Two dimensional behaviour of friction at a metal surface with a surface state

The contribution of electron–hole pair excitations to the friction coefficient of a charged particle traveling parallel to a metal surface is known to decay for large distances z0 to the surface as z0-4, provided the metal is well described by a semi-infinite jellium. Here we study the friction coefficient of a slow proton moving in front of the Cu(1 1 1) surface. The intrinsic characteristics of this surface, the existence of a wide energy gap in the band structure for electron motion along the surface normal and the existence of a partially occupied surface state, requires, in principle, a description more realistic than the jellium model. To do so, we use a one dimensional model potential that reproduces these features. The friction coefficient is calculated in linear response theory. We use the electronic states solution of the surface model potential to obtain the surface response function within the random phase approximation. Our results indicate that for large values of z0 the friction coefficient decays as z0-3. We show that this behaviour is due to the two dimensional character of the surface state.