Absence of a Dirac cone in silicene on Ag(111): First-principles density functional calculations with a modified effective band structure technique

We investigate the currently debated issue of the existence of the Dirac cone in silicene on an Ag(111) surface, using first-principles calculations based on density functional theory to obtain the band structure. By unfolding the band structure in the Brillouin zone of a supercell to that of a primitive cell, followed by projecting onto Ag and silicene subsystems, we demonstrate that the Dirac cone in silicene on Ag(111) is destroyed. Our results clearly indicate that the linear dispersions observed in both angular-resolved photoemission spectroscopy [P. Vogt et al., Phys. Rev. Lett. 108, 155501 (2012)] and scanning tunneling spectroscopy [L. Chen et al., Phys. Rev. Lett. 109, 056804 (2012)] come from the Ag substrate and not from silicene.

Figure 1

(a) Top and (b) side view of the silicene-Ag system (small balls: Si; big balls: Ag). (c) (projected) density of states of low-buckled silicene (line) and of silicene on Ag(111) surface (circles).

Figure 2

Si- and Ag-projected effective band structure (EBS) of the silicene-Ag system. (a) Si-projected effective band structures, with band structure of standalone low-buckled silicene plotted as blue dashed lines. Note that the band structure of low-buckled silicene was shifted downward by $1.1\text{eV}$. (b) Ag-projected effective band structures with experimental observed linear dispersions (red circles: measurements from Ref. 7, blue squares: measurements from Ref. 8).

Figure 3

(a) Effective band structures and (b) density of states of standalone silicene with additional buckling are compared with that of low-buckled silicene (red dashed lines).

Figure 4

Effective band structure projected onto silicene (a) and onto five Ag(111) layers (b)–(f). (b) corresponds to adjacent Ag(111) layer to silicene, (f) to the farthest Ag layer, and (c)–(e) in between. Band structure of standalone low-buckled silicene shifted by $-1.1$ eV is plotted as blue dashed lines in (a). Experimental observed linear dispersions are plotted in (b)–(f) (red circles: measurements from Ref. 7, blue squares: measurements from Ref. 8).