  Bulk electrical dissipation caused by charge-density-wave (CDW) depinning and
sliding is a classic subject. We present a novel local, nanoscale mechanism
describing the occurrence of mechanical dissipation peaks in the dynamics of an
atomic force microscope tip oscillating above the surface of a CDW material.
Local surface 2$\pi$ slips of the CDW phase are predicted to take place giving
rise to mechanical hysteresis and large dissipation at discrete tip surface
distances. The results of our static and dynamic numerical simulations are
believed to be relevant to recent experiments on NbSe$_2$; other candidate
systems in which similar effects should be observable are also discussed.
