Statistical detection of Josephson, Andreev, and single quasiparticle currents in scanning tunneling microscopy

We present a method to identify distinct tunneling modes in a tunable superconducting tunnel junction composed of a superconducting tip and a sample in a scanning tunneling microscope. Combining the relative decay constant of tunneling current extracted from $I-V-z$ spectroscopy with its statistical analysis over the atomic disorders in the sample surface, we identified the crossover of dominant tunneling modes between single charge tunneling, Andreev reflection (AR), and Josephson tunneling with respect to the bias voltage at a measurement temperature nearly half of the critical temperature. The method enables one to determine the specific tunneling regime independently of the spectral shapes and to reveal intrinsic modulation of AR and Josephson current by disorder that will be crucial for superconducting quantum information processing.

Figure 1

(a) Schematic of tunable superconductor tunnel junction composed of a superconducting scanning tunneling microscope (STM) tip and a superconducting sample. (b)–(d) Schematic diagrams of single charge tunneling, multiple Andreev reflection, and Josephson tunneling, respectively. Under each diagram, the expected formula of exponentially decaying current is written for the asymptotic case of large $z$.

Figure 2

(a) $I-V$ curves between Pb tip and Pb(110) for every 1 pm step as the tip approaches from 0 to −80 pm. $z=0$ is defined as the tip height at $V_b=4.6\mathrm{mV}$ and $I=10\mathrm{nA}$. (b) $dI/dV$ curves obtained by numerical differentiation of $I-V$ curves in (a). (c) Relative decay constant $\kappa /{\kappa }_N$ for Pb tip on Pb(110) and Au(111).

Figure 3

(a) Scanning tunneling microscope (STM) topograph of Pb(110) ($V_b=4.6\mathrm{mV}$, $I=10\mathrm{nA}$). (b) $\kappa /{\kappa }_N$ curves of four different types of sites in (a). (c)–(f) The maps of the relative decay constant at the biases labeled on top. (g) The probability density from the histogram of the $\kappa /{\kappa }_N$ values in the map at certain bias. (h) Kullback-Leibler (KL) divergence between the probability density of $\kappa /{\kappa }_N$ values at maximum bias and other biases, centered on the mean value.

Figure 4

(a) Schematic of the lattice structure of normal-superconductor junction for transport conductance simulation. (b) The conductance vs energy for different barrier heights. The superconducting gap was chosen as 0.1t, where $t$ is the hopping integral. (c) The relative decay constant for different barrier heights (shown in legends, in units of $t$). (d) The relative decay constant graphs with increasing thermal broadening (${\mathrm{\Delta }}_s=0.1t=1.35\mathrm{meV}$ for comparison with the experiment).

Figure 5

$dI/dV$ spectra of Pb(110) measured by normal metal tip (blue dots) and fitting of the curve with the Dynes formula (red line).

Figure 6

(a) $I-z$ curves for different $V_b$ fitted to the exponential function (red lines). Note that the $y$ axis is in log scale. (b) The relative decay constant $\kappa /{\kappa }_N$ and the $R^2$ from the fitting in (a). (c) $dI/dV\text{−}z$ curves for different $V_b$ fitted to the exponential function (red lines). Note that the $y$ axis is in log scale. (d) The relative decay constant $\kappa /{\kappa }_N$ and the $R^2$ from the fitting in (c).

Figure 7

(a) Fitting of $I-V$ curves in Fig. 2 with $P$($E$) theory. Note that the plot range of $I-V$ curves are zoomed in from Fig. 2 to make curves visible. (b) Comparison of Josephson critical current from the fitting in (a) and Ambegaokar-Baratoff (AB) formula.