vdW Josephson Junctions

• vdW Josephson junctions are quantum-coherent weak links built by stacking atomically thin superconducting and non-superconducting layers, offering precise phase and spin control.
• They are fabricated via mechanical exfoliation and deterministic stacking, enabling versatile device architectures including vertical, twisted, and planar configurations with tailored barrier properties.
• These junctions support phenomena like gate-tunable 0–π transitions, nonlocal Cooper pairing, and programmable phase biases, promising advances in quantum circuits and superconducting logic.

Van der Waals (vdW) Josephson junctions (JJs) are quantum-coherent weak links formed by stacking two-dimensional (2D) superconducting and non-superconducting materials using the weak, directionally anisotropic van der Waals forces that naturally bind these layered crystals. The emergence of atomically defined, defect-free vdW interfaces enables novel control of Josephson coupling, phase dynamics, spin structure, and device functionalities not accessible in conventional thin-film or oxide-barrier junctions. The exceptional modularity of vdW assembly allows for the realization of junctions with magnetic, semiconducting, or topological barriers, precise capacitance and damping engineering, and full exploitation of crystal symmetry, twist angle, and interfacial phenomena.

1. Device Architectures and Fabrication Methods

VdW JJs are fabricated by mechanical exfoliation and deterministic stacking of atomically thin flakes, typically in an inert atmosphere (Ar or N₂ glovebox) to protect air-sensitive materials. Vertical (out-of-plane) junction geometries predominate:

• Vertical Superconductor/Magnetic-Insulator/Superconductor (S/MI/S) Devices: Exemplified by NbSe₂/Cr₂Ge₂Te₆/NbSe₂ stacks, with barrier thicknesses 0.7–12 nm, fully assembled using dry-transfer methods, atomic force microscopy for flake thickness control, and in situ ion milling prior to metallization to ensure clean contacts. Lateral overlap typically defines the junction area (1–20 μm² range). The process extends to antiferromagnetic (e.g., NiPS₃) and nonmagnetic semiconductors (e.g., WSe₂) as the weak link (Idzuchi et al., 2020, González-Sánchez et al., 24 May 2025, Balgley et al., 24 Jan 2025).
• Twisted Josephson Junctions: By deliberately rotating two superconducting flakes (e.g., NbSe₂, Bi₂Sr₂CaCu₂O₈₊ₓ) by angle θ, control is achieved over the pairing symmetry and electronic registry at the interface, thereby modulating the Josephson channel’s transparency and phase structure (Farrar et al., 2021, Lee et al., 2021, Martini et al., 2023).
• Planar vdW JJs: As in few-layer black phosphorus (bP) with in-plane Nb contacts, enabling electrostatic tuning by back-gate and direct proximity coupling, though less common than vertical structures (Telesio et al., 2021).
• Area-Engineered Devices: Minimally invasive post-stacking microfabrication (e-beam lithography, RIE) allows precise tuning of overlap area and junction capacitance, facilitating the design of underdamped and overdamped regimes essential for superconducting logic (Sunny et al., 20 Jan 2025).

A representative summary of main material and structural variants is organized in Table 1.

Structure	Barrier Type	Notable Features
NbSe₂/WSe₂/NbSe₂	Semiconductor	Thick, uniform, highly reproducible, qubit-ready
NbSe₂/Cr₂Ge₂Te₆/NbSe₂	Ferromagnetic insulator	Phase (0–π–φ) control, bistability
NbSe₂/NiPS₃/NbSe₂	Antiferromagnetic insulator	Edge state–dominated transport, high-field SQUID
Twisted NbSe₂	Homostructure	θ-tunable Ic and damping, deep flux modulation
Planar bP	vdW semiconductor	Gate tunability, in-plane proximity effect
NbS₂/NbS₂	TMD superconductor	Multiband gap, strong Josephson coupling

2. Josephson Coupling Mechanisms and Phase Control

The quantum transport in vdW JJs is governed by several intertwined mechanisms:

