Graphene 3-Terminal Josephson Junction

• Graphene 3TJJ is a superconducting network where a graphene flake interfaces with three electrodes, enabling novel multipair and correlated transport phenomena.
• The device leverages hBN encapsulation and precise lithography to achieve tunable phase dynamics, low dissipation, and synthetic topological bands critical for quantum circuits.
• Experimental observations reveal nonreciprocal supercurrents, topological Andreev states, and correlated switching, offering promising pathways for advanced superconducting quantum applications.

A graphene three-terminal Josephson junction (3TJJ) is a mesoscopic superconducting network in which a monolayer graphene flake, encapsulated by hexagonal boron nitride (hBN), is interfaced with three superconducting electrodes. The resulting device supports multiple Josephson couplings facilitating coherent transport phenomena not accessible in two-terminal junctions. This platform is central to the exploration of multiterminal Josephson physics, correlated multipair transport, artificial topological bands, and nonreciprocal superconducting devices, with implications for both fundamental research and superconducting quantum technology.

1. Device Architecture and Fabrication

The prototypical 3TJJ consists of a monolayer graphene island encapsulated by hBN (typically with upper and lower flakes of 20–35 nm), etched into cross, Y, or T–shaped mesas through electron-beam lithography and reactive-ion etching (CHF₃/O₂ or SF₆/O₂ doses). Edge contacts of superconducting metals—most commonly molybdenum-rhenium (MoRe), titanium/aluminum (Ti/Al), or pure Al—are deposited and defined by lift-off. The inter-terminal separation ranges from 150 nm up to several microns depending on fabrication, while contact widths can approach ~1 μm. A highly doped Si substrate (typically with 280–300 nm SiO₂) acts as a global back-gate to continuously tune carrier density and Fermi energy in graphene (Kedves et al., 2024, Zhang et al., 2023, Draelos et al., 2018).

Phase-biasing and readout are implemented via independently wired current and voltage sources, often at dilution-refrigerator base temperatures (T ≲ 50 mK) with comprehensive line filtering. Some advanced designs introduce independent superconducting loop electrodes for flux-based phase control and implement a tunnel probe for spectroscopic access to Andreev bound states (ABS) (Rashid et al., 25 Jan 2026, Jung et al., 2024).

2. Circuit Modeling and Josephson Network Equations

The constituent Josephson couplings in a 3TJJ define a fully connected network of three nodes. Each branch (i, j) is described by a Resistively and Capacitively Shunted Junction (RCSJ) element with critical current I_{c,ij}, normal-state resistance R_{ij}, and capacitance C_{ij}. The time-dependent Josephson relations for each branch are:

$I_{ij} = I_{c,ij} \sin(\phi_i - \phi_j)$

with the phase evolution governed by the voltage via $\dot{\phi}_i = (2e/\hbar) V_i$ (Kedves et al., 2024, Chiles et al., 2022, Arnault et al., 2020).

Kirchhoff’s current conservation at the nodes yields a set of coupled equations for the phase variables. In the rigid-island approximation (held for junctions with strong inter-terminal coherence), the phase sum constraint

$\phi_1 + \phi_2 + \phi_3 = 2\pi n$

(with $n \in \mathbb{Z}$) governs the allowed phase configurations (Chiles et al., 2022). For circuit simulations across the parameter space, the RCSJ framework generalizes to a matrix equation for the phase vector $\vec{\Phi} = (\phi_1, \phi_2)^T$, incorporating the capacitance and conductance matrices built from the network topology and component values (Arnault et al., 2022).

Damping and quality factors for each junction are quantified by:

$$Q_i = \omega_{p,i} R_i C_i, \quad \omega_{p,i} = \sqrt{2e I_{c,i} / \hbar C_i}$$

where typical devices operate in a moderately damped regime (Q ≈ 1–10) (Kedves et al., 2024).

3. Self-Heating, Phase Dynamics, and Transport Signatures

The interplay between supercurrents and dissipative normal currents in multiterminal graphene JJs leads to pronounced self-heating effects due to graphene’s weak electron-phonon coupling and the gap-induced trapping of hot electrons by the superconducting leads. Dissipated Joule power

$P_J = \sum_i V_i^2 / R_i$

raises the local electron temperature $T_e$, which equilibrates via

$$P_{e-\text{ph}} = \Sigma (T_e^\delta - T_b^\delta), \quad \delta \approx 4$$

for encapsulated graphene (Kedves et al., 2024, Draelos et al., 2018). This self-heating narrows the zero-resistance "arms" in differential resistance maps, suppresses the critical currents far beyond what is attributable to lattice (bath) temperature, and triggers correlated switching across the junctions.

Switching current distributions (SCDs) reveal phase diffusion as the principal stochastic process at low temperatures: as $T_b$ increases, SCD width within the central SC region decreases, consistent with phase diffusion rather than simple thermal activation. Strong heating transitions the device from hysteretic, underdamped dynamics to overdamped, non-hysteretic $I$–$V$ traces, with broader SCDs and poorly resolved switching events on high-bias arms (Kedves et al., 2024).

