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

Recently, it was proposed that phonons are specularly reflected below about 0.5 K in ordinary single-crystal samples of high-T_c cuprates, and that the low-temperature thermal conductivity should be analyzed by fitting the data up to 0.5 K using an arbitrary power law. Such an analysis yields a result different from that obtained from the conventional analysis, in which the fitting is usually restricted to a region below 0.15 K. Here we show that the proposed new analysis is most likely flawed, because the specular phonon reflection means that the phonon mean free path ell gets LONGER than the mean sample width, while the estimated ell is actually much SHORTER than the mean sample width above 0.15 K.