The authors describe how acoustic phonons can directly tunnel through vacuum and, therefore, transmit energy and conduct heat between bodies that are separated by a vacuum gap. This effect is enabled by introducing a coupling mechanism, such as piezoelectricity, that strongly couples electric field and lattice deformation. The electric field leaks into the vacuum as an evanescent field, which leads to finite solid-vacuum-solid transmission probability. Due to strong resonances in the system some phonons can go through the vacuum gap with (or close to) unity transmission, which leads to significant thermal conductance and heat flux.
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