Phase relations associated with one-dimensional shell effects in thin metal films

Phys Rev Lett. 2009 Jun 12;102(23):236803. doi: 10.1103/PhysRevLett.102.236803. Epub 2009 Jun 11.

Abstract

The physical and chemical properties of thin metal films show damped oscillations as a function of film thickness (one-dimensional shell effects). While the oscillation period, determined by subband crossings of the Fermi level, is the same for all properties, the phases can be different. Specifically, oscillations in the work function and surface energy are offset by 1/4 of a period. For Pb(111) films, this offset is approximately 0.18 monolayers, a seemingly very small effect. However, aliasing caused by the discrete atomic layer structure leads to striking out-of-phase beating patterns displayed by these two quantities.