Abstract In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, likely mediated by phonons, has been proposed in one-dimensional copper-oxide chain Ba2−xSrxCuO3+δ. Yet, it is unclear how this strong near-neighbor attraction V influences the superconductivity pairing in the system. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion U > 0 and near-neighbor attraction V < 0 that could well describe the cuprate chain and likely other similar transition-metal materials with both strong correlations and lattice effects. We find a rich quantum phase diagram containing an intriguing Tomonaga-Luttinger liquid phase — besides the spin density wave and various phase separation phases — that can host dominant spin-triplet pairing correlations and divergent superconductive susceptibility. Upon doping, the spin-triplet superconducting regime can be further broadened, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate chains.
Abstract In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, likely mediated by phonons, has been proposed in one-dimensional copper-oxide chain Ba2−xSrxCuO3+δ. Yet, it is unclear how this strong near-neighbor attraction V influences the superconductivity pairing in the system. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion U > 0 and near-neighbor attraction V < 0 that could well describe the cuprate chain and likely other similar transition-metal materials with both strong correlations and lattice effects. We find a rich quantum phase diagram containing an intriguing Tomonaga-Luttinger liquid phase — besides the spin density wave and various phase separation phases — that can host dominant spin-triplet pairing correlations and divergent superconductive susceptibility. Upon doping, the spin-triplet superconducting regime can be further broadened, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate chains.
In quantum materials, the electronic interaction and the electron-phonon coupling are in general two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, mediated by phonons, has been unveiled in one-dimensional (1D) copper-oxide chain compound. Yet it is unclear how this strong near-neighbor (NN) attraction V influences the superconductivity pairing. In this work, we employ the density-matrix renormalization group (DMRG) method to study this experiment-relevant extended Hubbard model with on-site Coulomb repulsion U>0 and NN attraction V<0, relevant for the 1D cuprate chain and likely other similar transition-metal materials. We find this extended t-U-V model hosts a rich quantum phase diagram consisting of the spin density wave phase, phase separation phases, the Tomonaga-Luttinger liquid (TLL) phase, and especially an intriguing TLL regime with divergent superconducting susceptibility and dominant spin-triplet pair correlations. Upon doping, such a spin-triplet pairing regime can be further broadened in the parameter space and extends to larger U. Our results show robust triplet pairing induced by attractive interaction V, offering a feasible mechanism to realize p-wave superconductivity in 1D cuprates.
A recent experiment has unveiled an anomalously strong electron-electron attraction in the one-dimensional copper-oxide chain ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$. While the effect of the near-neighbor electron attraction V in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. Here, we report a density matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction V can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave (CDW) correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent ${K}_{sc}\ensuremath{\sim}1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model. The relevance of our numerical results to cuprate materials is also discussed.
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 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,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 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.
Motivated by significant discrepancies between experimental observations of electron-doped cuprates and numerical results of the Hubbard model, we investigate the role of nearest-neighbor (NN) electron interactions V by studying the t−U−V model on square lattices. Upon doping δ= 0.153, by using constrained path quantum Monte Carlo (CPQMC) method, we find that NN electron attraction V can notably drive an exotic p-wave spin-triplet pairing, while the NN electron repulsion V will suppress the dx2−y2-wave (d-wave) pairing and triggers the dxy-wave pairing. Especially in the intermediate coupling regime, as NN repulsion increases, the intensity of dxy-wave pairing also increases, further suppressing the presence of d-wave pairing, which may help explain the notable suppression of d-wave pairing in electron-doped cuprate superconductors. Besides the pairing phase, we also find that the NN electron attraction V has no significant effect on spin density wave (SDW) and charge density wave (CDW), but repulsion V significantly enhanced CDW and suppressed SDW. Our study suggests the t−U−V Hubbard model can serve as the minimal model to capture the essential physics of the electron-doped cuprates.
The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and B2g (dxy) pairing dominates in the absence of repulsive longer-range Coulomb interactions VNN, the latter induces pairing in other symmetry channels, including, e.g., A2g (g-wave), nodal A1g (extended s-wave), or nodal Eu (p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, VNN<0, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts Eu (p-wave) spin-triplet or B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.