  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.
