Local electronic structure of a quantum point contact observed with STM

We report the direct observation of electronic structures of quantum point contacts (QPCs) using a scanning tunneling microscope (STM) spectroscopy at $77\mathrm{K}$. The QPCs are formed across boundary gaps in a multidomain Bi film on a $\mathrm{Si}\left(111\right)\text{−}\beta \surd 3\times \surd 3\text{−}\mathrm{Bi}$ substrate. Since the QPCs are formed in the direction parallel to the substrate, the direct observations of the atomic and the local electronic structures by using STM are possible. The electronic structure of the QPCs is neither sensitive to the external electric field induced by the STM tip nor to the length of the bridging part, and is well explained by electronic confinement in a one-dimensional cylindrical potential well. We discuss the possibility to specify the effective mass of electrons in the QPC.

Figure 1

(Color online). (a) An STM image ($V_s=+0.5\mathrm{V}$, $I=1.0\mathrm{nA}$, $20\mathrm{nm}\times 15\mathrm{nm}$) including a domain boundary. 6 ML of Bi is deposited onto the $\beta \surd 3\text{−}\mathrm{Bi}$ substrate. (b), (c) Typical high-resolution STM images ($V_s=+0.5\mathrm{V}$, $I=1.0\mathrm{nA}$, $5\mathrm{nm}\times 5\mathrm{nm}$) of the QPCs formed across a domain boundary. (b) Single and (c) double bright spots are observed in the QPCs bridging over the gap as indicated by the arrows.

Figure 2

(Color online). The position dependence of the STM spectra at the eight points on the line passing through the QPC as shown in the inset. Each spectrum is averaged with the spectra at the points sorted with the same symbol in the inset. The characteristic states of the Bi{012} film are indicated with the broken lines. The curve (c) is the STM spectrum above the QPC. The electronic states localized at the QPC are indicated by the arrows. The bottom curve is the calculated DOS of the 1D metal with the radius of $1.5\mathrm{nm}$.

Figure 3

The tip-height dependence of the STM spectra above the QPC. The tip height is tuned by changing the tunneling current from $0.5–2.0\mathrm{nA}$ at the $V_S$ of $+0.5\mathrm{V}$. The broken lines correspond to the positions of the states localized at the QPC.

Figure 4

The STM spectra measured above the double and single spot QPCs shown in Figs. 1b, 1c, respectively. The broken lines indicate the positions of the states localized at the QPCs.

Figure 5

(a) The calculated DOS in the cylindrical potential well. (b)–(e) Contour maps of the cross-sectional wave functions for each eigenstate: (b) $E_{01}$, (c) $E_{11}$, (d) $E_{21}$, and (e) $E_{02}$ states. The radius of the dashed circles is $1.5\mathrm{nm}$, which is assumed as the size of the potential well in the calculations.