We demonstrate that silicene, a 2D honeycomb lattice consisting of Si atoms, loses its Dirac fermion characteristics due to substrate-induced symmetry breaking when synthesized on the Ag(111) surface. No Landau level sequences appear in the tunneling spectra under a magnetic field, and density functional theory calculations show that the band structure is drastically modified by the hybridization between the Si and Ag atoms. This is the first direct example demonstrating the lack of Dirac fermions in a single layer honeycomb lattice due to significant symmetry breaking.

Gundlach oscillation (or the standing-wave state) is a general phenomenon manifesting in the tunneling spectrum acquired from a metal surface using scanning tunneling spectroscopy. Previous studies relate the energy shift between peaks of the lowest-order Gundlach oscillation observed on the thin film and the metal substrate to the difference in their work functions. By observing Gundlach oscillations on $\mathrm{Ag}/\mathrm{Au}(111)$, $\mathrm{Ag}/\mathrm{Cu}(111)$, and $\mathrm{Co}/\mathrm{Cu}(111)$ systems, we demonstrate that the work function difference is not the energy shift of the lowest order but the ones of higher order where a constant energy shift exhibits. Higher order Gundlach oscillations can thus be applied to determine the work function of thin metal films precisely.