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为澄清铜氧化物高温超导材料具有不同的超导转变温度的原因以及自旋条纹序和超导电性之间的关系，基于铜基二轨道哈伯德模型采用大尺度无偏差的约束路径量子蒙特卡洛方法研究了Cu的d3z2-r2轨道对LSCO和HBCO两类典型的铜基超导体中的超导电性和自旋条纹序的影响。首先，利用不同类型的铜基超导材料的轨道能级差的差异，数值结果显示相比于LSCO超导材料，HBCO超导材料中的d波超导电子配对对称性的配对关联函数和有效配对关联函数的强度表现出更为显著的优势。此结果表明HBCO超导材料的超导转变温度高于LSCO超导材料的超导转变温度的原因与Cu的d3z2-r2轨道的作用有关。其次，通过考察LSCO和HBCO两类超导材料中的自旋条纹序的形成情况，数值模拟结果显示LSCO体系的自旋条纹序呈现出相对较长的单个畴区，而HBCO体系的自旋条纹序呈现出周期性且具有多个畴区。此结果说明LSCO体系存在局域有序的自旋条纹序，HBCO体系存在非局域长程有序的自旋条纹序，更为重要的是由于HBCO超导材料中d波超导电子配对对称性的配对关联函数和有效配对关联函数在长程序上表现出明显的优势，这说明长程有序的自旋条纹序有利于提高材料的超导电性，即自旋条纹序和超导电性存在协同效应。
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关键词:
- d波超导态 /
- 自旋条纹序 /
- 约束路径量子蒙特卡罗方法
To clarify the origin of the distinct superconducting transition temperatures in cuprate high-temperature superconductors and to elucidate the relationship between spin stripe order and superconductivity, we employ large-scale, unbiased constrained-path quantum Monte Carlo simulations based on a two-orbital Hubbard model for copper oxides. We investigate the influence of the Cu d3z2-r2 orbital on the superconducting properties and spin stripe order in two prototypical cuprates, LSCO and HBCO.
First, within square lattice models of sizes 8 × 8 and 16 × 16, we examine the effect of the Cu d3z2-r2 orbital on superconductivity. By exploiting the differences in orbital energy-level separations among different cuprate materials, our numerical results demonstrate that, compared with LSCO, HBCO exhibits a significantly stronger enhancement in both the pairing correlation function and the effective pairing correlation function associated with d-wave superconducting symmetry. This result indicates that the higher superconducting transition temperature of HBCO relative to LSCO is closely related to the role of the Cu d3z2-r2 orbital.
Second, considering that spin stripe order spontaneously breaks the rotational symmetry of the lattice and forms unidirectional, periodically modulated spin-density structures whose periodicity is generally incompatible with that of a square lattice, conventional periodic boundary conditions cannot accurately capture the intrinsic anisotropy of spin stripe order. To overcome this limitation, rectangular lattices are employed in our numerical simulations to describe the spin stripe configurations. This choice allows multiple stripe periods to be accommodated along the transverse direction, thereby faithfully capturing the spontaneously formed spin stripe structures in the electronic spin distribution and enabling a reliable analysis of their interplay with superconductivity. Based on this approach, we investigate the formation of spin stripe order in LSCO and HBCO using a 16 × 4 rectangular lattice. The numerical results show that LSCO develops relatively long single-domain spin stripes, whereas HBCO exhibits periodic spin stripe structures consisting of multiple domains. These findings indicate that LSCO hosts locally ordered spin stripes, while HBCO supports nonlocal, long-range ordered spin stripe order. More importantly, the pairing correlation and effective pairing correlation functions associated with d-wave superconductivity in HBCO retain a pronounced long-range enhancement, demonstrating that long-range ordered spin stripes are beneficial for enhancing superconductivity. This result reveals a cooperative interplay between spin stripe order and superconductivity.
Taken together, these results not only provide insight into the origin of the distinct superconducting transition temperatures in cuprate high-temperature superconductors and the correlations between different ordered phases, but also demonstrate that the Cu d3z2-r2 orbital plays a crucial role in tuning superconductivity and spin fluctuations in cuprate materials. Our study thus offers a new theoretical perspective for exploring strongly correlated cuprate systems.-
Keywords:
- d-wave superconducting state /
- Spin stripe order /
- Constrained-path quantum Monte Carlo method
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