Josephson spectroscopy study of kagome superconductors toward the deep point-contact regime

This study demonstrates that Josephson scanning tunneling microscopy (JSTM) on kagome superconductors in the deep point-contact regime exhibits a deviation from quadratic zero-bias conductance dependence and a saturation effect caused by series resistance, providing critical insights for interpreting exotic physics and identifying an optimal regime for probing pair-density wave states.

The Gist

Imagine you are trying to listen to a very quiet conversation between two people (two superconductors) by holding a tiny microphone (a scanning tunneling microscope tip) very close to them. This is the basic idea of Josephson Scanning Tunneling Microscopy (JSTM). Scientists use this technique to "hear" the secret language of superconducting electrons, specifically looking for a special signal called the "Josephson current" that flows when there is no voltage pushing it.

For a long time, scientists knew how to listen when the microphone was just near the speakers (the "tunneling regime"). In this state, the signal gets louder as you move the microphone closer, following a predictable, smooth pattern.

The Experiment: Pushing the Microphone Too Close
In this study, the researchers decided to push the microphone even closer—so close that it almost touches the speakers. They wanted to see what happens when the connection becomes a direct, physical "point contact" rather than just a whisper across a gap. They used a special type of superconducting material called a "kagome superconductor" (named after a Japanese basket-weaving pattern) to test this.

What They Found: The "Volume" Knob Stuck
As they pushed the connection deeper, they discovered three distinct stages:

1. The Whisper (Tunneling): When the gap is small but open, the signal gets louder quickly, just like turning up a volume knob. The loudness increases in a smooth, predictable curve.
2. The Shout (Point Contact): As they got even closer, the signal suddenly jumped up much faster than expected. It was like the speakers suddenly started shouting. This is likely because the electrons started bouncing back and forth multiple times between the tip and the sample (a phenomenon called "multiple Andreev reflections").
3. The Wall (Saturation): Finally, when they pushed the connection to its absolute limit, the signal stopped getting louder. It hit a "ceiling" and stayed flat, no matter how much closer they moved the tip.

The Big Surprise: It Wasn't a New Physics, It Was a Wiring Problem
At first, hitting that "ceiling" looked mysterious. In the world of quantum physics, flat signals often hint at exotic, magical new particles (like "Majorana zero modes"). The researchers initially wondered if they had discovered something new.

However, they realized the truth was much more mundane: It was just a wiring issue.

Think of it like trying to measure the water flow from a firehose, but your hose is connected to a very narrow, kinked garden hose before it reaches your bucket. No matter how much you open the firehose, the water flow into the bucket is limited by that narrow garden hose.

In their experiment, the "narrow garden hose" was the resistance in the cables and filters of their machine. Once the connection between the tip and the sample became so good (so low resistance) that it was smaller than the resistance of the cables, the cables became the bottleneck. The signal couldn't get any louder because the "wiring" was limiting it, not the physics of the material.

The Takeaway: How to Listen Correctly
The paper concludes with a very practical warning for other scientists:

• Don't trust the "ceiling": If you see a signal stop growing in these experiments, don't immediately assume you've found a new exotic particle. It might just be your equipment's wiring getting in the way.
• Find the "Goldilocks Zone": To use this microscope to study complex quantum states (like Pair-Density Waves, which are like ripples in the superconducting sea), you need to find the "just right" distance. You need to be close enough to hear the signal clearly, but not so close that you hit the "wiring ceiling" or accidentally break the delicate surface of the sample.

In short, the researchers mapped out exactly how far you can push this microscopic connection before the measurement stops telling you about the material and starts telling you about the wires in your lab.

Technical Summary

Technical Summary: Josephson Spectroscopy Study of Kagome Superconductors toward the Deep Point-Contact Regime

Problem Statement
Josephson Scanning Tunneling Microscopy (JSTM) is a established technique for probing the superconducting order parameter at the atomic scale by utilizing a superconducting tip and sample to form an ultrasmall superconductor-insulator-superconductor (SIS) junction. While the behavior of the Josephson current in the tunneling regime is well-understood via phase-diffusion models or dynamical Coulomb blockade theory, the behavior of the junction as it transitions into the deep point-contact regime (where the normal-state junction resistance $R_n$ approaches or falls below the resistance quantum $R_0 = h/2e^2 \approx 12.9$ k$\Omega$) remains less explored. A critical challenge arises when the junction resistance becomes extremely small: the zero-bias conductance (ZBC), a key metric for the Josephson current, is expected to increase. However, experimental observations of ZBC saturation in this regime have led to ambiguity, with potential misinterpretations of such saturation as signatures of exotic physics (e.g., Majorana zero modes) rather than instrumental artifacts. Furthermore, identifying the optimal operating regime for JSTM to reliably map novel quantum states, such as pair-density waves (PDW), in materials with low superconducting transition temperatures (like $AV_3Sb_5$) requires a precise understanding of the tip-sample coupling limits.

