Role of Spin-Orbit Splitting and Dynamical Fluctuations in the Si(557)-Au Surface

Our ab initio calculations show that spin-orbit coupling is crucial to understand the electronic structure of the Si(557)-Au surface. The spin-orbit splitting produces the two one-dimensional bands observed in photoemission, which were previously attributed to spin-charge separation in a Luttinger liquid. This spin splitting might have relevance for future device applications. We also show that the apparent Peierls-like transition observed in this surface by scanning tunneling microscopy is a result of the dynamical fluctuations of the step-edge structure which are quenched as the temperature is decreased.

Figure 1

(a) Calculated equilibrium structure of the Si(557)-Au reconstruction. The corresponding electronic band structure is shown for a calculation not including (b), and including (c), the spin-orbit interaction. Energies are referred to the Fermi level. Surface states have been marked with different symbols according to their main atomic character (see text).

Figure 2

Total energy (a) and position of the $B$ atom (b) as a function of the height of atom $A$. Heights are referred to that of atom $A$ in the ground-state configuration. The arrows in panel (b) mark the position of the two energy minima. The energy landscape shows two wells separated by a small energy barrier of $\sim 29\mathrm{m}\mathrm{e}\mathrm{V}$, and estimated zero-point energies of ${\omega }_0\sim 5$ and 9 meV.

Figure 3

Simulated STM images at low (a) and high temperature (b) for a $+0.7\mathrm{V}$ bias voltage (empty states). The upper part of panel (a) corresponds to the ground-state structure, while the lower part is obtained with the reversed step-edge configuration. Panel (b) combines both images.