Evidence for Dirac Fermions in a Honeycomb Lattice Based on Silicon

Silicene, a sheet of silicon atoms in a honeycomb lattice, was proposed to be a new Dirac-type electron system similar to graphene. We performed scanning tunneling microscopy and spectroscopy studies on the atomic and electronic properties of silicene on Ag(111). An unexpected $\sqrt{3}\times \sqrt{3}$ reconstruction was found, which is explained by an extra-buckling model. Pronounced quasiparticle interferences (QPI) patterns, originating from both the intervalley and intravalley scatter, were observed. From the QPI patterns we derived a linear energy-momentum dispersion and a large Fermi velocity, which prove the existence of Dirac fermions in silicene.

Figure 1

The STM image of a large area ($65\mathrm{nm}\times 65\mathrm{nm}$) consisting of a sheet of silicene on Ag(111) crossing two substrate steps. (b) The line profile as indicated by the black line in (a) shows that the island is one atom thick. (c) The high-resolution STM image ($10\mathrm{nm}\times 10\mathrm{nm}$) of the silicene surface taken at tip bias 1.0 V. The honeycomb structure is clearly observed. (d) The line profile as indicated by the black line in (c) showing both the lateral and vertical corrugation of the structure observed by STM.

Figure 2

(a),(b) The top view and side view of the lattice geometry of the low-buckled silicene structure ($AB$) and $\sqrt{3}\times \sqrt{3}$ superstructure ($AB\overline{A}$), respectively. Note that in the $\sqrt{3}\times \sqrt{3}$ superstructure a Si atom with planar coordinate $(2/3,2/3)$ is pulled downward. The red (black), yellow (light gray), and green (dark gray) balls represent the $A$, $B$, and $\overline{A}$ Si atoms, respectively. (c) The structural phase transition diagram of silicene depending on the lattice constants of $\sqrt{3}\times \sqrt{3}$ superstructure. (d) A larger schematic model illuminating the honeycomb structure of $\sqrt{3}\times \sqrt{3}$ reconstructed silicene.

Figure 3

(a) The STM image ($50\mathrm{nm}\times 45\mathrm{nm}$) of a silicene island taken at tip bias $-1.1\mathrm{V}$. The white squares label two typical defect sites, namely the step edge and point defect. where scattering patterns with hexagonal close packing structures were observed, as enlarged in (b) and (c). (d) Schematic of the 2D Brillouin zone [blue (thin gray) lines], constant energy contours [blue (gray) rings at $K$ points, and the two types of scattering vectors: $q_1$ [intravalley, short red (dark gray) arrow] and $q_2$ [intervalley, long red (dark gray) arrow].

Figure 4

(a) $dI/dV$ curves taken at 77 K. The position of the DP is labeled. (b) The STM image ($40\mathrm{nm}\times 40\mathrm{nm}$) of the 1 ML silicene surface containing an island of second layer taken at tip bias $-1.0\mathrm{V}$. (c), (d), and (e) $dI/dV$ maps of the same area as (b) taken at tip bias $-1.0$, $-0.8$, and $-0.5\mathrm{V}$, respectively. (f) Energy dispersion as a function of $\kappa$ for silicene determined from the wavelength of QPI patterns. The inset shows a schematic drawing of the overall band structure, with the relative location of the DP, $E_F$, and our data points [red (thick gray) line].