Restored quantum size effects of Pb overlayers at high coverages

Abnormally large stability of Pb nanostructures grown on metallic or semiconductor substrates has been observed even for heights of about 30 monolayers. Using both density-functional theory calculations and analytical models, we demonstrate that the stability at even higher coverages (N>30 ML) is supported by an extra second quantum beat pattern in the energetics of the metal film as a function of the number of atomic layers. This pattern is triggered by the butterflylike shape of the Fermi surface of lead in the (111) direction and supports the detection of stable magic islands of higher heights than measured up to now.