Imaging Heat Transport in Suspended Diamond Nanostructures with Integrated Spin Defect Thermometers

Among all materials, monocrystalline diamond has one of the highest measured thermal conductivities, with values above 2000 W/m/K at room temperature. Diamond nanostructures are increasingly used in photonics, electronics, and quantum technologies, where heat dissipation is critical. However, predicting nanoscale heat flow is made difficult by the predominance of momentum-conserving "normal" phonon-phonon scattering processes. Here, we use 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  μm^{2}, observing a strong reduction in the cantilevers' conductivity as 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 nondiffusive behavior. Our temperature-imaging method paves the way for the exploration of unconventional, nondiffusive heat-transport phenomena in devices and nanostructures of arbitrary geometries.