Impact of Atomic-Scale Contact Geometry on Andreev Reflection

Charge transport has been examined in junctions comprising the normal-metal tip of a low-temperature scanning tunneling microscope, the surface of a conventional superconductor, and adsorbed ${\mathrm{C}}_{60}$ molecules. The Bardeen-Cooper-Schrieffer energy gap gradually evolves into a zero-bias peak with decreasing electrode separation. The peak is assigned to the spectroscopic signature of Andreev reflection. The conductance due to Andreev reflection is determined by the atomic termination of the tip apex and the molecular adsorption orientation. Transport calculations unveil the finite temperature and the strong molecule-electrode hybridization as the origin to the surprisingly good agreement between spectroscopic data and the Blonder-Tinkham-Klapwijk model that was conceived for macroscopic point contacts.

Figure 1

(a) Sketch of a $\mathrm{W}-\mathrm{Nb}$ junction. (b) STM image of Nb atom chains on NbO(111) (100 mV, 500 nA, scale bar: 1 nm). The triangle indicates the preferred ${\text{C}}_{60}$ adsorption region. (c) Sketch of a $\mathrm{W}-{\mathrm{C}}_{60}$ junction. (d) STM image of individual ${\mathrm{C}}_{60}$ molecules adsorbed on NbO(111) (100 mV, 50 pA, scale bar: 3 nm). ${\mathrm{C}}_{60}$ molecules appear as circular protrusions with submolecular structure. (e) Sketch of a ${\mathrm{C}}_{60}-\mathrm{Nb}$ junction. (f) STM image of individual ${\mathrm{C}}_{60}$ molecules on NbO(111) acquired with a ${\mathrm{C}}_{60}$-terminated tip (100 mV, 50 pA, scale bar: 2 nm). Inset: STM image of an atomic protrusion on the surface revealing the ${\mathrm{C}}_{60}$ orientation at the tip apex (100 mV, 50 pA, scale bar: 0.5 nm). (g)–(i) Normalized $dI/dV$ spectra (dots) of $\mathrm{W}-\mathrm{Nb}$ (g), $\mathrm{W}-{\mathrm{C}}_{60}$ (h), ${\mathrm{C}}_{60}-\text{Nb}$ (i) junctions with decreasing electrode separation (from bottom to top). Junction conductances range from (g) 0.20 to $1.29G_0$, (h) 0.11 to $1.35G_0$, (i) 0.34 to $0.97G_0$. Spectra are offset vertically for clarity. Full lines represent fits according to the BTK model. The color of the data sets reflects the magnitude of the BTK transmission $\tau$ (green: $\tau =0$, red: $\tau =1$).

Figure 2

Variation of $\tau$ as a function of $dI/d{V}_n$ evaluated at $\pm 10\mathrm{mV}$ for (a) $\mathrm{W}-\mathrm{Nb}$, (b) ${\mathrm{C}}_{60}-\mathrm{Nb}$, (c) $\mathrm{W}-{\mathrm{C}}_{60}$ junctions. Depending on the junction geometry, experimental data grouped around linear $\tau$ variations with different slopes. In (a) the variation with the higher (lower) slope reflects data acquisition with a W tip terminated by a single atom (two atoms). In (b) the higher (lower) slope was obtained for the tip approaching a single Nb atom (the region between two Nb atom rows). In (c) different slopes were obtained for $\mathbf{6}$, $\mathbf{5}$, $\mathbf{6}:\mathbf{6}$ ${\mathrm{C}}_{60}$ orientations.

Figure 3

(a) Sketch of the model used for transport calculations. The molecule is represented by a single electronic level ${ϵ}_d$. ${\mathrm{\Gamma }}_N^{(\alpha )}$, ${\mathrm{\Gamma }}_N^{(\beta )}$ denote coupling strengths of the two transport channels with the N electrode. ${\mathrm{\Gamma }}_S$ is the hybridization of the single transport channel to the $S$ electrode. (b) Calculated $dI/dV$ data (dots) for ${\gamma }_N={\mathrm{\Gamma }}_N^{(\beta )}/{\mathrm{\Gamma }}_N^{(\alpha )}=0.2$ and $T=0\mathrm{K}$. Full lines are fits to calculated data on the basis of the BTK model. The color of the lines encodes the normal-state transmission of ${\tau }^{(\alpha )}>{\tau }^{(\beta )}$ (green: ${\tau }^{(\alpha )}=0$, red: ${\tau }^{(\alpha )}=1$). (c) Like (b) for $T=0.3{\mathrm{\Delta }}_0/k_B$ with ${\mathrm{\Delta }}_0=1.53\mathrm{meV}$ the average of experimentally determined gap widths. (d) $\tau$ extracted from single-channel BTK fits to calculated $dI/dV$ data as a function of $dI/d{V}_n$. The upper (lower) dashed line represents $\tau =1.0\cdot G_0^{-1}dI/d{V}_n$ ($\tau =0.5\cdot G_0^{-1}dI/d{V}_n$).