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The soft modes associated with continuous-order phase transitions areassociated with strong anharmonicity. This leads to the overdamped limit wherethe phonon quasi-particle picture can breakdown. However, this limit iscommonly restricted to a narrow temperature range, making it difficult toobserve its signature feature, namely the breakdown of the inverse relationshipbetween the relaxation time and damping. Here we present a physically intuitivepicture based on the relaxation times of the mode coordinate and its conjugatemomentum, which at the instability approach infinity and the inverse dampingfactor, respectively. We demonstrate this behavior for the cubic-to-tetragonalphase transition of the inorganic halide perovskite CsPbBr$_3$ via moleculardynamics, and show that the overdamped region extends almost 200 K above thetransition temperature. Further, we investigate how the dynamics of these softphonon modes change when crossing the phase transition.

Limits of the phonon quasi-particle picture at the cubic-to-tetragonal phase transition in halide perovskites