Slow cooling of hot polarons in halide perovskite solar cells

Halide perovskites show unusual thermalisation kinetics for above bandgap photo-excitation. We explain this as a consequence of excess energy being deposited into discrete large polaron states. The cross-over between low-fluence and high-fluence `phonon bottleneck' cooling is due to a Mott transition where the polarons overlap ($n \ge 10^{18}/\mathrm{cm}^3$) and the phonon sub-populations are shared. We calculate the initial rate of cooling (thermalisation) from the scattering time in the Fr\"ohlich polaron model to be 78 meVps$^{-1}$ for $\mathrm{CH}_3\mathrm{NH}_3\mathrm{PbI}_3$. This rapid initial thermalisation involves heat transfer into optical phonon modes coupled by a polar dielectric interaction. Further cooling to equilibrium over hundreds of picoseconds is limited by the ultra-low thermal conductivity of the perovskite lattice.