Spontaneous Symmetry Breaking and Dynamic Phase Transition in Monolayer Silicene

The $(\sqrt{3}\times \sqrt{3})R30°$ honeycomb of silicene monolayer on Ag(111) was found to undergo a phase transition to two types of mirror-symmetric boundary-separated rhombic phases at temperatures below 40 K by scanning tunneling microscopy. The first-principles calculations reveal that weak interactions between silicene and Ag(111) drive the spontaneous unusual buckling in the monolayer silicene, forming two energy-degenerate and mirror-symmetric $(\sqrt{3}\times \sqrt{3})R30°$ rhombic phases, in which the linear band dispersion near the Dirac point and a significant gap opening (150 meV) at the Dirac point were induced. The low transition barrier between these two phases enables them to be interchangeable through dynamic flip-flop motion, resulting in the $(\sqrt{3}\times \sqrt{3})R30°$ honeycomb structure observed at high temperature.

Figure 1

(a) The high resolution STM image of monolayer silicene taken at tip bias 1.0 V at 77 K. (b) LEED pattern taken at 51.4 eV on $\sqrt{3}\times \sqrt{3}R30°$ silicene. The white, red, and yellow circles represent the Ag(111) $1\times 1$ spot, silicene $1\times 1$ spots, and silicene $\sqrt{3}\times \sqrt{3}$ ones, respectively. (c), (d) The STM images of the same area on $\sqrt{3}\times \sqrt{3}R30°$ silicene taken at tip bias $-2.0\mathrm{V}$ and 0.1 V, respectively, at 5 K. (e) The filtered high-resolution STM image with high contrast taken at 0.1 V. The yellow rectangle marks the position of the domain boundary. The red triangles indicate the brighter protrusions in one unit cell in different domains. (f) $dI/dV$ curves taken at 77 K (red curve) and 5 K (black curve). The position of the DP is labeled.

Figure 2

(a) The STM image of silicene with domain boundaries taken at tip bias $-1.0\mathrm{V}$. (b), (c), (d) $dI/dV$ maps of the same area as (a) taken at tip bias $-1.1\mathrm{V}$, $-0.8\mathrm{V}$, and $-0.5\mathrm{V}$, respectively. (e) Schematic of two-dimensional Brillouin zone (gray lines), constant energy contours (blue rings) at $K$ points, and intravalley scattering vectors $q_1$ (red arrow). (f) Energy dispersion as a function of $\kappa$ (defined in text) for silicene determined from the wavelength in $dI/dV$ maps. The red line shows a linear fit to the data.

Figure 3

The top views (a), (b) and side views (c), (d) of two energy-degenerated $\sqrt{3}$ reconstructed structures of silicene sheet on an Ag(111) surface with an orientation angle of $\theta =30°$, which are obtained from DFT optimization in the case of both lattices of $\sqrt{3}$ silicene and silver substrate having identical direction. Color code: Blue, yellow, and red spheres denote Ag atoms, Si atoms in lower layer, and Si atoms in higher layer, respectively. The red triangles in (a) and (b) denote the orientations of the buckled Si patterns with respect to Ag(111).

Figure 4

(a) The interpolated potential energy curve for structural transition between the two mirror-symmetric $\sqrt{3}$ geometries on Ag(111). (b) The intermediate structure between the two rhombic $\sqrt{3}$ structures of silicene shown in Figs. 3a, 3b. (c), (d) Experimental STM images of the same area taken at $-2.0\mathrm{V}$ before and after a 3.0 V pulse (10 ms) was applied. The yellow dot marks the position of the pulse applied. (e), (f) The band structures of the $\sqrt{3}$ structure of silicene layer and the $1\times 1$ structure of freestanding silicene, respectively.