Substrate-Mediated Umklapp Scattering At The Incommensurate Interface Of A Monatomic Alloy Layer

Ultrathin Pb and Ge films deposited on Ag(111) surfaces have been investigated and compared. We found that at 1/3 ML, both films formed surface alloys, Ag2Pb and Ag2Ge, with root 3 x root 3R30 degrees and 19/20 root 3 x 19/20 root 3R30 degrees structures on Ag(111) but the surface electronic structures exhibit a most evident difference at the Ag(111) surface zone boundary (M) over bar (Ag(111)), where the single band and the splitting ones were observed, respectively. Up to 1 ML, Ag2Ge subsequently develops into germanene with a striped phase and then a quasifreestanding phase, as previously reported [Lin et al., Phys. Rev. Mater. 2, 024003 (2018)], while Ag2Pb evolves to a dense Pb(111) phase that also reveals splitting bands at (M) over bar (Ag(111)). We discover that the larger (smaller) atomic size of a Pb (Ge) atom with respect to an Ag atom causes the commensurate (incommensurate) interfaces and further demonstrate that the splitting bands of Ag2Ge surface alloy and 1-ML Pb film originated from the commonly incommensurate interface with Ag(111), which mediates umklapp scattering by inducing the mirror image of the pristine Ag2Ge and Pb(111) bands relative to (M) over bar (Ag(111)).