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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

Low-Temperature Coherent Thermal Conduction in Thin Phononic Crystal Membranes