Each unit cell in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ contains a pair of two-dimensional ${\mathrm{CuO}}_2$ layers. While the crystal structure is globally inversion symmetric, the individual layers are not. This leads, necessarily, to a nonvanishing Rashba spin-orbit coupling (SOC) in the ${\mathrm{CuO}}_2$ layers, with opposite signs of the coupling constant in each layer. These so-called Rashba bilayers generate hidden spin textures, with a vanishing net spin at each $\mathbf{k}$ point in the Brillouin zone, but nonvanishing spin textures in each layer separately. Here, we trace the microscopic origin of the Rashba splitting through the orbital structure of the ${\mathrm{CuO}}_2$ conduction bands, obtain a generic three-orbital model Hamiltonian, and show that the magnitude of the spin-splitting predicted by density functional theory is $\sim 10$ meV.

中文翻译：

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YBa2Cu3O6 + x中隐藏的Rashba效应的微观模型

每个单元格 ${\mathrm{Ba}}_2{铜}_3{\mathrm{Ø}}_{6+X}$ 包含一对二维 ${\mathrm{氧化铜}}_2$层。尽管晶体结构是整体反转对称的，但各个层却不是。这必然导致星云中Rashba自旋轨道耦合（SOC）消失。${\mathrm{氧化铜}}_2$层，每一层的耦合常数相反。这些所谓的Rashba双层生成隐藏的自旋纹理，每层的净自旋消失$\mathbf{ķ}$指向布里渊区，但每层中的旋转纹理分别消失。在这里，我们追踪了Rashba的微观起源，它是通过Rashba的轨道结构分裂的${\mathrm{氧化铜}}_2$ 导带，获得通用的三轨道模型哈密顿量，并证明密度泛函理论预测的自旋分裂幅度为 $〜10$ 影片