Low Temperature Thermal Conductivity of PVC

At very low temperatures, the tunnelling theory for amorphous solids predicts a thermal conductivity κ α Tm, with m = 2. However, most of the data in the literature in the temperature range 0.1–1 K report an m <  2. We want to show that this discrepancy often disappears for T→ 0 K. Here we report the case of Polyvinyl Chloride (PVC) whose thermal conductivity is known in the 0.2–100 K temperature range. A new technique is described which makes the measurement of the exponent m of the thermal conductivity independent of the spurious thermal power. Such technique is particularly useful for measurements of κ when working with a low power refrigerator. We carried out measurements down to 50 mK, obtaining a thermal conductivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa = (1.8 \pm 0.1) \times 10^{-4} T^{(2.05\pm 0.05)}}$$\end{document} W/cm K for our PVC sample below 120 mK.