Fig. 3: Model for EP-coupling resulting from distortions of the Pb–X sublattice.

a, Cartoon schematic of the sp-bonding in the CB and VB of LHPs. b, Computed shift in the energy of the bandgap (Eg) as a function of Pb–Br–Pb bending in orthorhombic Pnma CsPbBr3. c, Model for EP-coupling to phonons driving Pb–X octahedral tilting, where the presence of excitons shifts the minimum of the total energy of the excited state (e.s.) relative to the ground state (g.s.) towards the cubic phase. d, Computed partial phonon density of states (DOS) of CsPbBr3. Illustrations show the types of octahedral distortions driven by phonons in the specified ranges. e, EP-coupling strengths resulting from the coupling of the interband excitation of a single exciton to octahedral tilting in FAPbBr3 at 100 K, extracted from the magnitude of the measured changes in the 211 peak.