Effect of surface roughness on the universal thermal conductance

We explain the reduction of the thermal conductance below the predicted universal value observed by Schwab at al. [Nature (London) 404, 974 (2000)] in terms of the scattering of thermal phonons off surface roughness using a scalar model for the elastic waves. Our analysis shows that the thermal conductance depends oil two roughness parameters: the roughness amplitude delta and the correlation length a. At sufficiently low temperatures the ratio of the conductance to the universal value decreases quadratically with temperature at a rate proportional to delta (2)a. Values of delta equal to 22% and a equal to about 75% of the width of the conduction pathway give a good fit to the data.