Anomalous Thermal Diffusivity in Underdoped YBa$_2$Cu$_3$O$_{6+x}$

TL;DR

The paper investigates anomalous in-plane thermal transport in underdoped YBa$_2$Cu$_3$O$_{6+x}$, revealing that neither electrons nor phonons are well-defined quasiparticles in the high-temperature regime. Local photothermal measurements show that the diffusivity anisotropy tracks the electrical resistivity anisotropy and diminishes below the CDW transition, implying a strong electronic contribution to heat flow. The authors propose a diffusive, Planckian-limited electron–phonon 'soup' with a universal relaxation timescale, providing a quantitative fit to $D(T)$ and suggesting that entropy is carried by a combined electronic-phononic diffuse medium rather than by conventional quasiparticles. This framework extends the concept of incoherent transport to electron–phonon coupled systems and may illuminate transport in other bad-metallic materials.

Abstract

We present local optical measurements of thermal diffusivity in the $ab$ plane of underdoped YBCO crystals. We find that the diffusivity anisotropy is comparable to reported values of the electrical resistivity anisotropy, suggesting that the anisotropies have the same origin. The anisotropy drops sharply below the charge order transition. We interpret our results through a strong electron-phonon scattering picture and find that both electronic and phononic contributions to the diffusivity saturate a proposed bound. Our results suggest that neither well-defined electron nor phonon quasiparticles are present in this material.

Figures (7)

• Figure 1: (color online) Thermal diffusivity of YBCO$_{6.60}$ and YBCO$_{6.75}$ single crystals, extracted from phase measurement, plotted on a log-log scale as a function of temperature in the range $25-300$ K. Insets show diffusivity measured at room temperature as a function of orientation around the heating spot, with the solid lines representing fits to Eq. \ref{['anisoD']} (see text). Error bars are almost entirely due to uncertainty in determining lasers spots separation.
• Figure 1: (color online) The schematic shows the optical paths of the setup. (a) Path of the heating laser (b) Path of the probing laser. The reflected light traverse the same path before gathered by a photodetector. (c) Path of camera vision. Cross-polarized picture is obtained by polarizing the incoming illumination and placing an analyzer in front of the camera.
• Figure 2: (color online) Anisotropy of the $ab$-plane thermal diffusivity as a function of temperature of YBCO$_{6.60}$ (green circles) and YBCO$_{6.75}$ (orange squares). Charge density order occurs at around $140-150$ K in both materials (see e.g. Cyr2015), marked by the grey region. Note that anisotropies decrease significantly below the transition, signifying the non-trivial role the electronic system plays in the thermal transport. Solid line is the electrical anisotropy in the $ab$ plane on similar crystals adopted from LeBoeufThesis.
• Figure 2: (color online) Cross-polarized image of the samples showing both laser spots: left (smaller spot) is the 637nm heating spot and right (larger spot) is the 830nm probe laser spot. a) a typical area of single crystal detwinned YBCO$_{6.60}$, and b) a typical area of single crystal detwinned YBCO$_{6.75}$. Thin remnant strips of the opposite structural domain is visible as white lines, but have been shown to have negligible effect on the anisotropy measurements. Insets show pictures of the crystals measured.
• Figure 3: (color online) Inverse diffusivity along the $a$- (unfilled blue circles) and $b$-axis (filled red circles) for both materials. The solid lines are fits to Eq. \ref{['composite']} (see text.)