Abstract
In recent years, the idea of controlling phonon thermal transport coherently using phononic crystals has been introduced. Here, we extend our previous numerical studies of ballistic low-temperature heat transport in two-dimensional hole-array phononic crystals, and concentrate on the effect of the lattice periodicity. We find that thermal conductance can be either enhanced or reduced by large factors, depending on the the lattice period. Analysis shows that both the density of states and the average group velocity are strongly affected by the periodic structuring. The largest effect for the reduction seen for larger period structures comes from the strong reduction of the group velocities, but a contribution also comes from the reduction of the density of states. For the short period structures, the enhancement is due to the enhanced density of states.
Highlights
Both the density of states and group velocities are strongly modified [6,10,11], and these directly affect the thermal conductance at low temperatures as the phonon propagation is ballistic in the ultralow temperature regime [12], even in the thin membrane geometry [13]
We have extended our previous numerical work of low-temperature ballistic phonon thermal conduction in hole-array phononic crystals to higher frequencies, and studied mainly the influence of the length scale of the lattice on the thermal conduction
The interference conditions for coherent phonons in the structure change, leading to strong changes in the eigenmode spectra, or dispersion relations. These will in turn affect the density of states and group velocities, leading to strong enhancement and suppression effects for thermal conductance
Summary
Two-dimensional phononic crystals (PnC) are useful for controlling acoustic and elastic waves [1], but have recently been shown to offer great possibilities for engineering thermal conduction, even at room temperatures [2,3,4,5], but most notably at ultra-low temperatures below 1 K [6]. That leads to very strong coherent modification of the phonon dispersion relations [6], if micron length scale periodic phononic crystal structures such as hole arrays are fabricated In such structures, both the density of states and group velocities are strongly modified [6,10,11], and these directly affect the thermal conductance at low temperatures as the phonon propagation is ballistic in the ultralow temperature regime [12], even in the thin membrane geometry [13]. We predict that a thermal conductance enhancement is possible for the smaller lattice constant structures, at most by a factor 3.2 at 0.14 K for the smallest period 62.5 nm studied here. This is quite unintuitive, as we predict that by removing material thermal conductance can increase
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