Ultrafast Atomic Diffusion Inducing a Reversible $(2\sqrt{3}\times 2\sqrt{3})R30°\leftrightarrow (\sqrt{3}\times \sqrt{3})R30°$ Transition on $\mathrm{Sn}/\mathrm{Si}(111):\mathrm{B}$

Dynamical phase transitions are a challenge to identify experimentally and describe theoretically. Here, we study a new reconstruction of Sn on silicon and observe a reversible transition where the surface unit cell divides its area by a factor of 4 at $250°\mathrm{C}$. This phase transition is explained by the 24-fold degeneracy of the ground state and a novel diffusive mechanism, where four Sn atoms arranged in a snakelike cluster wiggle at the surface exploring collectively the different quantum mechanical ground states.

Figure 1

(a) $15\times 14.5{\mathrm{nm}}^2$ STM image of the $\mathrm{Sn}/\mathrm{Si}(111):\mathrm{B}\text{−}2\sqrt{3}$ surface ($-1.5\mathrm{V}$, 0.02 nA). LEED patterns of (b) the $2\sqrt{3}$ phase ground state at room temperature and (c) the $\sqrt{3}$ phase above 520 K (70 eV beam energy). See Supplemental Material [33] for a video of the reversibility.

Figure 2

Side and top views for the $\mathrm{Sn}/\mathrm{Si}(111):\mathrm{B}\text{−}2\sqrt{3}$ atomic structure. Large, medium, and small balls correspond to Sn (green) and Si (orange) first and second layer atoms, respectively; small grey balls in the side view represent $\mathrm{B}$ atoms. Inside the unit cell (indicated by black solid lines) Sn adatoms, lateral, and central tetramer atoms are plotted in different colors (brown, blue, and purple, respectively).

Figure 3

Experimental STM images for the $2\sqrt{3}$ reconstruction (left panels) and theoretical STM images for the structural model of Fig. 2 (right panels). The top right figure shows Sn atomic positions.

Figure 4

Band structure for the RT-$2\sqrt{3}$ phase along ${\overline{\mathrm{\Gamma }K}}_{\sqrt{3}}$. (a) Experimental band structure at $h\nu =27\mathrm{eV}$. $S_1$ and $S_2$ are Sn surface features and $B$ is a bulk band. (b) Calculated band structure for the model in Fig. 2 showing the four surface states $S_1^{\prime }$, $S_1^{\prime \prime }$, $S_2^{\prime }$, and $S_2^{\prime \prime }$ associated with the Sn atoms. Pink lines are a guide to the eye.

Figure 5

Top view of the motion of the six Sn atoms (different colors) from DFT MD simulations at 700 K. The open circles indicate the (ideal) positions of the Si surface atoms (Si DB sites). The solid green lines indicate the initial and final configurations for the Sn tetramers. The left panel shows one temporal evolution during 13 ps, showing how the system jumps to a new ground state geometry. The right panel shows another temporal evolution of 11.3 ps showing a more complicated evolution of the concerted motion of the Sn adatoms. See the corresponding videos in the Supplemental Material [33].