  Acoustic phonon transport is revealed as a potential radiation-to-conduction
transition mechanism for single-digit nanometer vacuum gaps. To show this, we
measure heat transfer from a feedback-controlled platinum nanoheater to a
laterally oscillating silicon tip as the tip-nanoheater vacuum gap distance is
precisely controlled from a single-digit nanometer down to bulk contact in a
high-vacuum shear force microscope. The measured thermal conductance shows a
gap dependence of $d^{-5.7\pm1.1}$ in the near-contact regime, which is in good
agreement with acoustic phonon transport modeling based on the atomistic
Green's function framework. The obtained experimental and theoretical results
suggest that acoustic phonon transport across a nanoscale vacuum gap can be the
dominant heat transfer mechanism in the near- and asperity-contact regimes and
can potentially be controlled by an external force stimuli.
