Thermal conductance through discrete quantum channels

We have observed a quantized limiting value of the thermal conductance for each propagating phonon channel in a one-dimensional (1D), ballistic phonon waveguide: g0=π2kB2T/3h. To achieve this we have developed nanostructures with full three-dimensional relief that incorporate integral thermometers and heaters. These devices are comprised of an isolated thermal reservoir (phonon cavity) suspended above the sample substrate by four narrow insulating beams (phonon waveguides) with lateral dimensions ∼100 nm. We employ DC SQUID noise thermometry to measure the temperature of the phonon cavity non-perturbatively. Direct electrical contact from the suspended nanostructure to the room-temperature environment, crucial for these experiments, is attained by means of a very significant level of electrical filtering. These first experiments provide access to the mesoscopic regime for phonons, and open intriguing future possibilities for exploring thermal transport in very small systems. We are currently adapting and improving the ultrasensitive, extremely low dissipation DC SQUID techniques utilized in this work toward the ultimate goal of detecting individual thermal phonons.