  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.