Methodology
The study employs JSTM experiments conducted in a dilution refrigerator at a base temperature of approximately 30 mK. Two primary kagome superconductor systems were investigated:

1. Cs(V$_{0.86}$Ta$_{0.14}$)$_3$Sb$_5$ ($T_c \approx 5$ K): Measured using a non-superconducting Pt-Ir tip initially, and subsequently with a superconducting tip created by intentionally picking up sample material.
2. KV$_3$Sb$_5$: Measured using a Niobium (Nb) superconducting tip.

The experimental approach involved systematically decreasing the tip-sample distance to drive the junction normal-state conductance ($G_n = 1/R_n$) from the tunneling regime ($R_n \gg R_0$) through the crossover region and into the deep point-contact regime ($R_n \lesssim R_0/2$). A crucial aspect of the methodology was the rigorous correction for series resistance ($R_{series} \approx 5.3$ k$\Omega$) inherent in the circuit (cables, filters, etc.). For low-resistance junctions, the actual junction bias ($V_J$) and conductance ($g_J$) were recalculated from the measured bias ($V_{Bias}$) and current ($I$) using the relations:
$$V_J = V_{Bias} - R_{series} \cdot I$$
$$g_J = \frac{dI/dV_{Bias}}{1 - (dI/dV_{Bias}) \cdot R_{series}}$$
This correction was essential to distinguish intrinsic junction physics from measurement-induced artifacts. The stability of the tip and sample was monitored via topographic imaging before and after spectroscopy sequences.

Key Results
The study characterizes the evolution of the zero-bias conductance (ZBC) as a function of the normal-state conductance ($G_n$), identifying three distinct regimes:

1. Tunneling Regime ($G_n \leq G_0$): The ZBC increases approximately quadratically with $G_n$ ($ZBC \propto G_n^{1.89}$), consistent with previous studies and theoretical expectations for weak coupling.
2. Crossover/Point-Contact Regime ($G_0 \leq G_n \leq 2G_0$): The ZBC deviates from the quadratic trend and increases more rapidly. The normalized conductance ($ZBC/G_n$) approaches 2, a behavior consistent with multiple Andreev reflections as predicted by Blonder-Tinkham-Klapwijk (BTK) theory.
3. Deep Point-Contact Regime ($G_n > 2G_0$): The ZBC exhibits a striking saturation, reaching a constant plateau. The authors demonstrate that this saturation is not an intrinsic property of the junction or a signature of exotic physics, but is instead a measurement artifact caused by the series resistance ($R_{series}$) in the circuit. As the junction conductance becomes very large, the total measured conductance is dominated by $R_{series}$, leading to the observed plateau ($g_{Lock-in} \leq 1/R_{series}$).

Additionally, the study confirms that while the tip and/or sample surface can be modified during high-conductance measurements (evidenced by topographic changes), the spectral features of the Josephson current remain repeatable and intrinsic to the junction state.

Significance and Claims
The paper claims to provide a comprehensive understanding of Josephson currents in JSTM from the tunneling limit to the deep point-contact regime. Its primary contributions are:

• Clarification of Saturation: It identifies the series resistance in the measurement circuit as the cause of ZBC saturation in the deep point-contact regime. This serves as a critical cautionary note for researchers studying exotic physics (such as Majorana zero modes), warning that observed ZBC saturation or quantization in low-resistance junctions may be instrumental artifacts rather than new physical phenomena.
• Optimization of JSTM for PDW Studies: The authors identify an "optimum regime" for using JSTM as an atomic-scale probe for pair-density wave (PDW) states. They argue that for materials with small superconducting gaps (like KV$_3$Sb$_5$), mapping should be performed in the linear regime of the ZBC vs. $G_n^2$ relationship (specifically where $G_n$ is moderate, avoiding the deep point-contact saturation). Operating in this linear regime minimizes errors introduced by surface roughness or vertical drift, ensuring that variations in the measured order parameter reflect true spatial modulations rather than changes in coupling strength.
• Methodological Rigor: The work emphasizes the necessity of correcting for series resistance when interpreting JSTM data in the low-resistance limit to avoid misinterpretation of the superconducting order parameter.

In conclusion, the study establishes that while JSTM is a powerful tool for atomic-scale superconductivity studies, its application in the deep point-contact regime requires careful calibration to distinguish intrinsic quantum states from circuit-induced limitations.