Thermal Diffusivity Above Mott-Ioffe-Regel Limit

We present high-resolution thermal diffusivity measurements on several near optimally doped electron- and hole-doped cuprate systems in a temperature range that passes through the Mott-Ioffe-Regel limit, above which the quasiparticle picture fails. Our primary observations are that the inverse thermal diffusivity is linear in temperature and can be fitted to $D_Q^{-1}=aT+b$. The slope $a$ is interpreted through the Planckian relaxation time $\tau\approx\hbar/k_BT$ and a thermal diffusion velocity $v_B$, which is close, but larger than the sound velocity. The intercept $b$ represent a crossover diffusion constant that separates coherent from incoherent quasiparticles. These observations suggest that both phonons and electrons participate in the thermal transport, while reaching the Planckian limit for relaxation time.