Anomalous phase relations of quantum size effects in ultrathin Pb films on Si(111)

Abstract

Quantum oscillations of work function and film stability as a function of the film thickness in Pb thin films on Si(111) are measured directly using scanning tunneling microscopy and spectroscopy in order to determine their phase relationship. The comparison of the phase relationship in quantum oscillations (surface energy vs work function) reveals a complete surprise: In contrast to a theoretically predicted quarter wavelength phase shift in the phase relationship, we found that their quantum oscillations have identical phase for this particular system. A conjecture to resolve this contradiction is also provided.