Absence and presence of Dirac electrons in silicene on substrates

We report on the total-energy electronic-structure calculations on the basis of the density-functional theory that clarify atomic and electronic structures of the silicene on the Ag(111), the hexagonal BN, and the hydrogen-processed Si(111) surfaces. On the Ag(111) surfaces which are most commonly used as substrates for the silicene in current experiments, we find several stable and metastable structures with the 4 x 4, [radic]13 x [radic]13, and 2[radic]3 x 2[radic]3 periodicities with respect to the 1 x 1 Ag(111) lateral cell within the total-energy difference of 70 meV per Si atom. The absence of Dirac electrons caused in this way is found to be common to all the stable and metastable structures of the silicene on the Ag(111) substrates. We also find that the interaction between the [pi] + and the substrate orbitals should be weak enough to preserve Dirac electrons and at the same time be sizable to keep the system stable.