Heat transfer across a vacuum gap induced by piezoelectrically mediated acoustic phonon tunneling

In contradictin to the common concept that acoustic phonons can only travel inside a material medium, they can in fact "tunnel" across a vacuum gap with the help of piezoelectricity, transmitting a significantly stronger heat flux than that of blackbody radiation. Here, we present a theoretical formulation for the heat flux of such piezoelectrically mediated heat transfer, applicable to any anisotropic piezoelectric crystals with an arbitrary orientation. A few numerical results are demonstrated and compared to heat transfer driven by other close-range mechanisms, including near-field radiative heat transfer and other acoustic phonon tunneling mechanisms. We find that piezoelectrically mediated heat transfer has a significant effect when the vacuum gap size is smaller than the phonon characteristic thermal wavelength, and its heat flux can dominate heat transfer between piezoelectric solids over all other known heat transfer mechanisms at temperatures below 50 K.