Thermal diffusivity above the 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 τ≈h/k_BT and a thermal diffusion velocity v_B, which is close, but larger than the sound velocity. The intercept b≈h/m represent a crossover (quantum) diffusion constant that separates coherent from incoherent quasiparticles. These observations suggest that both phonons and electrons participate in the thermal transport and both reach the Planckian limit for relaxation time. Where itinerant electrons are absent, a similar behavior is obtained for the insulating phases where the constant b is absent.