Controlling phonon thermal conduction at low temperatures using pillar phononic crystals

Phononic crystals (PnC) are periodic structures which can have a strong impact on the phonon dispersions and thus group velocities and the density of states, if coherence is maintained. We have shown before [1,2] that such coherent modification of thermal conductance was possible at sub-Kelvin temperature range, using periodic arrays of holes etched into 2D silicon membranes. Here, we consider an alternative geometry for the PnC structure, that of a periodic array of superconducting pillars on an unperforated SiN membrane. Somewhat unintuitively, even if the membrane itself is left untouched, our coherent calculations still predict a strong effect on the thermal conductance. We have also performed sub-Kelvin experiments with two different pillar PnC structures with lattice constants 1 µm and 5 µm, both of which produced a sizeable reduction in thermal conductance, up to an order of magnitude, with the shorter period producing a stronger effect contrary to the coherent simulations. This possibly indicates a partial destruction of the coherence for the larger period structure due to scattering from the rough pillar edges.
[1] N. Zen et al., Nat. Comm. 5, 3435 (2014)
[2] Y. Tian et al., Phys. Rev. Appl. 12, 014008 (2019)