Imaging heat transport in suspended diamond nanostructures with integrated spin defect thermometers

Among all materials, mono-crystalline diamond has one of the highest measured thermal conductivities, with values above 2000 W/m/K at room temperature. This stems from momentum-conserving normal' phonon-phonon scattering processes dominating over momentum-dissipating Umklapp’ processes, a feature that also suggests diamond as an ideal platform to experimentally investigate phonon heat transport phenomena that violate Fourier’s law. Here, we introduce dilute nitrogen-vacancy color centers as in-situ, highly precise spin defect thermometers to image temperature inhomogeneities in single-crystal diamond microstructures heated from ambient conditions. We analyze cantilevers with cross-sections in the range from about 0.2 to 2.6 $\mu$m${}^2$, observing a strong reduction of the cantilevers’ conductivity as the width decreases. We use first-principles simulations based on the linearized phonon Boltzmann transport equation and viscous heat equations to quantitatively predict the cantilevers’ thermal transport properties, rationalizing how the interplay between intrinsic and extrinsic phonon scattering mechanisms determines the observed non-diffusive behavior. Our temperature-imaging method paves the way for the exploration of unconventional, non-diffusive heat transport phenomena in devices and nanostructures of arbitrary geometries.