Coupled Pb Chains on Si(557): Origin of One-Dimensional Conductance

The $\mathrm{Pb}/\mathrm{Si}(557)$ system exhibits a strong anisotropy in conductance below 78 K, with the evolution of a characteristic chain structure. Here we show, using angle-resolved photoemission, that chain ordering results in complete Fermi-like nesting in the direction normal to the chains; in addition, the domain structure along the chains forms split-off valence bands with mesoscopic Fermi wavelengths which induce the 1D conductance without further instabilities at low temperatures.

Figure 1

(a) Top-view and side-view model of the wire structure with 1.3 ML of Pb obtained from STM and LEED measurements. The light gray (orange) circles denote Pb atoms on H3 positions. The full monolayer structure is shown only for the first $\sqrt{3}\times \sqrt{3}$ unit cell. (b) STM of the Pb wires ($T=40\mathrm{K}$). The interchain distance $d$ is found to be $1.5\pm 0.1\mathrm{nm}$, whereas along the wire structure a tenfold periodicity $s=3.8\mathrm{nm}$ can be observed [11, 12, 13].

Figure 2

(a), (b) Energy dispersion curves of the 1.3 ML Pb structure ($T_s=40\mathrm{K}$, high intensity in white) in $k_x$ and $k_y$ directions along the dotted lines marked in (c). Here the DOS in the ($k_x$, $k_y$) plane, as measured by ARPES, is plotted at constant energy $E_F-0.1\mathrm{eV}$. In (b), complete filling of the topmost band is demonstrated by the coincidence of the reciprocal lattice vector $g=\frac{2\pi }{d}$ ($d$ is the interchain distance) with $2k_F$ at $E_F$. Further away from $E_F$, as shown in (c), a set of ellipses centered at the $\overline{\Gamma }$ points of the (111) terraces and at centers shifted by $g$ describes most of the intensity distribution. Deviations leading to Fermi nesting are best visible within the square at the center (see Fig. 3).

Figure 3

(a) Constant energy plot, but at $E_F\mathrm{\text{−}}0.03\mathrm{eV}$, of the section marked by a square in Fig. 2c (low intensity in yellow). (b) Schematic drawing of the nesting points. The rectangles show the SBZ of the Pb-wire structure. (c), (d) Momentum distribution curves (MDCs) from (a) taken along $k_y$ and $k_x$, respectively, reflecting the interchain distance $d$ and the tenfold periodicity $s$. (e) Sequence of MDC curves along $k_x$ at $k_y=2.25{\AA }^{-1}$ at different energies around $E_F$. $T_s=40\mathrm{K}$.

Figure 4

Energy distribution curves taken along $k_y$ at $k_x=0{\AA }^{-1}$ (left) and along $k_x$ at $k_y=1.8{\AA }^{-1}$, respectively, below [$T_s=40\mathrm{K}$, solid (blue) line] and above the phase transition [$T_s=100\mathrm{K}$, dashed (red) line].