Hybrid Al/AlOₓ/4Hb-TaS₂ Josephson Junction

• The paper introduces a hybrid Josephson junction combining 4Hb-TaS₂ with Al/AlOₓ barriers to enable flux-tunable transmon qubits in circuit QED experiments.
• It details a precise fabrication protocol employing sequential aluminum deposition and in-situ oxidation to achieve an ultrathin tunnel barrier with junction areas of 0.01–1 μm².
• Experimental results reveal a significant deviation from the Ambegaokar–Baratoff relation, highlighting nontrivial tunneling effects and subgap excitations that impact qubit performance.

The Al/AlO$_x$/4Hb-TaS$_2$ Josephson junction is a hybrid element integrating a van der Waals (vdW) superconductor, specifically 4Hb-TaS$_2$, with established aluminum-based tunnel junction technology. By inserting this junction as the nonlinear inductive element in a flux-tunable transmon qubit, the architecture enables circuit quantum electrodynamics (cQED) studies that probe the unconventional superconducting condensates and subgap excitations characteristic of vdW materials. The fabrication protocol utilizes in-situ oxidation and sequential deposition of ultrathin aluminum layers to reliably form a tunnel barrier atop an exfoliated 4Hb-TaS$_2$ flake, all in a manner compatible with standard transmon workflows and microwave cavity integration (Blumenthal et al., 27 Jan 2026).

1. Fabrication Protocol of the Hybrid Josephson Junction

The construction begins with substrate preparation: a Si (250 μm)/SiO$_2$ (285 nm) wafer patterned with alignment marks (Pt/Cr 20 nm/5 nm or Nb 25 nm). Sequential ultrasonic cleaning (acetone, ethanol, IPA) and baking at 180 °C precede the dry-transfer and optical localization of exfoliated 4Hb-TaS$_2$ flakes. Electron-beam lithography (PMMA trilayer; 495 A4, 950 A2; 10 kV) patterns the junction geometry. After plasma ashing, in situ Ar$^+$ ion milling at 45° exposes fresh vdW surfaces and forms side contacts, followed by Ti gettering evaporation.

Tunnel barrier formation involves 2–3 cycles of 5 Å aluminum deposition at 10° tilt (rate ≈0.5 Å/s), each followed by full oxidation at 80 Torr (5% O$_2$/Ar) for 40 min, resulting in a cumulative AlO$_x$ thickness near 1 nm. A top electrode of ≈200 nm aluminum is deposited at identical tilt. Lift-off is performed in N-methyl-2-pyrrolidone (80 °C for 3 h), finished by IPA rinsing and N$_2$ blow-drying. The explicit junction area is unquoted, but lateral dimensions inferred from lithography and micrographs suggest a typical range of 0.01–1 μm$^2$.

2. Theoretical Framework and Key Relations

The hybrid Josephson junction is characterized using standard superconducting theory. The Ambegaokar–Baratoff (AB) relation connects critical current ($I_c$) and normal-state resistance ($R_n$):

• Finite-$T$: $I_c R_n = (\pi \Delta / 2e) \tanh(\Delta/2k_B T)$
• As $T \rightarrow 0$: $I_c R_n = \pi \Delta / 2e$

The Josephson energy is $E_J = \hbar I_c / 2e$, while the transmon’s charging energy is $E_C = e^2/2C$, with $C$ the total island capacitance. Flux dependence is encapsulated by:

• Ideal symmetric SQUID: $$E_J(\Phi) = E_{J, \text{max}} |\cos(\pi\Phi/\Phi_0)|$$
• Asymmetric case (used in study): $$E_J(\Phi) = E_{J,\Sigma} \cos(\pi\Phi/\Phi_0) \sqrt{1 + d^2 \tan^2(\pi\Phi/\Phi_0)}$$, where $E_{J,\Sigma} = E_{J1}+E_{J2}$, $d = (E_{J2}-E_{J1})/(E_{J1}+E_{J2})$, and $\Phi_0 = h/2e$.

In the circuit QED context, the transmon–cavity Hamiltonian (dressed basis) is

$$H = \hbar \omega_c a^\dagger a + 4 E_C \hat{n}^2 - E_J(\Phi) \cos \hat{\phi} + \hbar g (a^\dagger + a) \hat{n}$$

where $\omega_c$ is the cavity frequency, $g$ the coupling rate.

