hole-doped cuprate ${\text{Ba}}_{2+x}{\text{Sr}}_{x}{\text{CuO}}_{3+\ensuremath{\delta}}$, we investigate the $d$ -wave superconducting property of an extended checkerboard Hubbard model, which includes an intraplaquette nearest-neighbor attraction $V$ . Our quantum Monte Carlo simulations reveal that, for small interplaquette hopping integral ${t}^{\ensuremath{'}}$, $V$ induces a drastic enhancement of long-range $d$ -wave pairing correlations in the parameter range of $0.0\ensuremath{\le}U\ensuremath{\le}6.0t$ ( $t$ is the intraplaquette hopping integral) when the electron density lies between half-filling and quarter-filling. At $V=\ensuremath{-}0.4t$, one order of magnitude larger $d$ -wave pairing correlations are observed compared to the ones at $V=0.0t$ and, more importantly, they exceed the values of the free electron system, signifying the existence of $d$ -wave superconductivity. The exact diagonalization calculations on the $2\ifmmode\times\else\texttimes\fi{}2$ plaquette indicate that the enhancement of $d$ -wave pairing correlations can be attributed to the $V$ -induced enhancement of pair-binding energy. Our findings provide a new perspective on the realization of high-temperature $d$ -wave superconductivity via the combination of nearest-neighbor attraction and electronic inhomogeneity.Motivated by the recent discovery of anomalously strong nearest-neighbor attraction in the one-dimensional hole-doped cuprate ${\text{Ba}}_{2+x}{\text{Sr}}_{x}{\text{CuO}}_{3+\ensuremath{\delta}}$, we investigate the $d$-wave superconducting property of an extended checkerboard Hubbard model, which includes an intraplaquette nearest-neighbor attraction $V$. Our quantum Monte Carlo simulations reveal that, for small interplaquette hopping integral ${t}^{\ensuremath{'}}$, $V$ induces a drastic enhancement of long-range $d$-wave pairing correlations in the parameter range of $0.0\ensuremath{\le}U\ensuremath{\le}6.0t$ ($t$ is the intraplaquette hopping integral) when the electron density lies between half-filling and quarter-filling. At $V=\ensuremath{-}0.4t$, one order of magnitude larger $d$-wave pairing correlations are observed compared to the ones at $V=0.0t$ and, more importantly, they exceed the values of the free electron system, signifying the existence of $d$-wave superconductivity. The exact diagonalization calculations on the $2\ifmmode\times\else\texttimes\fi{}2$ plaquette indicate that the enhancement of $d$-wave pairing correlations can be attributed to the $V$-induced enhancement of pair-binding energy. Our findings provide a new perspective on the realization of high-temperature $d$-wave superconductivity via the combination of nearest-neighbor attraction and electronic inhomogeneity.

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Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of $d$ -wave pairing when a nearest-neighbor Coulomb repulsion $V$ is present in addition to the on-site Coulomb repulsion $U$ . We find that $d$ -wave pairing and the superconducting transition temperature ${T}_{c}$ are only weakly suppressed as long as $V$ does not exceed $U/2$ . This stability is traced to the strongly retarded nature of pairing that allows the $d$ -wave pairs to minimize the repulsive effect of $V$ . When $V$ approaches $U/2$ , large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of $d$ -wave pairing and ${T}_{c}$ than for smaller $V$ .Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of $d$-wave pairing when a nearest-neighbor Coulomb repulsion $V$ is present in addition to the on-site Coulomb repulsion $U$. We find that $d$-wave pairing and the superconducting transition temperature ${T}_{c}$ are only weakly suppressed as long as $V$ does not exceed $U/2$. This stability is traced to the strongly retarded nature of pairing that allows the $d$-wave pairs to minimize the repulsive effect of $V$. When $V$ approaches $U/2$, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of $d$-wave pairing and ${T}_{c}$ than for smaller $V$.

