Mining single-electron spectra of the interface states from a supercell band structure of silicene on an Ag(111) substrate with band-unfolding methodology

We develop a new position-resolved band-unfolding method based on the density functional theory to clarify the single-electron energy spectrum of $(3\ifmmode\times\else\texttimes\fi{}3)$ silicene on $\mathrm{Ag}(111)$ substrate. The position-resolved scheme enables us to clarify each contribution from each spatial region to the single-electron spectrum, which facilitates the chemical identification of each electron state. We find interface states which are distributed in the region of silicene and top two layers of the Ag substrate near the Fermi level and also below the Fermi level. The states are unique in silicene on a substrate in the sense that they are mixtures of Si and Ag orbitals. The obtained electronic structure near the Fermi level is interesting, featuring a hyperbolic-paraboloid-shaped energy band which leads to 12 Dirac-like cones at the boundary of the primitive Brillouin zone of $\mathrm{Ag}(111)$. Characteristics of measured photoemission spectra are satisfactorily explained by the obtained unfolded bands.