Flux-tunable transmon incorporating a van der Waals superconductor via an Al/AlO$_x$/4Hb-TaS$_2$ Josephson junction

This work demonstrates the fabrication and characterization of a flux-tunable transmon qubit incorporating an Al/AlO$_x$/4Hb-TaS$_2$ Josephson junction, establishing a viable pathway for integrating van der Waals superconductors into superconducting quantum circuits while revealing distinct discrepancies between spectroscopic and resistive Josephson energy estimates.

The Gist

Imagine you have a very sensitive musical instrument, a "quantum guitar" called a transmon, which is used to study the strange world of superconductors (materials that conduct electricity with zero resistance). Usually, the part of this guitar that makes the music interesting—the "bridge" where the strings vibrate—is made of standard aluminum. It works well, but it's like playing only on a piano; you can't hear the unique sounds of other instruments.

This paper describes an experiment where the researchers tried to replace that standard aluminum bridge with a new, exotic material called 4Hb-TaS2. This material is a "van der Waals superconductor," which is a fancy way of saying it's a crystal made of atom-thin layers that can be peeled off like a sticker. Scientists think this material might hold secrets about how electrons pair up in weird, non-standard ways, potentially hiding special "ghost" states at its edges or inside magnetic vortices.

Here is the story of what they did and what they found, using simple analogies:

1. Building the Hybrid Bridge

The researchers had to build a bridge between the standard aluminum world and the exotic 4Hb-TaS2 world.

• The Process: They took a flake of the exotic material (peeled off like a sticker) and built a tunnel barrier on top of it. Imagine laying down a very thin layer of aluminum, letting it rust slightly in a controlled way to create a barrier (like a thin wall of glass), and then capping it with more aluminum.
• The Result: They successfully created a "hybrid junction." It's like building a door that connects a standard house to a mysterious, unexplored cave. They then put this door inside a copper box (a 3D cavity) to act as their quantum guitar.

2. Tuning the Instrument

Just like a real guitar, they wanted to see if they could tune this quantum instrument.

• The Tuning Knob: They used a magnetic field as a tuning knob. When they turned this knob, the "notes" (energy levels) of the quantum system shifted up and down, just like a standard guitar string changes pitch when you tighten it.
• The Confirmation: The way the notes shifted matched the standard mathematical rules for these quantum guitars perfectly. This proved that the exotic material could indeed function as a working part of a quantum circuit.

3. The Mystery of the Missing Energy

Here is where things got interesting and a bit confusing.

• The Expectation: In the world of standard superconductors, there is a famous rule (the Ambegaokar–Baratoff relation) that acts like a recipe. If you know how much the material resists electricity at room temperature, you can predict exactly how strong the "super-current" should be at cold temperatures.
• The Reality: When the researchers measured the resistance of their new hybrid bridge, the recipe predicted a certain strength. But when they actually measured the strength of the super-current, it was five times weaker than the recipe said it should be.
• The Analogy: It's like weighing a bag of flour and expecting it to make a huge cake, but when you bake it, the cake is tiny. The researchers suspect this is because the exotic 4Hb-TaS2 material has a complex internal structure (maybe multiple "flavors" of superconductivity or weird electron pairings) that breaks the standard recipe.

4. The "Flickering" Light (Coherence Issues)

To be useful for quantum computing, these instruments need to hold their state (the "note") for a while without fading away.

• The Problem: The researchers tried to measure how long the "note" lasted. They found that the sound faded away very quickly—faster than their stopwatch could even click.
• The Numbers: The energy lasted for only a tiny fraction of a microsecond (0.08 to 0.69 microseconds).
• The Guess: They suspect the exotic material might be "noisy." Perhaps there are extra, unwanted particles (quasiparticles) inside the 4Hb-TaS2 that are jiggling around and knocking the quantum state out of tune before it can be measured properly.

5. Did They Find the "Ghost" States?

The main reason for using this exotic material was to find those special "ghost" states (subgap modes) that scientists think exist at the edges of the material.

• The Outcome: In this specific setup, they did not see these ghost states.
• Why? The researchers think the "road" the electricity took was too wide. Instead of being forced to travel along the edges where the ghosts might be hiding, the electricity took a shortcut through the middle (the bulk) of the material, effectively drowning out the edge signals.
• The Takeaway: Even though they didn't find the ghosts this time, they proved that you can build a working quantum circuit with this material. It's like proving you can drive a car into a cave; now that the road is open, future experiments can build a narrower, more precise path to actually see what's hiding inside.

Summary

In short, the paper says: "We successfully built a quantum circuit using a new, exotic material. It works, it can be tuned, and it behaves like a standard quantum guitar. However, it behaves strangely compared to our standard recipes (the energy is weaker than expected), and it loses its 'memory' very fast. We didn't find the special edge states we were looking for yet, likely because our design was too broad, but we have paved the way for future experiments to look closer."

