Fig. 3

Theoretical calculation of phonon–phonon coupling and the two-temperature model. a Projected phonon density of states (phDOS) of pseudo-cubic MAPbI₃ and phase space for phonon emission, both plotted as functions of energy and are shown in arbitrary units. Low-energy phonon modes (LEPMs) (<20 meV) and high-energy phonon modes (HEPMs) (>20 meV) are highlighted. b Top: calculated dependences of τ_eqb and G_pp on T₂ (varied from 60 K to 120 K in increments of 10 K) with a fixed ΔT of 10 K. Bottom: representative temperature evolution of the two phonon subsets with an initial T₂ of 80 K and T₁ of 90 K