Electronic structure of silicene on Ag(111): Strong hybridization effects

The electronic structure of the recently synthesized ($3\times 3$) reconstructed silicene on ($4\times 4$) Ag(111) is investigated by first-principles calculations. New states emerge due to the strong hybridization between silicene and Ag. Analyzing the nature and composition of these hybridized states, we show that (i) it is possible to clearly distinguish them from states coming from the Dirac cone of free-standing silicene or from the $sp$ bands of bulk Ag and (ii) assign their contribution to the description of the linearly dispersing band observed in photoemission. Furthermore, we show that silicene atoms contribute to the Fermi level, which leads to similar scanning tunneling microscopy patterns as observed below or above the Fermi level. Our findings are crucial for the proper interpretation of experimental observations.

Figure 1

(a) Constant current STM images of reconstructed ($3\times 3$) silicene on Ag substrate calculated at $-1.4$ eV, $-0.5$ eV, 0.0 eV, and 0.6 eV. (b) The band structure (side panels) and band decomposed charge density isosurfaces (inner panels) of reconstructed silicene in the absence (left side) and presence (right side) of the Ag substrate is shown. The red color indicates the states contributed by $p_z$ orbitals of six Si atoms pointing outwards, whereas the green and light gray lines correspond to the states contributed by Si and Ag atoms, respectively. This correspondence is found by calculating projections of each state to specific atomic orbitals. Si and first layer of Ag atoms are represented by blue and gray balls in the charge density plots. States of interest are labeled by Roman numerals. States corresponding to charge density isosurfaces are shown by arrows where the black circles with little, medium, and large sizes indicate the single, double, and triple degenerate states, respectively.

Figure 2

Left panel: bands of reconstructed ($3\times 3$) silicene in the absence of Ag substrate (unsupported silicene) unfolded to BZ of ($1\times 1$) silicene are shown by red dots. The radii of dots correspond to the weight of unfolding. The band structure of ideally buckled silicene is shown by green lines. Right panel: unfolded band structure of silicene on Ag. Red dots correspond to states with significant contribution from silicene.

Figure 3

(a) Band structure of silicene with 11 Ag layers around K point. Blue and orange dots correspond to bulk Ag states and hybridized silicene/Ag states. Gray dots come from foldings of finite slab and can be ignored. Contribution of three Ag layers at the surface in the (b) absence and (c) presence of silicene. (d) $\pi$ bands of unsupported silicene. (e) $\sigma$ bands of unsupported silicene around $\Gamma$ point. (f) Same as (a) around $\Gamma$ point. The solid black lines in (a), (c), and (f) are representational sketches of the experimental data.[16] It is starting from $-0.3$ eV and has a slope corresponding to $v_F=1.3\times {10}^6$ m/s. It is recommended, however, to compare our data directly with the ARPES data.[16]