Low-temperature phonon thermal conductivity of cuprate single crystals

TL;DR

This study investigates how sample size and surface roughness influence phonon thermal conductivity in Nd$_2$CuO$_4$ crystals at very low temperatures, revealing boundary scattering effects and the role of surface conditions.

Contribution

It demonstrates the impact of surface roughness on phonon boundary scattering and proposes an empirical power law for thermal conductivity in cuprates, clarifying previous experimental discrepancies.

Findings

$\kappa_p$ scales with $\sqrt{A}$ at 0.5 K

Surface roughening restores $T^3$ dependence of $\kappa_p$

Supports universal heat conductivity of d-wave quasiparticles

Abstract

The effect of sample size and surface roughness on the phonon thermal conductivity $\kappa_p$ of Nd$_2$CuO$_4$ single crystals was studied down to 50 mK. At 0.5 K, $\kappa_p$ is proportional to $\sqrt{A}$, where $A$ is the cross-sectional area of the sample. This demonstrates that $\kappa_p$ is dominated by boundary scattering below 0.5 K or so. However, the expected $T^3$ dependence of $\kappa_p$ is not observed down to 50 mK. Upon roughing the surfaces, the $T^3$ dependence is restored, showing that departures from $T^3$ are due to specular reflection of phonons off the mirror-like sample surfaces. We propose an empirical power law fit, to $\kappa_p \sim T^{\alpha}$ (where $\alpha < 3$) in cuprate single crystals. Using this method, we show that recent thermal conductivity studies of Zn doping in YBa$_2$Cu$_3$O$_y$ re-affirm the universal heat conductivity of d-wave quasiparticles at $T \to 0$.