Anomalous thickness dependence of the Hall effect in ultrathin Pb layers on Si(111)

The magnetoconductive properties of ultrathin Pb films deposited on Si(111) are measured and compared with density-functional electronic band-structure calculations on two-dimensional, free-standing, 1 to 8 monolayers thick Pb(111) slabs. A description with free-standing slabs is possible because it turned out that the Hall coefficient is independent of the substrate and of the crystalline order in the film. We show that the oscillations in sign of the Hall coefficient observed as a function of film thickness can be explained directly from the thickness dependent variations of the electronic bandstructure at the Fermi energy.