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arXiv:2504.17212 · Physical review. B./Physical review. B

Dual role of the stripe phase in superconducting correlations in a bilayer square lattice

Ting Guo, Lufeng Zhang, Tianxing Ma, Hai‐Qing Lin

Published May 14, 2025• 0 citations
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Abstract

While the stripe phase has been observed not only in monolayer cuprates but also in bilayer cuprates, research on its behavior in bilayer cuprates has been limited. Using constrained path quantum Monte Carlo, we explore the effect of stripes on the bilayer square lattice. We find the system exhibits short-range antiferromagnetism, which is enhanced by stripes and is strongest when the electron density of the interstriped rows reaches half-filling. The hole doping concentration plays a crucial role in the interaction between stripes and superconductivity. The $d$-wave pairing is enhanced by stripe potential ${V}_{0}$ at the hole doping ${\ensuremath{\delta}}_{h}=1/4$, whereas it is suppressed by stripe potential ${V}_{0}$ at the hole doping ${\ensuremath{\delta}}_{h}=1/8$. We elucidate this phenomenon through an analysis of the magnetism of the interstriped rows. Furthermore, the effective $d$-wave pairing is stronger in the bilayer model compared to the monolayer model when stripes are introduced on the square lattice. Overall, our unbiased numerical simulations provide a further understanding of the crossed bilayer square lattice model.

DOI
10.1103/physrevb.111.195127

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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 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.
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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 $\ensuremath{\delta}$ = 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.
The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the ddd-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration ($\ensuremath{\delta}$) dependence of the Hubbard model in the ground states on a square lattice at strong coupling U/t=10U/t=10U/t=10, for the on-site interaction UUU and the transfer ttt, using a variational Monte Carlo method. The method, which combines tensor network and Lanczos methods on top of Pfaffian wave functions, reveals a rich phase diagram, in which many orders compete severely and degenerate within the energy range of 0.01t0.01t0.01t. We have identified distinct phases including a uniform ddd-wave superconducting phase for $0.17\ensuremath{\lesssim}\ensuremath{\delta}\ensuremath{\lesssim}0.22$ and a stripe charge/spin ordered phase for $\ensuremath{\delta}\ensuremath{\lesssim}0.17$ with the stripe period depending on $\ensuremath{\delta}$, together with presumable spatially coexisting antiferromagnetic and stripe order for $\ensuremath{\delta}\ensuremath{\lesssim}0.07$ and coexisting stripe and ddd-wave superconductivity for $0.07\ensuremath{\lesssim}\ensuremath{\delta}\ensuremath{\lesssim}0.17$. The present, improved method revealed a wider region of a charge uniform superconducting phase than the previous studies and shows a qualitative similarity to the phase diagram of the cuprate superconductors. The superconducting order parameter is largest at doping of around $\ensuremath{\delta}=0.17$ in the ground state, which undergoes phase transitions from an inhomogeneous to a uniform state.
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