Insensitivity of atomic point contact conductance to a moiré structure

To elucidate the mechanism of electron transport through atomic point contacts, we investigated the contact-site dependence of electrical conductance on the periodical structure of a moiré pattern observed on a Pb overlayer by scanning tunneling microscopy (STM). In order to eliminate the influence of atomic-site dependence on the conductance, we measured the point contact conductance on sites equivalent in an atomic surface lattice but different in the moiré periodical structure, and found that the conductance does not depend on the contrast of the moiré pattern. The moiré-insensitive conductance indicates a dominant role of local atomic geometry in the point contact conductance. We also revealed that apparent barrier height in the tunneling regime is dependent on the contrast of the moiré pattern, and that the moiré contrast observed by STM on a 7-monolayer thin film originates from the barrier height difference at small bias voltages.

Figure 1

(a) STM image of 11-monolayer (ML) Pb overlayer grown on a Si(111) substrate. (Size: 10 nm×10 nm, sample bias voltage $V_{\mathrm{s}}:10\mathrm{mV}$; tunneling current $I_{\mathrm{t}}:4\mathrm{nA}$.) Surface atoms and a moiré pattern are clearly visible. The inset shows a cross-sectional profile measured along a black dashed line drawn in the image. (b) Tunneling spectra taken at A, B, and C marked in (a), which correspond to dark, intermediate, and bright regions, respectively, in the moiré structure. The spectra were obtained by a lock-in technique with a modulated rms voltage amplitude of 5 mV and a frequency of 525 Hz. The tip-surface distance was stabilized with a tunneling condition of $V_{\mathrm{s}}=2\mathrm{V}$ and $I_{\mathrm{t}}=600\mathrm{pA}$.

Figure 2

(a) STM image $\left(V_{\mathrm{S}}:3.8\mathrm{mV};I_{\mathrm{t}}:30\mathrm{nA}\right)$ taken on a 7-ML Pb thin film and (b–d) simultaneously obtained conductance mappings at (b) $\mathrm{\Delta }z=100\mathrm{pm}$, (c) $\mathrm{\Delta }z=50\mathrm{pm}$, and (d) $\mathrm{\Delta }z=-37\mathrm{pm}$, obtained from the measured conductance traces taken at each pixel during the scanning (image size: 5.0 nm×5.0 nm). A, B, and C marked in (a) and (b) correspond to the sites in dark-, intermediate-, and bright-contrasted areas, respectively, due to the moiré structure. Black dotted circles drawn in (a,b) indicate dark-contracted areas (A) of the moiré pattern.

Figure 3

(a) Conductance traces taken at the sites marked in the conductance mapping taken at $\mathrm{\Delta }z=100\mathrm{pm}$. (b) Black, blue, and red colors correspond to the curves taken at on-top, fcc, and hcp sites, respectively, and dark, intermediate, and light colors indicate the dark-, intermediate-, and bright-contrasted area, respectively, in the moiré pattern. In the image of (b), A, B, and C correspond to the dark, intermediate, and bright areas in the moiré structure, respectively. (c,d) Conductance traces taken at on-top (c) and hcp (d) sites in the dark- and bright-contrasted areas are indicated in (black, red) and (gray, pink), respectively. The upper panels show the traces without compensation (raw) and the lower panels show the ones whose $\mathrm{\Delta }z$ was compensated by the height difference in the corresponding STM image. (e) All the compensated conductance traces taken at the marked sites in (b) are shown in a range of $-60\mathrm{pm}<\mathrm{\Delta }z<-15\mathrm{pm}$.

Figure 4

Zoomed plot of the conductance traces taken from the sites marked in Fig. 3. For all the curves $\mathrm{\Delta }z$ was compensated. A, B, and C correspond to the dark, intermediate, and bright regions in the moiré structure, respectively. The colors of the curves are the same as those in Fig. 3.