Revealing the substrate origin of the linear dispersion of silicene/Ag(111)

The band structure of the recently synthesized (3$\times$3) silicene monolayer on (4$\times$4) Ag(111) is investigated using density functional theory. A $k$-projection technique that includes the $k_{\mathrm{\perp }}$-dependence of the surface bands is used to separate the contributions arising from the silicene and the substrate, allowing a consistent comparison between the calculations and the angle-resolved photoemission experiments. Our calculations not only reproduce the observed gap and linear dispersion across the K point of (1$\times$1) silicene, but also demonstrate that these originate from the $k_{\mathrm{\perp }}$-dependence of Ag(111) substrate states (modified by interactions with the silicene) and $\mathit{\text{not}}$ from a Dirac state.