Multiple Andreev Reflection Effects in Asymmetric STM Josephson Junctions

TL;DR

This work probes MAR in asymmetric Nb–Nb STM Josephson junctions by tuning $R_n$ through tip–surface distance and measuring $I$–$V$ and $dI/dV$ spectra at $T=50$ mK and 1.5 K. It generalizes the Averin–Bardas MAR theory to junctions with unequal gaps ${\Delta}_L$ and ${\Delta}_R$, enabling extraction of ${\Delta}_s$, ${\Delta}_t$, barrier transparency $D$, and effective channel number $N$ from fits, and shows that gap asymmetry is crucial for accurately modeling subgap MAR features. The data reveal how $D$ and $N$ evolve with $R_n$, reveal a decrease of the tip gap ${\Delta}_t$ with increased transparency, and indicate that the observed switching currents are suppressed by phase diffusion and dissipation, with possible MQT contributions. The results advance parameter extraction in superconducting STM junctions and highlight the need for a more complete theory that includes phase dynamics, charging effects, and environmental noise for tiny Josephson systems.

Abstract

We have examined the electrical behavior of Josephson junctions formed by a scanning tunneling microscope (STM) with a Nb sample and a Nb tip, with normal-state resistances Rn varying between 1 kOhm and 10 MOhm. Current-voltage characteristics were obtained as a function of Rn by varying the distance between the tip and sample at temperatures of 50 mK and 1.5 K. Rn decreases as the tip-sample separation is reduced, and the junction evolves from a phase-diffusion regime to an underdamped small junction regime, and then to a point contact regime. The subgap structure exhibits pronounced multiple Andreev reflection (MAR) features whose amplitudes and onset energies depend sensitively on junction transparency and gap asymmetry. To interpret these spectra, we generalize the Averin-Bardas MAR theory to superconductors with unequal gap magnitudes, providing a quantitative model appropriate for asymmetric STM junctions. The resulting fits yield the superconducting gaps of the electrodes, barrier transparency, and number of conduction channels as a function of Rn. Combining this analysis with Josephson junction dynamics, we further account for the observed switching and retrapping currents and the finite resistance of the supercurrent branch. Our results demonstrate that incorporating intrinsic electrode asymmetry is essential for reliably extracting transport parameters in STM-based superconducting weak links.

Figures (18)

• Figure 1: Illustration showing MAR wavefunction components of the generalized AB model for the case of electron-like source quasiparticles incident from the left. The left lead is a superconductor with gap $\Delta_{L}$ and the right lead is a superconductor with gap $\Delta_{R}$. A voltage bias $V$ is applied to the right lead with respect to the left lead. The barrier in the center acts as a scattering region for quasiparticles and is characterized by transparency $D$ (distinct from the incident hole term $D_n$). The superconductor-to-normal metal interfaces (blue) have unity transparency.
• Figure 2: $I-V$ characteristics for superconducting gap ratios ${\Delta}_{L}$/${\Delta}_{R}=0.25$ (blue), $0.5$ (red), $0.75$ (green) and $1$ (orange) at transparency $D=0.4$ for $T=0$ K. Circles at $V=0$ show corresponding critical currents from \ref{['ic']}. For comparison, also shown is the $I-V$ curve for a symmetric junction with $D=0.01$ (black), near the conventional tunnel limit.
• Figure 3: Normalized critical current as a function of $D$ for ${\Delta}_{L}$/${\Delta}_{R}=0.25$ (blue), $0.5$ (red), $0.75$ (green) and $1$ (orange) at $T=0$ K.
• Figure 4: Effects of temperature on calculated $I-V$ characteristics for transparency $D=0.25$ and ${\Delta}_{L}$/${\Delta}_{R}=0.5$. The curves correspond to $k_{B}T/{\Delta}_{R}$ values of 1 (black), 0.8 (orange), 0.6 (green), 0.4 (red), and 0.2 (blue).
• Figure 5: Topography of representative regions on the Nb(100) crystal surface obtained using a Nb STM tip at (a) 1.5 K and (b) 50 mK. Image (b) shows atomically flat regions with single layer steps of about 0.3 nm.