Two-dimensional crossover and strong coupling of plasmon excitations in arrays of one-dimensional atomic wires

Dimensional crossover is of high relevance to understanding real-world quasi-one-dimensional (1D) systems. Here we study the collective excitations, measured as plasmon dispersions in an electron energy loss experiment, in a tunable family of model systems, namely, Au chains on stepped Si($hhk$) substrates, that allow variations of chain widths and interchain spacings. We indeed observe 1D-like dispersions, but with a significant influence of higher dimensions. Surprisingly, we find that it is not the interchain coupling but the width of the conduction channel, as confirmed by tunneling spectroscopy, that dominates the excitations.

Figure 1

(a) LEED patterns of the chain structures of Si(553)-Au and Si(775)-Au. (b) STM image of the Si(775)-Au chain structure (tunneling conditions $U=-1.25$ V, $I=300$ pA): $\alpha ,\beta ,\gamma$ mark the Si terrace edge, a row of Si adatoms accompanied by Si restatoms, and a Au double chain with $\times 2$ period doubling, respectively [26]. STM experiments were performed at 77 K, and LEED at 300 K. Bright protrusion could be identified as an adatom defect [26].

Figure 2

Electron energy loss spectra (primary energy 20 eV) of Au chains grown on Si(553) as a function of $k$ parallel and normal to the wires, as indicated.

Figure 3

Plasmon dispersion for Au quantum wires grown on Si(553) and on Si(775). Lines are fits according to Eq. (1). Dashed-dotted lines: First terms of Eq. (1) for both systems. Dotted line: Same for Si(557)-Au; fitted data from Ref. [28].

Figure 4

(a) Combined image of tunneling microscopy and spectroscopy of Au on Si(553). Bottom: Topography image ($U=0.1$ V, 50 pA) with Si edge (bright) and period doubled Au chains, very similar to Si(775)-Au (see Fig. 1). Top: $dI/dU$ map of the same sample area recorded with the lock-in technique ($U_{\text{mod}}=10$ mV) displayed close to $E_F$ ($U_{\text{dc}}=+6.4$ meV). The density of states (DOS) is significantly enhanced at the Au chain position. (b) Line scan through the $dI/dU$ map from above normal to the steps indicated by the white dashed line; the fit is given by the red curve.