Probing quasi-one-dimensional band structures by plasmon spectroscopy

The plasmon dispersion is inherently related to the continuum of electron-hole pair excitations. Therefore, the comparison of this continuum, as derived from band structure calculations, with experimental data of plasmon dispersion, can yield direct information about the form of the occupied as well as the unoccupied band structure in the vicinity of the Fermi level. The relevance of this statement is illustrated by a detailed analysis of plasmon dispersions in quasi-one-dimensional systems combining experimental electron energy loss spectroscopy with quantitative density-functional theory (DFT) calculations. Si(557)-Au and Si(335)-Au with single atomic chains per terrace are compared with the Si(775)-Au system, which has a double Au chain on each terrace. We demonstrate that both hybridization between Si surface states and the Au chains as well as electronic correlations lead to increasing deviations from the nearly free electron picture that is suggested by a too simple interpretation of data of angular resolved photoemission (ARPES) of these systems, particularly for the double chain system. These deviations are consistently predicted by the DFT calculations. Thus also dimensional crossover can be explained.

Figure 1

Structural model of the topmost atomic layer of (a) the Si(553)-Au system and (b) the spin-polarized Si(775)-Au HCW system (top view). Yellow and blue balls correspond to Au and Si atoms, respectively. The ($5\times 2$) and ($7\times 4$) surface unit cells as well as the terrace width are highlighted. Dotted circles indicate the position of the Si adatoms.

Figure 2

Structural model of the topmost atomic layer of (a) the Si(335)-Au system and (b) Si(557)-Au system (top view). Yellow and blue balls correspond to Au and Si atoms, respectively. The ($3\times 2$) and ($5\times 2$) surface unit cells as well as the terrace width are highlighted. Dotted circles indicate the position of the Si adatoms.

Figure 3

Sample EEL spectra of the Si(335)-Au system with $k_{\perp }$ or $k_{\parallel }$ as parameter. Left: Perpendicular to steps. Right: Parallel to steps. A dispersing loss is only seen in the $\left[1\overline{1}0\right]$ direction parallel to the steps.

Figure 4

Comparison of plasmon dispersions with the electron-hole continuum (colored areas) as derived from photoemission data [25] with the assumption of a NFEG for Si(335)-Au (a), Si(557)-Au (b), and Si(775)-Au (c). Contrary to the general requirements, the plasmon dispersion curves completely cross the e-h continuum for all systems except Si(557)-Au. In the inset, the experimental conditions are specified: Energy of primary beam (in eV), surface temperatures LT = 100 K, RT = 300 K. Lines: Semiempirical fits with model of coupled wires from Ref. [30].

Figure 5

Band structure (black lines) along the wires calculated without SO interaction according to the model proposed in Ref. [25] and shown in Fig. 2 for the Si(557)-Au system. Green balls show the dispersion of ${\omega }_{+}$, as calculated with the assumption that excitations of the dashed red band to $E_F$ correspond to ${\omega }_{-}$. Triangles: Same, but for dominant hole excitations (for details, see text).

Figure 6

Band structure calculated without SO interaction according to the model proposed in Ref. [29] of the Si(335)-Au system for different degrees of buckling of the step edge atoms. The buckling is indicated by the height difference $\mathrm{\Delta }z$ of the step edge atoms expressed in Å. See text for details.

Figure 7

Band structure (dark gray lines) calculated without SO interaction according to the model proposed in Ref. [29] and shown in Fig. 2 of the Si(335)-Au system. Buckling of the step edge atoms: 0.817 Å. Green crosses: Dispersion of ${\omega }_{+}$, as calculated with the method described in the text. The yellow band corresponds to the occupied Au-induced band measured by ARPES.

Figure 8

Calculated spin-averaged band structure of the Si(775)-Au system at a gold concentration of 0.32 ML (dark gray lines). Only bands that hybridize with Au chains are shown. Blue circles: ${\omega }_{+}$ as derived from the plasmon dispersion shown in Fig. 4. The Si honeycomb state is schematically depicted in red. Yellow: Extrapolation of the experimental dispersion of occupied Au states to $E_F$ (from Ref. [25]). For details, see text.