Minimizing Coherent Thermal Conductance by Controlling the Periodicity of Two-Dimensional Phononic Crystals

Periodic hole-array phononic crystals (PnCs) can strongly modify phonon dispersion relations and have been shown to influence thermal conductance coherently, especially at low temperatures where bulk scattering is suppressed. One very important parameter influencing this effect is the period of the structure. Here, we measure the subkelvin thermal conductance of nanofabricated PnCs with identical hole-filling factors but three different periodicities, of 4, 8, and 16 mu m, using superconducting tunnel-junction thermometry. We find that all the measured samples can suppress thermal conductance by an order of magnitude and have a lower thermal conductance than the previously measured smaller-period 1-mu m and 2.4-mu m structures. The 8-mu m-period PnC gives the lowest thermal conductance of all the above samples and has the lowest specific conductance per unit heater length observed to date in PnCs. In contrast, coherent transport theory predicts that the longest period should have the lowest thermal conductance. Comparison with incoherent simulations suggests that diffusive boundary scattering is likely the mechanism behind the partial breakdown of the coherent theory.