arXiv:1707.06093Physical review. B./Physical review. BMay 17, 201831 citations

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Recent experimental results of angle-resolved photoemission spectroscopy suggested that an additional strong nearest neighbor attraction in the Hubbard model might be significant for the doped cuprates. The stripe-ordered patterns, which are formed by the inhomogeneous distribution of spin, charge, and pairing correlations in ${\mathrm{CuO}}_{2}$ planes, are a well-known feature of the doped cuprates. By employing constrained path quantum Monte Carlo, we examine the effect of the nearest neighbor attraction on a two-dimensional repulsive Hubbard model. Within and across the stripe regions, the ground-state spin correlations and the $d$ -wave pairing correlation are calculated. We found that the spin-spin correlation is the largest when the interstripe region is nearly half filled, and we also found the $d$ -wave superconducting correlation of the neighboring sites is enhanced in the presence of the stripe pattern. This reveals the crucial effects of the strong nearest neighbor attraction on superconductivity in doped cuprates.Recent experimental results of angle-resolved photoemission spectroscopy suggested that an additional strong nearest neighbor attraction in the Hubbard model might be significant for the doped cuprates. The stripe-ordered patterns, which are formed by the inhomogeneous distribution of spin, charge, and pairing correlations in ${\mathrm{CuO}}_{2}$ planes, are a well-known feature of the doped cuprates. By employing constrained path quantum Monte Carlo, we examine the effect of the nearest neighbor attraction on a two-dimensional repulsive Hubbard model. Within and across the stripe regions, the ground-state spin correlations and the $d$-wave pairing correlation are calculated. We found that the spin-spin correlation is the largest when the interstripe region is nearly half filled, and we also found the $d$-wave superconducting correlation of the neighboring sites is enhanced in the presence of the stripe pattern. This reveals the crucial effects of the strong nearest neighbor attraction on superconductivity in doped cuprates.

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Zhangkai Cao, Jianyu Li, Jiahao Su +2 more

The two-dimensional Hubbard model is widely believed to capture the key ingredients of high-temperature superconductivity in cuprate materials. Here we report a constrained path quantum Monte Carlo study of the square-lattice extended Hubbard model with on-site Coulomb repulsion $U$ and nearest-neighbor (NN) electron attraction $V$ . Upon doping $\ensuremath{\delta}$ = 0.125, we find that NN electron attraction $V$ significantly promotes an exotic spin-triplet ( $p$ -wave) pairing, with the $p$ -wave pairing correlations growing stronger as $V$ increases. Meanwhile, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave ( $d$ -wave) pairing in the intermediate coupling regime shows an insignificant response to the increase of $V$ . The spin density wave order, which is observed near half filling in the particle-hole channel, is also almost unaffected by the NN electron attraction $V$ , reinforcing the established relationship between $d$ -wave superconductivity (SC) and spin order. As the doping becomes heavier (i.e., $\ensuremath{\delta}$ increases), the dominant region of $p$ -wave pairing expands, further suppressing the presence of $d$ -wave pairing. Our paper suggests the $p$ -wave pairing region can be induced and further broadened by the NN electron attraction $V$ , offering a feasible mechanism to realize $p$ -wave SC in realistic cuprate materials.The two-dimensional Hubbard model is widely believed to capture the key ingredients of high-temperature superconductivity in cuprate materials. Here we report a constrained path quantum Monte Carlo study of the square-lattice extended Hubbard model with on-site Coulomb repulsion $U$ and nearest-neighbor (NN) electron attraction $V$. Upon doping $\ensuremath{\delta}$ = 0.125, we find that NN electron attraction $V$ significantly promotes an exotic spin-triplet ($p$-wave) pairing, with the $p$-wave pairing correlations growing stronger as $V$ increases. Meanwhile, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave ($d$-wave) pairing in the intermediate coupling regime shows an insignificant response to the increase of $V$. The spin density wave order, which is observed near half filling in the particle-hole channel, is also almost unaffected by the NN electron attraction $V$, reinforcing the established relationship between $d$-wave superconductivity (SC) and spin order. As the doping becomes heavier (i.e., $\ensuremath{\delta}$ increases), the dominant region of $p$-wave pairing expands, further suppressing the presence of $d$-wave pairing. Our paper suggests the $p$-wave pairing region can be induced and further broadened by the NN electron attraction $V$, offering a feasible mechanism to realize $p$-wave SC in realistic cuprate materials.

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Quantum Monte Carlo study of Spin, Charge, and Pairing correlations in the t−t′−U Hubbard model

Zhongbing Huang, Hua Lin, James E. Gubernatis

To clarify the effects of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the spin, charge, and pairing correlations, we studied the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ Hubbard model using the constrained-path Monte Carlo technique. We found that a negative ${t}^{\ensuremath{'}}$ suppresses the spin fluctuations near the Brillouin zone point $M=(\ensuremath{\pi},\ensuremath{\pi})$ and the charge fluctuations near the point $X=(\ensuremath{\pi},0),$ while a positive ${t}^{\ensuremath{'}}$ has the opposite effect. For a negative ${t}^{\ensuremath{'}},$ we also found that the long-range vertex contributions to the pairing correlations are heavily suppressed, but the local contributions are enhanced. Over the entire hole doping range studied, the d-wave long-range vertex contributions to pairing dominated those of the extended s-wave vertex contributions. In general, we did not find any tendency for these correlations to grow with increasing system size. We also did a limited number of simulations with an attractive nearest neighbor density-density interaction added to the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ model. It enhanced the long-range vertex contributions to the pairing correlations only for weak values of U.To clarify the effects of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the spin, charge, and pairing correlations, we studied the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ Hubbard model using the constrained-path Monte Carlo technique. We found that a negative ${t}^{\ensuremath{'}}$ suppresses the spin fluctuations near the Brillouin zone point $M=(\ensuremath{\pi},\ensuremath{\pi})$ and the charge fluctuations near the point $X=(\ensuremath{\pi},0),$ while a positive ${t}^{\ensuremath{'}}$ has the opposite effect. For a negative ${t}^{\ensuremath{'}},$ we also found that the long-range vertex contributions to the pairing correlations are heavily suppressed, but the local contributions are enhanced. Over the entire hole doping range studied, the d-wave long-range vertex contributions to pairing dominated those of the extended s-wave vertex contributions. In general, we did not find any tendency for these correlations to grow with increasing system size. We also did a limited number of simulations with an attractive nearest neighbor density-density interaction added to the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ model. It enhanced the long-range vertex contributions to the pairing correlations only for weak values of U.

