Extracting transport channel transmissions in scanning tunneling microscopy using superconducting excess current

Transport through quantum coherent conductors, such as atomic junctions, is described by conduction channels. Information about the number of channels and their transmissions can be extracted from various sources, such as multiple Andreev reflections, dynamical Coulomb blockade, or shot noise. We complement this set of methods by introducing the superconducting excess current as a new tool to continuously extract the transport channel transmissions of an atomic scale junction in a scanning tunneling microscope. In conjunction with ab initio simulations, we employ this technique in atomic aluminum junctions to determine the influence of the structure adjacent to the contact atoms on the transport properties.

Figure 1

(a) Sketch of the single-atom junction studied in the experiment. The tip height $z$ is adjusted in the course of the experiment. (b) Quasiparticle spectrum at low set-point conductance (blue) with corresponding fit. (c) Conductance curve $G_{\mathrm{N}}(z$) recorded above an Al adatom, showing a clear initial exponential increase of the conductance (set-point 1.5 mV at 1 nA). The inset: Topographic image of an Al adatom on the Al(100) surface. (d) $I\left(V\right)$ curve of the superconducting sample at $G_{\mathrm{N}}=0.69G_0$. The currents in the superconducting state (red, SC) and in the normal state (yellow, Ohmic) correspond to the currents $I_{\mathrm{S},\mathrm{N}}$ in Eq. (1), respectively. The excess current is the $y$-axis intercept of the curve at $eV>2\mathrm{\Delta }$. The dashed vertical line indicates $2\mathrm{\Delta }=360\mu \mathrm{eV}$.

Figure 2

(a) and (b) $I\left(V\right)$ curves at various conductances for two typical Al adatoms. MARs appear as steps in the current at fractions of $2\mathrm{\Delta }$. Fits to the data are superimposed on black dotted lines. The shaded areas for small voltages ($V<50\mu \mathrm{V}$) are excluded from the analysis due to the presence of the Josephson current. (c) and (d) Channel transmission analysis from the MAR model for the junctions in panels (a) and (b), respectively, as circles. The purple curve shows the total transmission, i.e. the conductance $G_{\mathrm{N}}\left(z\right)$ in units of $G_0$.

Figure 3

(a) and (b) Measured current (yellow) and reconstructed $G_{\mathrm{N}}\left(z\right)V$ (purple) signals for junctions A and B, respectively. The difference between the two curves results from the excess current. The blue and orange crosses show the same quantities from the MAR point spectra in Figs. 2. (c), (d) Excess current (blue lines) as a function of total transmission ${\tau }_{\mathrm{t}}$ for junctions A and B, respectively. The crosses ($\times$) indicate the excess current independently extracted from the corresponding MAR analysis for comparison. Note that the curves show the approach curve of the tip, i.e., the arrows indicate the direction of decreasing $z$.

Figure 4

(a) and (b) Channel transmission analysis using the excess current for junctions A and B, respectively, with the dominant channel in orange and the degenerate channels shown in blue. The circles show the result of the full MAR analysis from Fig. 2.

Figure 5

(a) and (b) Calculated channel transmissions for a (111) and a (100) terminated tip, respectively, above an Al adatom on Al(100) as a function of tip-sample separation. (c) Transmission through two coupled chains according to Eq. (4). The model qualitatively reproduces the experimental data.