• Conventional Josephson Effect: Vertical S/S or S/semiconductor/S junctions yield $I_s = I_c \sin \phi$, with $I_c$ dependent on barrier thickness, transparency, and inplane registry; the Ambegaokar–Baratoff theory and its extensions apply in relevant limits (Balgley et al., 24 Jan 2025, Sunny et al., 20 Jan 2025, Zhao et al., 2022).
• Spin Structure and π/φ Junctions: In S/ferromagnet/S or magnetic-insulator weak links, spin splitting (exchange energy $J$) of the barrier modifies the current–phase relation (CPR), allowing transitions from 0 to π junction behavior. Out-of-plane magnetization yields a π shift if $J>V$, where $V$ is the spin-conserving tunneling amplitude. Domains with mixed in-plane/out-of-plane magnetization generate spatial regions of 0 and π coupling, giving rise to φ-phase JJs with doubly degenerate ground states at $\phi_1, \phi_2 \ne 0, \pi$ (Idzuchi et al., 2020, Kang et al., 2022, Ai et al., 2021).
• Gate-Tunable 0–π Transitions and Nonlocal Cooper Pairing: In vdW bilayer magnetic junctions, the proximity effect supports both local (same-layer) and nonlocal (bi-layer) Cooper pairs. The nonlocal FFLO wavevector $q_{nl}\approx\delta\varepsilon/v_F$ is set by the on-site energy difference between layers and can be dynamically controlled by a gate voltage. This enables electrostatic tuning of 0–π transitions, a functionality absent in bulk S/F systems (Bobkov et al., 14 Oct 2024).
• Twist-Tunable Tunneling: In high-T$_c$ twisted heterostructures, the Josephson coupling is governed by the momentum-space overlap of the superconducting order parameters. For d-wave cuprates (e.g., Bi-2212), $I_c(\theta)\propto|\cos 2\theta|$, fully suppressing the supercurrent at $\theta=45^\circ$ due to destructive interference between dx$^2$–y$^2$ lobes; a similar effect, but weaker, occurs in twisted NbSe₂ due to its gap anisotropy (Lee et al., 2021, Martini et al., 2023, Farrar et al., 2021).

3. Quantum Dynamics: Damping, Capacitance, and Electrical Transport

• Damping Control: The Stewart–McCumber parameter, $\beta_c = (2e/\hbar)I_cR_N^2C$, determines the junction dynamics. Overdamped ($\beta_c<1$) devices are engineered by reducing the junction area (thus $C$), critical for RSFQ and digital logic where latching must be avoided. Underdamped ($\beta_c>1$) JJs support hysteretic switching and are suitable for phase-slip and quantum readout applications. In vdW JJs, both regimes are accessible on identical materials platforms by microfabrication to sub-10 μm$^2$ scales (Sunny et al., 20 Jan 2025, Zhao et al., 2022).
• Transport Regimes: Standard measurements include four-terminal I–V characteristics from 300 K to dilution-refrigerator temperatures. Critical current densities up to $10^7$ A/m$^2$ and normal resistances of a few Ω (for areas $\sim10$ μm$^2$) are reported for NbSe₂–based structures. Ambegaokar–Baratoff fits to $I_c(T)$ validate Josephson physics in both s-wave and multiband TMD superconductors (Zhao et al., 2022, Balgley et al., 24 Jan 2025).
• Flux Interference Patterns: Fraunhofer diffraction is observed in uniform JJs, while inhomogeneous 0–π and π–φ phase distributions (set by thickness, magnetic domain structure, or gating) manifest as anomalous lobe suppression or symmetric side-lobe patterns in $I_c(B)$, directly evidencing phase segmentation and domain-scale interference (Kang et al., 2022, Ai et al., 2021).
• SQUID and Edge-State Transport: In AF vdW JJs (e.g., NbSe₂/NiPS₃/NbSe₂), spontaneous formation of edge states at S/AFI interfaces localizes the Josephson current into two dominant channels, yielding SQUID-like interference even in the absence of macroscopic loop lithography. These edge-mediated devices exhibit robust oscillations up to 6 T in-plane fields, providing unique high-field quantum interference functionality (González-Sánchez et al., 24 May 2025).

