Nanoscale solid-solid contacts define a wealth of material behaviours from the electrical and thermal conductivity in modern electronic devices to friction and losses in micro- and nanoelectromechanical systems. For modern ultra-high integration processor chips, power electronic devices and thermoelectrics one of the most essential, but thus far most challenging, aspects is the assessment of the heat transport at the nanoscale sized interfaces between their components. While this can be effectively addressed by a scanning thermal microscopy, or SThM, which demonstrates the highest spatial resolution to thermal transport to date, SThM quantitative capability is undermined by the poorly defined nature of the nanoscale contact between the probe tip and the sample. Here we show that simultaneous measurements of the shear force and the heat flow in the probe-sample junction shows distinct correlation between thermal conductance and maximal shear force in the junction for multiple probe-material combinations. Quantitative analysis of this correlation confirmed the intrinsic ballistic nature of the heat transport in the tip-surface nanoscale contact suggesting that they are, ultimately, composed of near-atomic sized regions. Furthermore, in analogy to the Wiedemann-Franz law, which links electrical and thermal conductivity in metals, we suggest and experimentally confirm a general relation that links shear strength and thermal conductance in nanoscale contacts via the fundamental material properties of heat capacity and heat carrier group velocity, thus opening new avenues for quantitative exploration of thermal transport on the nanoscale.
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