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 $\tau \approx \hslash /k_{B}T$ and a thermal diffusion velocity $v_B$, which is close, but larger than the sound velocity. The intercept $b$ represents 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.

Figure 1

Examples for thermal diffusivity in the $ab$ plane measured as a function of temperature using the optical setup. (a) ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$ annealed, and (b) optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CeCu}}_2{\mathrm{O}}_{8+x}$ with $T_c=92\text{K}$. Statistical error is smaller than the data points. A systematic error of $\sim 5\%$ is estimated as a result of calibration of the optical paths, and the finite size of the focused laser spots.

Figure 2

Inverse thermal diffusivity $D_Q^{-1}\left(T\right)$ as a function of temperature of optimal electron-doped NCCO, SCCO, PCCO, optimal hole-doped BSCCO crystal, and two underdoped YBCO crystals from [9]. Solid lines show linear fit in the form $D_Q^{-1}=aT+b$ to the data above 300 K for electron-doped cuprates, above 250 K for BSCCO, and above 200 K for YBCOs. Dotted lines show the same fit extended to lower temperatures. Insets in (a), (b), and (f) show four-terminal resistance measured on the same crystals in arbitrary units.