Two-dimensional phononic thermal conductance in thin membranes in the Casimir limit

We discuss computational analysis of phononic thermal conduction in the suspended membrane geometry, in the experimentally commonly appearing case where heat can flow out radially in two dimensions from a central source. As we are mostly interested in the low-temperature behavior where bulk scattering of phonons becomes irrelevant, we study the limit where all phonon scattering takes place at the membrane surfaces. Moreover, we limit the discussion here to the case where this surface scattering is fully diffusive, the so called Casimir limit. Our analysis shows that in the two-dimensional case, no analytic results are available, in contrast to the well known 1D Casimir limit. Numerical solutions are presented for the temperature profiles in the membrane radial direction, for several different membrane thicknesses. Our results can be applied, for example, in the design of membrane-supported bolometric radiation detectors

Complete tunneling of acoustic waves between closely spaced piezoelectric crystals

When two piezoelectric solids are placed in close proximity, acoustic waves can "tunnel" across a vacuum gap transmitting energy between the two solids. Here, we demonstrate analytically that not only is such a phenomenon possible, but that a simple resonance condition exists for which the complete transmission of the incoming wave is possible. This result is derived for an arbitrary anisotropic crystal symmetry and orientation. We also show that the complete transmission condition can be related to the surface electric impedance and the effective surface permittivity of the piezoelectric material, making it possible to be determined experimentally. In addition, we present numerical results for the maximum power transmittance of a slow transverse wave, tunneling between identical ZnO crystals, as function of all possible crystal orientations. The results show a large range of orientations for which complete tunneling can be achieved.Comment: 10 pages, 4 figure