[论文解读] Coexistence of superconductivity with partially filled stripes in the Hubbard model

Hao Xu, Chia-Min Chung+4 more|arXiv (Cornell University)|Mar 15, 2023

Physics of Superconductivity and Magnetism参考文献 51被引用 22

一句话总结

本研究在二维哈伯模型中，在存在最近邻耦合 t 与次近邻跳跃 t' 的情况下，电子掺杂和空穴掺杂两种情形均显示出 d-wave 超导性，并在空穴掺杂侧与条纹序同时存在，其中条纹被部分填充（f ≈ 0.6–0.8）。电子掺杂一侧的超导性较弱，呈现均匀或弱调制的反铁磁性。

ABSTRACT

Combining the complementary capabilities of two of the most powerful modern computational methods, we find superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model (with next nearest neighbor hopping). In the electron-doped regime, superconductivity is weaker and is accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexists with stripe order, which persists into the overdoped region with weaker hole density modulation. These stripe orders, neither filled as in the pure Hubbard model (no next nearest neighbor hopping) nor half-filled as seen in previous state-of-the-art calculations, vary in fillings between 0.6 and 0.8. The resolution of the tiny energy scales separating competing orders requires exceedingly high accuracy combined with averaging and extrapolating with a wide range of system sizes and boundary conditions. These results validate the applicability of this iconic model for describing cuprate high-$T_c$ superconductivity.

研究动机与目标

• 评估含 t' 的单带哈伯模型是否能捕捉到类似铜氧材料的超导性及其竞争序。
• 确定超导性在电子掺杂和空穴掺杂区间如何与自旋/电荷条纹序共存。
• 解析微小的能量尺度和有限尺寸效应，以外推到热力学极限。
• 以扭曲平均边界条件为基准，验证并对比互补的数值方法（AFQMC 与 DMRG）。

提出的方法

• 在方格晶格上，使用最近邻耦合 t、次近邻耦合 t'（t' = ±0.2）和 U = 8 的哈伯模型。
• 同时应用 DMRG（适应 U(1) 与 SU(2) 对称性）和带自洽试波函数的约束路径 AFQMC。
• 采用扭曲平均边界条件（TABC）来取样低能态并减少边界条件伪影。
• 通过系统的尺寸缩放和 d-wave 配对序参数对 h_d → 0 的外推，执行大尺度系统的热力学极限外推。
• 在边缘引入自旋密度和电荷密度定锚，以可视化条纹和反铁磁相关性。
• 在窄圆柱上交叉验证 DMRG 与 AFQMC 的结果，并将 AFQMC 扩展到更宽的系统。

实验结果

研究问题

• RQ1 Does the t-t'-U Hubbard model with cuprate-relevant parameters exhibit superconductivity in both electron- and hole-doped regimes?
• RQ2 How do stripe or spin-density-wave orders interact with d-wave superconductivity across doping and system size?
• RQ3 What are the stripe fillings in the presence of t' and how do they depend on doping, system size, and boundary conditions?
• RQ4 To what extent do boundary conditions and finite-size effects obscure or mimic pairing tendencies, and can TABC reliably reveal the true thermodynamic behavior?

主要发现

• Superconductivity with dome-like d-wave pairing appears in both electron- and hole-doped regimes upon extrapolation to the thermodynamic limit.
• Hole-doped stripes coexist with superconductivity and are partially filled, with stripe fillings varying between 0.6 and 0.8 depending on δ, system size, and boundary conditions.
• Electron-doped regime shows stronger uniform antiferromagnetic correlations and weaker or absent superconductivity, with pairing highly sensitive to boundary conditions.
• Stripes on the hole-doped side are not fully filled (IPS) nor strictly half-filled (NIPS on narrow widths); fillings vary with system size and BC, indicating fragile stripe patterns in wider systems with t' ≠ 0.
• Twist-averaged boundary conditions (TABC) are essential for reliable thermodynamic-limit extrapolations and consistent agreement between AFQMC and DMRG across parameter sets.
• The results support the single-band t-t'-U Hubbard model as a viable descriptor for cuprate superconductivity, highlighting the role of partially filled stripes in stabilizing long-range coherence.