3. Experimental Parameters and Device Characterization

Room-temperature normal resistances for representative devices are $R_n \approx 2.4$ kΩ (Device 1A) and $1.9$ kΩ (Device 1B). Spectroscopic analysis for Device 1A reveals:

• $E_C/h \approx 140$ MHz
• $E_{J,\Sigma}/h \approx 11.6$ GHz
• Junction asymmetry $d \approx 0.35$
• Maximum qubit transition frequency $\omega_{01}/2\pi \approx 3.46$ GHz
• Transmon regime metric $E_J/E_C \approx 83$
• Critical current $$I_{c,\text{max}} = 2e E_J / \hbar \Rightarrow I_{c,\text{max}} \approx 23$$ nA

The flux-tunable device, embedded in a three-dimensional copper cavity, manifests a SQUID-like spectrum accurately fit by diagonalizing the above Hamiltonian as a function of flux $\Phi$.

4. Discrepancy versus Ambegaokar–Baratoff Relation

A pronounced inconsistency is observed between Josephson energy ($E_J$) derived from spectroscopy and the value anticipated via the AB relation using measured room-temperature $R_n$. For $R_n \approx 2$ kΩ and $\Delta_{Al} \approx 162$ μeV, AB predicts $E_J/h \approx 2$–$3$ GHz, whereas spectroscopy finds $E_J/h \approx 11$–$14$ GHz. This yields an effective $\Delta_\text{eff} \approx 33$–$35$ μeV, distinctly below both $\Delta_{Al}$ and the reported gap of 4Hb-TaS$_2$ ($\Delta_{4Hb-TaS_2} \approx 390$ μeV).

Interpreted mechanisms include multiband/anisotropic pairing in 4Hb-TaS$_2$ selectively suppressing $I_c$, interface tunneling matrix-element effects, and contributions from subgap/edge modes or enhanced density of states that reduce net Josephson coupling. This suggests nontrivial junction physics in the hybrid Al/AlO$_x$/4Hb-TaS$_2$ system.

5. Coherence and Dissipative Dynamics

Energy relaxation ($T_1$) is measured at $0.08 \pm 0.01$ μs (Device 1A) and $0.69 \pm 0.03$ μs (Device 2A). Dephasing time ($T_2^*$) is limited by measurement resolution, with Ramsey decay faster than $16$ ns ($T_2^* < 16$ ns). These metrics are sub-microsecond—an order of magnitude below optimized conventional Al/AlO$_x$/Al transmons, which routinely reach $T_1,T_2 \sim 10$–$100$ μs. The short coherence indicates additional dissipation and dephasing mechanisms, plausibly linked to quasiparticles or flux noise associated with the hybrid interface.

Device	$R_n$ (kΩ)	$T_1$ (μs)	$T_2^*$ (ns)
1A	2.4	0.08 ± 0.01	<16
2A	—	0.69 ± 0.03	—

6. Implications, Limitations, and Future Directions

The Al/AlO$_x$/4Hb-TaS$_2$ junction process is robust, fully in-situ, and compatible with standard transmon fabrication, marking a practical entry point for cQED experiments leveraging vdW superconductors. Material-specific subgap modes are not resolved in the present geometry, but the device lineage establishes a baseline for edge-sensitive designs aimed at amplifying coupling to boundary and subgap degrees of freedom inherent to 4Hb-TaS$_2$.

Advancing the detection of zero-bias edge modes, vortex-core states, and signatures of unconventional pairing in future cQED experiments could involve:

• Patterning 4Hb-TaS$_2$ into nanowires/strips to localize supercurrent at edges
• Thinning or reducing oxidation cycles of the tunnel barrier to enhance Andreev bound-state coupling (“transparency tuning”; Editor's term)
• Geometric arrangements that eliminate bulk shunting, localizing phase drop at controlled, edge-sensitive weak links

A plausible implication is that refinement of junction geometry and barrier properties can enable direct microwave access to exotic boundary and subgap phenomena in vdW superconductors, supporting the broader goal of integrating such materials into coherent quantum technologies (Blumenthal et al., 27 Jan 2026).