Thermal conductivity in glasses below 1 K: New technique and results

Using the capacitance of a glass sample as its own thermometer, we have measured the thermal conductivity of two glasses below 700 mK. This technique avoids any thermal boundary resistance between the thermometer and the sample. In addition, since the loss tangent goes to zero as the temperature is lowered, the amount of heat dissipated in a capacitive measurement is very small at low temperatures. We were able to measure the thermal conductivity at temperatures which were previously experimentally inaccessible and found that the thermal conductivity, kappa, scales as T-1.86 down to 10 mK, in agreement with the two-level system model.