Microscopic model for the hidden Rashba effect in YBa2Cu3O6+x

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 $\ensuremath{\sim}10$ meV.