Electric field and strain induced Rashba effect in hybrid halide perovskites

Using first principles density functional theory calculations, we show how Rashba-type energy band splitting in the hybrid organic-inorganic halide perovskites APbX$_3$ (A=CH$_3$NH$_3^+$, CH(NH$_2$)$_2^+$, Cs$^+$ and X=I, Br) can be tuned and enhanced with electric fields and anisotropic strain. In particular, we demonstrate that the magnitude of the Rashba splitting of tetragonal (CH$_3$NH$_3$)PbI$_3$ grows with increasing macroscopic alignment of the organic cations and electric polarization, indicating appreciable tunability with experimentally-feasible applied fields, even at room temperature. Further, we quantify the degree to which this effect can be tuned via chemical substitution at the A and X sites, which alters amplitudes of different polar distortion patterns of the inorganic PbX$_3$ cage that directly impact Rashba splitting. In addition, we predict that polar phases of CsPbI$_3$ and (CH$_3$NH$_3$)PbI$_3$ with $R3c$ symmetry possessing considerable Rashba splitting might be accessible at room temperature via anisotropic strain induced by epitaxy, even in the absence of electric fields.