Physical review. B, Condensed matterOct 18, 200149 citations

p-wave superconductivity induced by nearest-neighbor attraction in the square-lattice extended Hubbard model

Zhangkai Cao, J. Y. Li, Jiahao Su +2 more

The two-dimensional (2D) Hubbard model is widely believed to contain the key ingredients of high-temperature superconductivity in cuprate materials. Here, we report a constrained path quantum Monte Carlo (CPQMC) study of the square-lattice extended Hubbard model with on-site Coulomb repulsion U and nearest-neighbor (NN) electron attraction V. Upon doping $δ$ = 0.125, we find that the NN electron attraction V can notably drive an exotic spin-triplet (p-wave) superconducting (SC) phase, and enhance the p-wave SC correlations with the increase of V. But in the intermediate coupling regime, the $d_{x^2-y^2}$ -wave (d-wave) does not significantly increase with the increase of V, indicating that the d-wave is not affected by V in strongly correlated system. Besides the pairing phase, a spin density wave (SDW) only exists near the half-filling in the particle-hole channel, and doping disrupts the formation of SDW order. Especially, the NN electron attraction V has no significant effect on SDW, reflecting the consistent relationship between d-wave SC and spin correlation. Moreover, as doping increases, the dominant region of p-wave also expands, further suppressing the presence of d-wave, which may help explain the disappearance of d-wave SC in overdoped cuprate superconductors. We also find the d-wave exhibits a singular nonzero (near point ( $2π/3, π$ )) condensation structure in momentum space, resulting in a different staggered behavior in the x and y direction with distance in real space. On the contrary, the p-wave condensed at zero momentum, and the p-wave correlation exhibits exponential decay in real space. Our work suggests the p-wave SC region can be induced and further broadened by the NN electron attraction V, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate materials.The two-dimensional (2D) Hubbard model is widely believed to contain the key ingredients of high-temperature superconductivity in cuprate materials. Here, we report a constrained path quantum Monte Carlo (CPQMC) study of the square-lattice extended Hubbard model with on-site Coulomb repulsion U and nearest-neighbor (NN) electron attraction V. Upon doping $δ$= 0.125, we find that the NN electron attraction V can notably drive an exotic spin-triplet (p-wave) superconducting (SC) phase, and enhance the p-wave SC correlations with the increase of V. But in the intermediate coupling regime, the $d_{x^2-y^2}$-wave (d-wave) does not significantly increase with the increase of V, indicating that the d-wave is not affected by V in strongly correlated system. Besides the pairing phase, a spin density wave (SDW) only exists near the half-filling in the particle-hole channel, and doping disrupts the formation of SDW order. Especially, the NN electron attraction V has no significant effect on SDW, reflecting the consistent relationship between d-wave SC and spin correlation. Moreover, as doping increases, the dominant region of p-wave also expands, further suppressing the presence of d-wave, which may help explain the disappearance of d-wave SC in overdoped cuprate superconductors. We also find the d-wave exhibits a singular nonzero (near point ($2π/3, π$)) condensation structure in momentum space, resulting in a different staggered behavior in the x and y direction with distance in real space. On the contrary, the p-wave condensed at zero momentum, and the p-wave correlation exhibits exponential decay in real space. Our work suggests the p-wave SC region can be induced and further broadened by the NN electron attraction V, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate materials.

arXiv:2408.01113Aug 2, 20240 citations

d

-wave superconductivity based on dynamic cluster quantum Monte Carlo calculations of a doped two-dimensional extended Hubbard model with nearest-neighbor attraction