4. Magnetic Textures, Spin Physics, and Topological Phases

• Ising Superconductivity and Spin–Valley Locking: NbSe₂ and certain TMDs possess strong spin–orbit coupling, orienting spins out of plane (“Ising” regime). The conservation of in-plane momentum suppresses spin-flip tunneling, enforcing a robust sin φ CPR in appropriate magnetic domain configurations. Spin–valley locking introduces further constraints on allowed pairing and can, in principle, support nonreciprocal Josephson effects under symmetry-breaking conditions (Idzuchi et al., 2020, Zhao et al., 2022).
• Magnetic Domain Engineering: The precise thickness, domain configuration, and alignment in Cr₂Ge₂Te₆ barriers enable the creation of programmable 0–π–φ phase landscapes. Bistable φ-junction states function as passive, dissipationless memory bits, analogous to a two-level quantum system for nonvolatile superconducting memories and phase batteries (Idzuchi et al., 2020, Kang et al., 2022).
• Triplet and Topological Pairing: AFI/S structures with engineered edge states (e.g., at AFI–S boundaries) combine superconductivity, magnetism, and spin–orbit coupling—ideal conditions for emergent spin-triplet pairing and realization of one-dimensional topological superconducting modes at the sample perimeter (González-Sánchez et al., 24 May 2025).
• Gate Control of Exotic Phases: The ability to continuously tune the relative Fermi energies in bilayer magnetic barriers affords full electrostatic control over nonlocal FFLO-like pairing and direct access to gate-driven 0–π transitions, a modality unique to atomically thin vdW heterostructures (Bobkov et al., 14 Oct 2024).

5. Quantum Devices and Applications

• Transmon and Merge-Element Qubits: Vertical vdW JJs with semiconducting barriers (e.g., WSe₂) deliver reproducible Josephson coupling across 2–12 nm, enabling merged-element transmon (MET) qubits without external shunt capacitors. Atomically clean crystalline barriers yield footprint reduction by $>10^3\times$ and microsecond T₁, with coherence primarily limited by junction dielectric loss (tan δ ≈ 10^{-5})—parameters confirmed by direct microwave and relaxation measurements (Balgley et al., 24 Jan 2025, Balgley et al., 8 Dec 2025).
• SQUIDs and Magnetometers: Deep critical current modulations (Δ$I_c$/$I_c$ up to 75%), large flux-to-voltage transfer (Δ$V$ ≈ 1.4 mV), and twist/damping tunability offer superior performance relative to planar Al–AlOx junctions. Edge-induced SQUID effects in AF JJs achieve operation up to high magnetic fields (≥6 T) (Farrar et al., 2021, González-Sánchez et al., 24 May 2025).
• Nonvolatile Phase Memories and Phase Batteries: φ-junctions realized via engineered magnetic barriers provide dissipationless phase bias, bistability for superconducting memory, and ratchet potentials for rectification/quantum ratchet devices (Idzuchi et al., 2020).
• Topological Superconducting Circuits: The combination of spin–orbit coupling, magnetism, and tunable interface phases enables on-chip realization and probing of time-reversal symmetry breaking, triplet-pairing, and potentially Majorana physics, particularly in twisted cuprates and tailored heterostructures (Lee et al., 2021, González-Sánchez et al., 24 May 2025).
• Programmable Logic: Electrostatic/thermal control of domain configurations enables dynamically reconfigurable phase landscapes for flux logic, quiet π-qubits, and programmable superconducting circuits (Kang et al., 2022).

6. Outlook and Perspectives

VdW Josephson junctions have established a versatile and scalable platform for integrating superconductivity, magnetism, and controlled interface effects with unprecedented precision. The atomically defined barrier thickness, clean stacking interfaces, and deterministic domain/state control enable direct engineering of Josephson energy, damping, and spin phase, as summarized in the phenomenology below:

Tuning Parameter	Effect on JJ Behavior
Barrier thickness	0–π–φ transitions, $I_c$ amplitude, junction regime
Twist angle (θ)	$I_c(\theta)$ suppression/enhancement, order parameter symmetry
Domain structure	Mixed 0–π–φ landscapes, bistability, memory
Electrostatic gate	0–π transitions (bilayers), chemical potential
Area/overlap	Capacitance and damping (β_c), logic compatibility

Continued development in the synthesis of 2D magnets, topological insulators, unconventional superconductors, and doped semiconductors will further expand the design phase space. A plausible implication is the emergence of large-scale, integrated quantum circuits with arbitrary geometry, topologically protected modes, and field-robust operation. These developments position vdW JJs as pivotal elements for next-generation quantum information processing, cryogenic computation, and hybrid quantum sensors.