Structural dynamics in hybrid halide perovskites: Bulk Rashba splitting, spin texture, and carrier localization

The extended charge carrier lifetime in hybrid halide perovskites was attributed to a quasi-indirect band gap that arises due to a Rashba splitting in both conduction and valence band edges. In this paper, we present results for an effective relativistic band structure of $({\mathrm{CH}}₃{\mathrm{NH}}₃){\mathrm{PbI}}₃$ with the focus on the dispersion of electronic states near the band edges of $({\mathrm{CH}}₃{\mathrm{NH}}₃){\mathrm{PbI}}₃$ affected by thermal structural fluctuations. We establish a relationship between the magnitude of the Rashba splitting and a deviation of the Pb atom from its centrosymmetric site position in the ${\mathrm{PbI}}₆$ octahedron. For the splitting energy to reach the thermal energy ${k}_{\text{B}}T\ensuremath{\approx}26$ meV (room temperature), the displacement should be on the order of $0.3\phantom{\rule{0.28em}{0ex}}\AA{}$, which is far above the static displacements of Pb atoms in the tetragonal phase of $({\mathrm{CH}}₃{\mathrm{NH}}₃){\mathrm{PbI}}₃$. The significant dynamic enhancement of the Rashba splitting observed at earlier simulation times (less than 2 ps) later weakens and becomes less than the thermal energy despite the average displacement of Pb atoms remaining large (0.37 \AA{}). A randomization of Pb-displacement vectors and associated cancellation of the net effective magnetic field acting on electrons at the conduction band edge is responsible for reduction of the Rashba splitting. The lattice dynamics also leads to deterioration of a Bloch character for states in the valence band leading to the subsequent localization of holes, which affects the bipolar mobility of charge carriers in $({\mathrm{CH}}₃{\mathrm{NH}}₃){\mathrm{PbI}}₃$. These results call into question the quasi-indirect band gap as a reason for the long carrier lifetime observed in $({\mathrm{CH}}₃{\mathrm{NH}}₃){\mathrm{PbI}}₃$ at room temperature. Analysis of spin projections and the spin overlap at the band edges also rules out the spin helicity as a possible cause for a long lifetime of optical excitations in perovskite structures. An alternative mechanism involves dynamic localization of holes and their reduced overlap with electrons in reciprocal space.