Evolution from intralayer to interlayer superconductivity in a bilayer $t$-$J$ model
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
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2025
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| _version_ | 1866912474450624512 |
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| author | Yang, Yuan Lu, Xin Wan, Yuan Chen, Wei-Qiang Gong, Shou-Shu |
| author_facet | Yang, Yuan Lu, Xin Wan, Yuan Chen, Wei-Qiang Gong, Shou-Shu |
| contents | Motivated by the bilayer cuprate superconductors and nickelate superconductor La$_3$Ni$_2$O$_7$, we investigate the evolution from intralayer to interlayer superconductivity based on a bilayer two-leg $t$-$J$-$J_{\bot}$ model, where $t$ is the in-plane electron hopping, $J$ is the in-plane spin interaction, and $J_{\bot}$ is the inter-plane spin interaction. By means of the density matrix renormalization group calculations, we obtain the quantum phase diagram of the system by tuning $J_{\bot}$ in a large doping range $δ= 1/8 - 1/2$. We find that a large $J_{\bot}$ can always drive an interlayer superconductivity by coupling the two layers in both the Luther-Emery liquid and Luttinger liquid states. By coupling two Luther-Emery liquid states, the in-plane superconductivity evolves to inter-plane superconductivity either through an intermediate charge density wave (CDW) phase or directly, depending on doping ratio. This emergent CDW phase, which exists over a finite doping range, appears to develop from the CDW state of the two-leg ladder at $δ= 1/4$. By coupling two Luttinger liquids, the in-plane Luttinger liquids show a transition to the inter-plane superconducting phase at large $J_{\bot}$, as reported in previous literature. Interestingly, in the intermediate $J_{\bot}$ regime we find that while the in-plane Luttinger-liquid features remain stable, the inter-plane superconductivity can develop an enhanced quasi-long-range order with the power exponent $K^{zz}_{\rm SC} \sim 1$. At last, we show that the interlayer superconductivity is also stable by coupling the bilayer three-leg $t$-$J$ ladders by a strong $J_{\bot}$ interaction, from both the Luther-Emery liquid and Luttinger-liquid states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evolution from intralayer to interlayer superconductivity in a bilayer $t$-$J$ model Yang, Yuan Lu, Xin Wan, Yuan Chen, Wei-Qiang Gong, Shou-Shu Strongly Correlated Electrons Motivated by the bilayer cuprate superconductors and nickelate superconductor La$_3$Ni$_2$O$_7$, we investigate the evolution from intralayer to interlayer superconductivity based on a bilayer two-leg $t$-$J$-$J_{\bot}$ model, where $t$ is the in-plane electron hopping, $J$ is the in-plane spin interaction, and $J_{\bot}$ is the inter-plane spin interaction. By means of the density matrix renormalization group calculations, we obtain the quantum phase diagram of the system by tuning $J_{\bot}$ in a large doping range $δ= 1/8 - 1/2$. We find that a large $J_{\bot}$ can always drive an interlayer superconductivity by coupling the two layers in both the Luther-Emery liquid and Luttinger liquid states. By coupling two Luther-Emery liquid states, the in-plane superconductivity evolves to inter-plane superconductivity either through an intermediate charge density wave (CDW) phase or directly, depending on doping ratio. This emergent CDW phase, which exists over a finite doping range, appears to develop from the CDW state of the two-leg ladder at $δ= 1/4$. By coupling two Luttinger liquids, the in-plane Luttinger liquids show a transition to the inter-plane superconducting phase at large $J_{\bot}$, as reported in previous literature. Interestingly, in the intermediate $J_{\bot}$ regime we find that while the in-plane Luttinger-liquid features remain stable, the inter-plane superconductivity can develop an enhanced quasi-long-range order with the power exponent $K^{zz}_{\rm SC} \sim 1$. At last, we show that the interlayer superconductivity is also stable by coupling the bilayer three-leg $t$-$J$ ladders by a strong $J_{\bot}$ interaction, from both the Luther-Emery liquid and Luttinger-liquid states. |
| title | Evolution from intralayer to interlayer superconductivity in a bilayer $t$-$J$ model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2507.07545 |