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

Physical review. B./Physical review. B

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

Kai Cheng, Shi-Chao Fang, Zhongbing Huang

Published Jan 31, 2024• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.109.014519

Related papers

Strong enhancement of d-wave superconductivity in an extended checkerboard Hubbard ladder

Huang, Xichen, Saisai He, Jize Zhao +1 more

By employing the density-matrix renormalization group method, we study an extended checkerboard Hubbard model on the two-leg ladder, which includes an intraplaquette nearest-neighbour attraction V. The simulated results show that V plays a significant role in enhancing the d-wave superconductivity when the electron density is close to half-filling. In the homogeneous case t'=t (t and t' are the intraplaquette and interplaquette hopping integrals), large critical |Vc| is required to induce the superconducting ground state. With decreasing t', |Vc| is substantially diminished and the pair state has a nearly C4 symmetry. In the extremely inhomogeneous case t'<0.2t, the system transits to the d-wave superconducting phase at V\sim-0.3t and V\sim-0.4t for U=8t and U=12t, respectively, accompanying with a shift of spin and single-particle excitations from gapless to gapped type.

arXiv:2509.24415•Sep 29, 2025•0 citations

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

Mi Jiang

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.

arXiv:2108.12950•Physical review. B./Physical review. B•Jan 13, 2022•30 citations

Enhancement of d -wave pairing in the striped phase with nearest neighbor attraction

Lufeng Zhang, Ting Guo, Yingping Mou +2 more

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.

arXiv:2109.00213•Physical review. B./Physical review. B•Apr 27, 2022•12 citations

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

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.

Physical review. B./Physical review. B•Jan 22, 2025•9 citations

Enhanced pairing in the checkerboard Hubbard ladder

George Karakonstantakis, Erez Berg, Steven R. White +1 more

We study signatures of superconductivity in a two-leg ``checkerboard'' Hubbard ladder model, defined as a one-dimensional (period 2) array of square plaquettes with an intraplaquette hopping $t$ and interplaquette hopping ${t}^{\ensuremath{'}}$, using the density-matrix renormalization-group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half-filling, $U\ensuremath{\approx}6t$ and ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.6$. Other forms of modulated hopping parameters, with periods of either one or three lattice constants, are also found to enhance pairing relative to the uniform two-leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.

arXiv:1008.3908•Physical Review B•Feb 22, 2011•30 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.

arXiv:2408.01113•Aug 2, 2024•0 citations
Motivated by the recent discovery of anomalously strong nearest-neighbor attraction in the one-dimensional hole-doped cuprate Ba2+xSrxCuO3+\ensuremathδ{\text{Ba}}_{2+x}{\text{Sr}}_{x}{\text{CuO}}_{3+\ensuremath{\delta}}Ba2+x​Srx​CuO3+\ensuremathδ​, we investigate the ddd-wave superconducting property of an extended checkerboard Hubbard model, which includes an intraplaquette nearest-neighbor attraction VVV. Our quantum Monte Carlo simulations reveal that, for small interplaquette hopping integral t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′, VVV induces a drastic enhancement of long-range ddd-wave pairing correlations in the parameter range of 0.0\ensuremath≤U\ensuremath≤6.0t0.0\ensuremath{\le}U\ensuremath{\le}6.0t0.0\ensuremath≤U\ensuremath≤6.0t (ttt is the intraplaquette hopping integral) when the electron density lies between half-filling and quarter-filling. At V=\ensuremath−0.4tV=\ensuremath{-}0.4tV=\ensuremath−0.4t, one order of magnitude larger ddd-wave pairing correlations are observed compared to the ones at V=0.0tV=0.0tV=0.0t and, more importantly, they exceed the values of the free electron system, signifying the existence of ddd-wave superconductivity. The exact diagonalization calculations on the 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 plaquette indicate that the enhancement of ddd-wave pairing correlations can be attributed to the VVV-induced enhancement of pair-binding energy. Our findings provide a new perspective on the realization of high-temperature ddd-wave superconductivity via the combination of nearest-neighbor attraction and electronic inhomogeneity.
By employing the density-matrix renormalization group method, we study an extended checkerboard Hubbard model on the two-leg ladder, which includes an intraplaquette nearest-neighbour attraction V. The simulated results show that V plays a significant role in enhancing the d-wave superconductivity when the electron density is close to half-filling. In the homogeneous case t'=t (t and t' are the intraplaquette and interplaquette hopping integrals), large critical |Vc| is required to induce the superconducting ground state. With decreasing t', |Vc| is substantially diminished and the pair state has a nearly C4 symmetry. In the extremely inhomogeneous case t'<0.2t, the system transits to the d-wave superconducting phase at V\sim-0.3t and V\sim-0.4t for U=8t and U=12t, respectively, accompanying with a shift of spin and single-particle excitations from gapless to gapped type.
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 ddd-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 ddd-wave projected pairing interaction is attractive at all frequencies and increases with ∣V∣|V|∣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 ddd-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.
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 CuO2{\mathrm{CuO}}_{2}CuO2​ 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 ddd-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 ddd-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.
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 UUU and nearest-neighbor (NN) electron attraction VVV. Upon doping $\ensuremath{\delta}$ = 0.125, we find that NN electron attraction VVV significantly promotes an exotic spin-triplet (ppp-wave) pairing, with the ppp-wave pairing correlations growing stronger as VVV increases. Meanwhile, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave (ddd-wave) pairing in the intermediate coupling regime shows an insignificant response to the increase of VVV. 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 VVV, reinforcing the established relationship between ddd-wave superconductivity (SC) and spin order. As the doping becomes heavier (i.e., $\ensuremath{\delta}$ increases), the dominant region of ppp-wave pairing expands, further suppressing the presence of ddd-wave pairing. Our paper suggests the ppp-wave pairing region can be induced and further broadened by the NN electron attraction VVV, offering a feasible mechanism to realize ppp-wave SC in realistic cuprate materials.
We study signatures of superconductivity in a two-leg ``checkerboard'' Hubbard ladder model, defined as a one-dimensional (period 2) array of square plaquettes with an intraplaquette hopping ttt and interplaquette hopping ${t}^{\ensuremath{'}}$, using the density-matrix renormalization-group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half-filling, $U\ensuremath{\approx}6t$ and ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.6$. Other forms of modulated hopping parameters, with periods of either one or three lattice constants, are also found to enhance pairing relative to the uniform two-leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.
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 δδδ= 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 dx2−y2d_{x^2-y^2}dx2−y2​-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,π2π/3, π2π/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.