# Minimizing coherent thermal conductance by controlling the periodicity of two-dimensional phononic crystals

## TL;DR

This study investigates how the periodicity of two-dimensional phononic crystals affects their ability to suppress thermal conductance at sub-Kelvin temperatures, revealing that certain periodicities outperform smaller ones contrary to coherent transport predictions.

## Contribution

It provides experimental measurements of thermal conductance in PnCs with different periods, showing that an 8 μm period achieves the lowest conductance, challenging existing coherent transport theories.

## Key findings

- All samples suppressed thermal conductance by an order of magnitude.
- The 8 μm period PnC has the lowest thermal conductance among tested structures.
- Comparison suggests diffusive boundary scattering affects coherent transport predictions.

## Abstract

Periodic hole array phononic crystals (PnC) can strongly modify the phonon dispersion relations, and have been shown to influence thermal conductance coherently, especially at low temperatures where scattering is suppressed. One very important parameter influencing this effect is the period of the structure. Here, we measured the sub-Kelvin thermal conductance of nanofabricated PnCs with identical hole filling factors, but three different periodicities, 4, 8, and 16 $\mu$m, using superconducting tunnel junction thermometry. We found 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 samples above, and has the lowest specific conductance/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 to incoherent simulations suggests that diffusive boundary scattering is likely the mechanism behind the partial breakdown of the coherent theory.