Fig. 6: First principles simulations on 2D Cs₂PbBr₄ models.

a, b Representative (√2 × √2) − R45° Cs₂PbBr₄ models with symmetrical in-plane (a) and out-of-plane (b) tilting of adjacent PbBr₆ octahedra, i.e., with \(\Delta \beta \,=\,0\). c, d Representative (√2 × √2) − R45° Cs₂PbBr₄ models with asymmetrical in-plane (c) and out-of-plane (d) tilting of adjacent PbBr₆ octahedra with \(\Delta {\beta }_{{in},{out}}\,=\,20^\circ\). e Plots showing the evolution of lowest conduction subband energy width, \({{{{{{\bf{k}}}}}}}_{0}\), and \(\Delta {E}^{\pm }\) along the spin-splitting k-path as a function of \(\Delta {\beta }_{{in}}\) and \(\Delta {\beta }_{{out}}\) in the series of Cs₂PbBr₄ models. See Supplementary Fig. 16 and Supplementary Note 2 for details. The legends \(\Delta {\beta }_{{out\_}1}\) and \(\Delta {\beta }_{{out\_}2}\) in (e) correspond to the models with and without formal dipole on the Pb site, respectively. The shaded regions in (e) are 95% confidence intervals of fitting as a function of \({\Delta \beta }_{{in}}\) in Fig. 5.