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The electronic structure of the 4 × 4 silicene monolayer on a semi-infinite Ag(111) substrate is calculated within density functional theory by using the embedded Green’s function technique. The present calculation confirms the conclusion of previous studies that the two-dimensional (2D) Dirac bands do not exist on this surface as a result of the symmetry breaking and strong orbital hybridizations between the Si π and Ag sp states. In addition, by making use of the advantage of the semi-infinite calculation in which the energy continuum of the bulk Ag bands is fully reproduced, we investigate details of the silicene-induced electronic states, including not only their energy dispersion with 2D wave vector ${\bf k}$ but also their spectral shape as a function of energy at each ${\bf k}$ .