Pitfalls in the analysis of low-temperature thermal conductivity of high-Tc cuprates

Recently, it was proposed that phonons are specularly reflected below ∼0.5 K in ordinary single-crystal samples of high-Tc cuprates, and that the low-temperature thermal conductivity κ should be analyzed by fitting the data up to ∼0.5 K with the formula κ = aT + bTα where α is a fitting parameter. Such an analysis yields a result different from that obtained from the conventional analysis in which the fitting is restricted to a region below ∼0.15 K, where κ has been found to obey κ = aT + bT 3 very well, which means that phonons are in the boundary scattering regime without specular reflection. Here we show that the proposed new analysis is most likely flawed, because the specular phonon reflection means that the phonon mean free path l gets longer than the mean sample width, while the estimated l is actually much shorter than the mean sample width above ∼0.15 K.