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Physical review. B./Physical review. B

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

Zhangkai Cao, Jianyu Li, Jiahao Su, Tao Ying, Ho-Kin Tang

Published Jan 22, 2025• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.111.024509

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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 \ensuremathδ\ensuremath{\delta}\ensuremathδ = 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 dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-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., \ensuremathδ\ensuremath{\delta}\ensuremathδ 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.
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.
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 VVV by studying the t−U−Vt-U-Vt−U−V model on square lattices. Upon doping δδδ= 0.153, by using constrained path quantum Monte Carlo (CPQMC) method, we find that NN electron attraction VVV can notably drive an exotic ppp-wave spin-triplet pairing, while the NN electron repulsion VVV will suppress the dx2−y2d_{x^2-y^2}dx2−y2​-wave (ddd-wave) pairing and triggers the dxyd_{xy}dxy​-wave pairing. Especially in the intermediate coupling regime, as NN repulsion increases, the intensity of dxyd_{xy}dxy​-wave pairing also increases, further suppressing the presence of ddd-wave pairing, which may help explain the notable suppression of ddd-wave pairing in electron-doped cuprate superconductors. Besides the pairing phase, we also find that the NN electron attraction VVV has no significant effect on spin density wave (SDW) and charge density wave (CDW), but repulsion VVV significantly enhanced CDW and suppressed SDW. Our study suggests the t−U−Vt-U-Vt−U−V Hubbard model can serve as the minimal model to capture the essential physics of the electron-doped cuprates.
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 VVV 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>0U>0U>0 and NN attraction V<0V<0V<0, relevant for the 1D cuprate chain and likely other similar transition-metal materials. We find this extended ttt-UUU-VVV 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 UUU. Our results show robust triplet pairing induced by attractive interaction VVV, offering a feasible mechanism to realize ppp-wave superconductivity in 1D cuprates.
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.
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.
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (UUU) and nearest-neighbor (VVV) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when 4V>U4V>U4V>U gives way to a dxy{d}_{xy}dxy​-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive VVV and a range of on-site repulsive interaction UUU. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​)-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while dxy{d}_{xy}dxy​ pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.