Enhancement of noncontact friction between closely spaced bodies by   two-dimensional systems
  . We consider the effect of an external bias voltage and the spatial variation of the surface potential, on the damping of cantilever vibrations. The electrostatic friction is due to energy losses in the sample created by the electromagnetic field from the oscillating charges induced on the surface of the tip by the bias voltage and spatial variation of the surface potential. A similar effect arises when the tip is oscillating in the electrostatic field created by charged defects in a dielectric substrate. The electrostatic friction is compared with the van der Waals friction originating from the fluctuating electromagnetic field due to quantum and thermal fluctuation of the current density inside the bodies. We show that the electrostatic and van der Waals friction can be greatly enhanced if on the surfaces of the sample and the tip there are two-dimension (2D) systems, e.g. a 2D-electron system or incommensurate layers of adsorbed ions exhibiting acoustic vibrations. We show that the damping of the cantilever vibrations due to the electrostatic friction may be of similar magnitude as the damping observed in recent experiments of Stipe \textit{et al} [B.C.Stipe, H.J.Mamin, T.D.Stowe, T.W.Kenny, and D.Rugar, Phys.Rev. Lett.% \textbf{87}, 0982001]. We also show that at short separation the van der Waals friction may be large enough to be measured experimentally. 
A.I.Volokitin and B.N.J.Persson