Technical Summary

Technical Summary: Flux-Tunable Transmon with a Van der Waals Superconductor Josephson Junction

Problem and Motivation
Superconducting transmon qubits typically rely on conventional Al/AlOx/Al tunnel junctions. While these offer reliable fabrication and low loss, they restrict circuit-QED (cQED) studies to the properties of conventional s-wave aluminum. There is a need to extend cQED to van der Waals (vdW) quantum materials, specifically correlated and topological superconductors, to probe unconventional order parameters, low-energy quasiparticles, and boundary modes. A primary challenge in this integration is establishing a repeatable fabrication process that forms a robust tunnel barrier on an exfoliated vdW surface while remaining compatible with standard transmon architectures. The authors focus on 4Hb-TaS2, a transition-metal dichalcogenide with a naturally occurring heterostructure of alternating 1T and 1H layers, which exhibits superconductivity at $T_c \approx 2.7$ K and signatures of time-reversal symmetry breaking and potential topological nodal superconductivity.

Methodology
The authors fabricated a flux-tunable transmon where the nonlinear inductive element is a hybrid Al/AlOx/4Hb-TaS2 Josephson junction. The fabrication process involved:

1. Substrate Preparation: 4Hb-TaS2 flakes were exfoliated via dry transfer onto Si/SiO2 substrates pre-patterned with alignment markers.
2. Junction Formation: A controlled tunnel barrier was created using sequential deposition and full in-situ oxidation of ultrathin aluminum layers (2–3 layers of $\sim$5 Å) on the exfoliated 4Hb-TaS2. This was preceded by an in-situ Ar ion mill to clean the surface and ensure robust side-contact. A top Al electrode ($\sim$200 nm) was deposited to complete the junction.
3. Device Geometry: Two SQUID-based transmon layouts were implemented. Design 1 routed supercurrent through the flake between capacitor pads, while Design 2 utilized an asymmetric SQUID geometry (one hybrid branch, one conventional Al/AlOx/Al branch) to reduce sensitivity to bulk transport through the flake.
4. Measurement: Devices were mounted in a 3D copper cavity and cooled to $\sim$10 mK. Spectroscopy was performed using two-tone drives to probe transmon transitions, and time-domain measurements (Ramsey and relaxation) were conducted to assess coherence.

Key Results

• Spectroscopy and Tunability: The devices exhibited a flux-dependent spectrum characteristic of a SQUID, quantitatively reproduced by a standard dressed transmon–cavity Hamiltonian. Parameters extracted for Device 1A placed the system in the transmon regime ($E_J/E_C \gg 1$) with a maximum qubit frequency of $\sim$3.46 GHz.
• Anomalous Josephson Energy: A significant discrepancy was observed between the Josephson energy ($E_J$) inferred from spectroscopy and that predicted by the Ambegaokar–Baratoff relation using room-temperature junction resistances. For Device 1B, the measured $E_J$ implied a gap of only 33–35 $\mu$V, which is inconsistent with the known gaps of aluminum ($\sim$162 $\mu$V) and 4Hb-TaS2 ($\sim$390 $\mu$V). This suggests nontrivial junction physics, potentially arising from multigap structures, anisotropic pairing, or interface-dependent tunneling matrix elements.
• Coherence Times: Energy relaxation times ($T_1$) were measured in the sub-microsecond range, varying from 0.08 $\mu$s to 0.69 $\mu$s across different devices. Ramsey interferometry failed to resolve fringes, indicating dephasing ($T_2^*$) occurs on a timescale faster than the experimental resolution of 16 ns.
• Absence of Resolved Subgap Modes: Despite the motivation to probe boundary and subgap states, the current geometry did not resolve material-specific subgap modes in the spectroscopy.

Significance and Claims
The paper establishes a practical route for integrating exfoliable vdW superconductors, specifically 4Hb-TaS2, into coherent superconducting circuits. The primary contribution is the demonstration that an Al/AlOx/4Hb-TaS2 junction, fabricated via a full-oxidation layer process, functions as a coherent Josephson element within a transmon qubit.

The authors modestly frame this work as a foundational step rather than a definitive characterization of the material's exotic properties. They note that while the current geometry suppresses the visibility of edge modes (likely due to bulk-dominated supercurrent pathways), the successful integration provides a necessary baseline for future "edge-sensitive" designs. The observed rapid dephasing and the discrepancy in Josephson energy are identified as key areas for future investigation, potentially linked to quasiparticle dynamics, enhanced subgap density of states, or extrinsic fabrication issues. The work validates the cQED toolbox as a viable spectroscopic probe for this class of unconventional superconductors, setting the stage for future studies targeting boundary and subgap physics.