We have mapped the electronic structure of atomically uniform films of Ag grown on Ge(111) by angle-resolved photoemission. Cuts in the momentum space at constant energies near the Fermi surface reveal intricate patterns resembling interfering waves emanating from multiple centers. The measured dispersion relations exhibit zigzag patterns with multiple energy gaps. These features are attributed to the mixing of electronic standing waves by the Ag-Ge interface potential as confirmed by the observed pattern symmetry and by an experimentally deduced interaction strength that scales as the inverse film thickness.
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