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 4×4, √13×√13, and 2√3×2√3 periodicities with respect to the 1×1 Ag(111) lateral cell within the total-energy difference of 70 meV per Si atom. Those stable structures show the excellent agreement with the scanning tunneling microscopy measurement in their structural characteristics. The metastable structures with comparable total energies await experimental observations. In all the stable and metastable structures, the silicene is buckled substantially so that the π state rehybridizes with the σ state, leading to the π+ state, and then the linear energy dispersion peculiar to the Dirac electrons disappears in several cases associated with the opening of the energy gap. Moreover, we find that the substantial mixing of the π+ state, generated in such a way, with the states of the Ag atoms in the substrate converts the π+ state to the mixed π+ state and thus makes the state shift downwards or upwards, eventually annihilating Dirac electrons near the Fermi level. 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 π+ and the substrate orbitals should be weak enough to preserve Dirac electrons and at the same time be sizable to keep the system stable. We then propose two specific substrates as good candidates for the silicene with Dirac electrons, i.e., hexagonal BN and the hydrogen-processed Si(111) surface. We clarify that the silicene on those substrates are stable enough with the binding energy comparable to or twice that of the graphite and preserve Dirac electrons near the Fermi level.