Fig. 6. The effects of model SOC fields.

a Spin textures in the k_x − k_y plane of the CsPbBr₃ system with model Rashba SOC. ${\mathbf{S}}^{\exp }\equiv \left(S_x^{\exp },S_y^{\exp },S_z^{\exp }\right)$ with $S_i^{\exp }$ being spin expectation value along direction i and is the diagonal element of spin matrix s_i in Bloch basis. The arrow represents the spin orientation in the $S_x^{\exp }-S_y^{\exp }$ plane. The color scales $S_z^{\exp }$. b Spin textures in the k_y − k_z plane of the CsPbBr₃ system with model PSH (persistent spin helix) SOC. c Spin lifetime τ_s and carrier lifetime τ_p of CsPbBr₃ holes at 300 K considering the effects of Rashba or PSH SOC. α is the Rashba/PSH SOC strength coefficient. Rashba fields have spin texture perpendicular to k direction, in the same plane (xy plane here) surrounding Γ point. PSH fields have spin texture parallel along the same axis (y axis here). The detailed forms of the model SOC fields and Hamiltonians are given in Eqs. (18)-(22) in “Methods” section. τ_s is perpendicular to the SOC-field plane for Rashba SOC and is along the high-spin-polarization axis for PSH SOC respectively. d The band structure of valence bands considering PSH SOC with α=7 eVÅ. The color scales the $S_y^{\exp }$ in d.