4. Nonreciprocal Transport and Superconducting Diode Effect

A key feature of 3TJJs is their ability to realize nonreciprocal (diode-like) supercurrent transport in the absence of external magnetic fields. This requires explicit geometrical or critical current asymmetry between the branches. Formalized by the nonreciprocity efficiency

$$\eta_{jk}^\pm = \frac{ |I^{\pm}_{c,jk}| - |I^{\pm}_{c,kj}| }{ |I^{\pm}_{c,jk}| + |I^{\pm}_{c,kj}| }$$

devices with controlled asymmetry achieve $\eta \gtrsim 24\%$ in two-port network configurations (Zhang et al., 2023). Under the Josephson triode protocol,

$$\eta = \frac{ I_c^+ - |I_c^-| }{ I_c^+ + |I_c^-| } \times 100\%$$

efficiencies up to ≈90% have been demonstrated at zero field with control-current tuning, outperforming earlier semiconductor or nanowire-based platforms (Chiles et al., 2022).

Nonreciprocal operation is toggled by which terminal is grounded and which ports are biased, enabling in situ reconfigurability between reciprocal and nonreciprocal behavior. Such diode modes permit directional supercurrent rectification and have direct implications for logic, isolation, and circulator architectures in quantum circuits.

5. Multiplet Supercurrents, Quartet Modes, and Topological Effects

Multiterminal Josephson networks host correlated multiparticle transfer processes beyond conventional Cooper-pair tunneling. In the 3TJJ, "quartet" supercurrents—correlated tunneling of two Cooper pairs among three nodes—are stabilized dynamically when the bias voltages satisfy $nV_L + mV_R = 0$ for integers $(n, m)$ (Arnault et al., 2022). Quartets manifest in low-bias transport as additional zero-resistance resonances and can be dynamically stabilized via the interplay of phase dynamics and dissipation. The existence of robust “cos 2\phi” energy terms in the effective potential enables the engineering of protected Josephson qubits based on higher harmonics of the phase variable.

Andreev bound states in multiterminal devices form multidimensional band structures over the torus defined by two (or more) independent phase differences. Tunneling spectroscopy tomographically resolves ABS dispersion in (φ_L, φ_R) space, revealing nodal lines, gapless–gapped transitions, and quantized topological windings. Quartet resonances trace closed loops of fixed combinations (e.g., $2\phi_L - \phi_R = \text{const}$), which corresponds to topological winding of phase trajectories around T^2. At avoided crossings of quartet lines, hybridization of distinct ABS modes is directly observed, evidencing quantum topological effects in the spectrum (Rashid et al., 25 Jan 2026, Jung et al., 2024).

Topological invariants—Berry curvature, Chern numbers, and Z₂ Berry phase—are defined for the ABS bands over phase space, with nodal loops carrying π-Berry flux and demarcating topological transitions between gapped and gapless regimes. The geometrical control afforded by (φ_L, φ_R) is analogous to engineering synthetic Brillouin zones, and opens routes to simulate higher-dimensional and nontrivial band topologies in hybrid quantum devices.

6. Experimental Observations and Phenomenology

Experiments consistently reveal the following transport and spectral features:

• Differential resistance maps: Central zero-resistance domains where all junctions are superconducting, surrounded by arms aligned with each branch going resistive. Heating narrows these arms and enhances inter-branch correlations. Outside the central superconducting region, strongly elevated Te and overdamped characteristics are observed (Kedves et al., 2024, Draelos et al., 2018).
• Shapiro steps and phase locking: Under microwave drive, fractional (e.g., ½) Shapiro steps and phase-locked switching are observed, validated by 2D RCSJ modeling. The step widths follow expected Bessel-function amplitude dependencies, signifying true topological locking rather than harmonic generation (Arnault et al., 2020).
• Correlated switching: Real-time, simultaneous switching events and statistical analyses of SCDs confirm that switching is collective, especially under strong heating and multiplet resonance conditions. The phase configuration of the full network determines the switching landscape.
• Spectroscopic tomography: ABS dispersions mapped as a function of (φ_L, φ_R) display Dirac-like nodal points and loop crossings, with quartet modes identified as minima in tunneling conductance along specific phase-space trajectories. Phase hybridizations and the coexistence of multiple winding modes directly evidence topological engineering (Rashid et al., 25 Jan 2026, Jung et al., 2024).

7. Implications for Device Engineering and Applications

3TJJ devices constitute a testbed for multi-terminal proximity effects, synthetic topologies, and correlated electron physics in mesoscopic superconductors. Their salient features—gate-tunability, ballistic transport, strong phase control, and low disorder (afforded by hBN encapsulation and edge contacts)—facilitate high-coherence operation ideal for quantum circuit integration and topological quantum computation.

Self-heating, while an intrinsic consequence of multiterminal operation, can lead to performance degradation by suppressing supercurrents and inducing damping. Design strategies to mitigate self-heating include phonon engineering, utilization of quasiparticle traps, minimization of normal-state dissipation, and optimized cooling pathways (Kedves et al., 2024). Damping can be strategically controlled by adjusting carrier density, bias conditions, and temperature.

Functional applications encompass superconducting diodes, nonreciprocal circuit elements, multi-mode phase qubits, and the simulation of higher-dimensional topological phases. Multiplet (quartet, sextet) transport and topological Andreev bands afford new paradigms for qubit encoding and protected circuit design (Arnault et al., 2022, Rashid et al., 25 Jan 2026, Jung et al., 2024). The platform further enables Andreev interferometry, Thouless pumping, and potential explorations of Majorana and Weyl physics in tailored band structures.

In sum, graphene three-terminal Josephson junctions exemplify a versatile and controllable platform for exploring the interplay of nonlocal superconductivity, electronic topology, correlated transport, and quantum circuit design (Kedves et al., 2024, Zhang et al., 2023, Chiles et al., 2022, Arnault et al., 2022, Arnault et al., 2020, Rashid et al., 25 Jan 2026, Jung et al., 2024, Draelos et al., 2018).