\ensuremath{-}V

. Focusing on the range of

0<\ensuremath{-}V/t\ensuremath{\le}2

, our simulations indicate that the dynamics of

d

-wave projected pairing interaction is attractive at all frequencies and increases with

|V|

. Moreover, turning on

\ensuremath{-}V

attraction enhances the

(\ensuremath{\pi},\ensuremath{\pi})

spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at

V/t=\ensuremath{-}1

relevant to the ``holon folding branch'', the charge fluctuations are insufficient to compete with the

d

d

-wave superconducting property of an extended checkerboard Hubbard model, which includes an intraplaquette nearest-neighbor attraction

V

. Our quantum Monte Carlo simulations reveal that, for small interplaquette hopping integral ${t}^{\ensuremath{'}}$,

V

induces a drastic enhancement of long-range

d

-wave pairing correlations in the parameter range of $0.0\ensuremath{\le}U\ensuremath{\le}6.0t$ (

t

is the intraplaquette hopping integral) when the electron density lies between half-filling and quarter-filling. At $V=\ensuremath{-}0.4t$, one order of magnitude larger

d

-wave pairing correlations are observed compared to the ones at

V=0.0t

and, more importantly, they exceed the values of the free electron system, signifying the existence of

d

-wave superconductivity. The exact diagonalization calculations on the $2\ifmmode\times\else\texttimes\fi{}2$ plaquette indicate that the enhancement of

d

-wave pairing correlations can be attributed to the

V

-induced enhancement of pair-binding energy. Our findings provide a new perspective on the realization of high-temperature

d

-wave superconductivity via the combination of nearest-neighbor attraction and electronic inhomogeneity.

Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of

d

-wave pairing when a nearest-neighbor Coulomb repulsion

V

is present in addition to the on-site Coulomb repulsion

U

. We find that

d

-wave pairing and the superconducting transition temperature

{T}_{c}

are only weakly suppressed as long as

V

does not exceed

U/2

. This stability is traced to the strongly retarded nature of pairing that allows the

d

-wave pairs to minimize the repulsive effect of

V

. When

V

approaches

U/2

, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of

d

-wave pairing and

{T}_{c}

than for smaller

V

{\mathrm{CuO}}_{2}

planes, are a well-known feature of the doped cuprates. By employing constrained path quantum Monte Carlo, we examine the effect of the nearest neighbor attraction on a two-dimensional repulsive Hubbard model. Within and across the stripe regions, the ground-state spin correlations and the

d

-wave pairing correlation are calculated. We found that the spin-spin correlation is the largest when the interstripe region is nearly half filled, and we also found the

d

-wave superconducting correlation of the neighboring sites is enhanced in the presence of the stripe pattern. This reveals the crucial effects of the strong nearest neighbor attraction on superconductivity in doped cuprates.

U

and nearest-neighbor (NN) electron attraction

V

. Upon doping $\ensuremath{\delta}$ = 0.125, we find that NN electron attraction

V

significantly promotes an exotic spin-triplet (

p

-wave) pairing, with the

p

-wave pairing correlations growing stronger as

V

increases. Meanwhile, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave (

d

-wave) pairing in the intermediate coupling regime shows an insignificant response to the increase of

V

. The spin density wave order, which is observed near half filling in the particle-hole channel, is also almost unaffected by the NN electron attraction

V

, reinforcing the established relationship between

d

-wave superconductivity (SC) and spin order. As the doping becomes heavier (i.e., $\ensuremath{\delta}$ increases), the dominant region of

p

-wave pairing expands, further suppressing the presence of

d

-wave pairing. Our paper suggests the

p

-wave pairing region can be induced and further broadened by the NN electron attraction

V

, offering a feasible mechanism to realize

p

-wave SC in realistic cuprate materials.

δ

= 0.125, we find that the NN electron attraction V can notably drive an exotic spin-triplet (p-wave) superconducting (SC) phase, and enhance the p-wave SC correlations with the increase of V. But in the intermediate coupling regime, the

d_{x^2-y^2}

-wave (d-wave) does not significantly increase with the increase of V, indicating that the d-wave is not affected by V in strongly correlated system. Besides the pairing phase, a spin density wave (SDW) only exists near the half-filling in the particle-hole channel, and doping disrupts the formation of SDW order. Especially, the NN electron attraction V has no significant effect on SDW, reflecting the consistent relationship between d-wave SC and spin correlation. Moreover, as doping increases, the dominant region of p-wave also expands, further suppressing the presence of d-wave, which may help explain the disappearance of d-wave SC in overdoped cuprate superconductors. We also find the d-wave exhibits a singular nonzero (near point (

2π/3, π

)) condensation structure in momentum space, resulting in a different staggered behavior in the x and y direction with distance in real space. On the contrary, the p-wave condensed at zero momentum, and the p-wave correlation exhibits exponential decay in real space. Our work suggests the p-wave SC region can be induced and further broadened by the NN electron attraction V, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate materials.