Voltage-Tunable Josephson Junctions

• Voltage-tunable Josephson junctions (VT-JJs) are superconducting devices that use gate voltage to modulate supercurrent, Josephson energy, and current-phase relations.
• They span diverse platforms—including semiconductor–superconductor hybrids, graphene, and all-metal weak links—facilitating functionalities like qubit tuning and nonreciprocal transport.
• Voltage control in VT-JJs allows precise tuning of inductance, diode effects, and microwave responses, driving innovations in quantum circuits and superconducting applications.

Voltage-tunable Josephson junctions (VT-JJs) are Josephson elements in which a voltage—most commonly an electrostatic gate bias, but in some cases a direct voltage bias that fixes phase evolution—controls the supercurrent, the Josephson energy, the Josephson inductance, the current-phase relation (CPR), or the resulting circuit functionality. In the literature, VT-JJs span semiconductor–superconductor weak links, hybrid ferromagnetic nanowires, graphene and magic-angle twisted bilayer graphene junctions, all-metal weak links, and voltage-biased anomalous-phase structures. Across these implementations, voltage control has been used to modulate $I_c$, reshape CPR harmonics, generate nonreciprocal supercurrent, tune resonator coupling, define gate-programmable qubits, and realize metrologically accurate low-noise voltage biasing without conventional flux-bias infrastructure (Sardashti et al., 2020, Telkamp et al., 16 Aug 2025, Paolucci et al., 2019, Banszerus et al., 2024, Strickland et al., 2024, Smirr et al., 2024).

1. Definition and governing quantities

The common theoretical core of VT-JJs is the Josephson relation between supercurrent, phase difference, and voltage. In its standard form, the supercurrent is written $I_s = I_c \sin \varphi$, while the AC Josephson relation is $V = (\Phi_0/2\pi)\dot{\varphi}$, with $\Phi_0 = h/2e$. Gate control acts primarily by changing the weak-link carrier density, transparency, or electrostatic environment, thereby tuning $I_c$ and the derived Josephson energy $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$. In small-signal operation the Josephson inductance is correspondingly tunable, with $L_J = \Phi_0/(2\pi I_c \cos \phi)$, and for $\phi = 0$ one has $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$ (Sardashti et al., 2020, Thompson et al., 26 Jun 2026).

A defining feature of many VT-JJs is that voltage tuning does not merely scale $I_c$; it also changes the shape of the CPR. A generic harmonic expansion is

$I_s = I_c \sin \varphi$0

and several platforms realize gate-controlled evolution from nearly sinusoidal behavior to strongly nonsinusoidal or sawtooth-like CPRs. In hybrid junctions with broken inversion and time-reversal symmetry, an anomalous phase shift can appear, giving

$I_s = I_c \sin \varphi$1

with nonreciprocity when $I_s = I_c \sin \varphi$2 (Banszerus et al., 2024, Monroe et al., 2022).

The term “voltage-tunable” therefore covers two distinct but related operational modes. In the more common mode, a gate voltage changes the junction properties at fixed bias conditions. In a second mode, a direct voltage bias sets the phase evolution itself and thereby tunes the emitted or delivered Josephson voltage. The latter is exemplified by a Josephson-effect-based voltage source operating through Shapiro locking, where the time-averaged DC voltage on the $I_s = I_c \sin \varphi$3th step is $I_s = I_c \sin \varphi$4 and continuous tunability is obtained by sweeping the microwave frequency $I_s = I_c \sin \varphi$5 (Smirr et al., 2024).

2. Material platforms and device realizations

The modern VT-JJ landscape is heterogeneous in both materials and device geometry. Electrostatic tunability appears in planar semiconductor heterostructures, nanowires, atomically thin materials, and entirely metallic weak links, while symmetry-broken variants add ferromagnetism or strong spin-orbit coupling.

Platform class	Voltage-control mechanism	Representative reported behavior
Epitaxial Al/InAs quantum wells and related hybrid 2DEGs	Local or global gates tune weak-link density and transparency	Gate-tunable $I_s = I_c \sin \varphi$6, $I_s = I_c \sin \varphi$7, CPR harmonics, tunable couplers, gatemonium, and series-junction harmonic synthesis (Sardashti et al., 2020, Banszerus et al., 2024, Strickland et al., 2024)
Hybrid InAs–EuS–Al nanowires	Back gate tunes carrier distribution and SOC balance in a symmetry-broken nanowire junction	Gate-tunable Josephson diode effect that survives at zero applied field via remanent EuS magnetization (Telkamp et al., 16 Aug 2025)
Graphene and magic-angle twisted bilayer graphene	Local top gates and global back gates tune density, moiré filling, and current distribution	Directly measured gate-tunable skewed CPR in ballistic graphene; gate-defined JJs and gate-tunable Josephson diodes in MATBG (Nanda et al., 2016, Vries et al., 2020, Rothstein et al., 17 Oct 2025)
All-metal weak links	Capacitively coupled side or top gates act on metallic constrictions or nano-bridges	Independent gating of Ti Dayem bridges and 3D Nb nano-bridges, with strong $I_s = I_c \sin \varphi$8 suppression and gate-tunable interference (Paolucci et al., 2019, Yu et al., 2023)
Planar Ge quantum wells with in-situ Al	Top gate tunes a lateral S–Sm–S weak link on a deep mesa	Gate-tunable supercurrent over 100 nA, ballistic short-junction transport, and a process aimed at low-loss circuit integration (Thompson et al., 26 Jun 2026)
$I_s = I_c \sin \varphi$9-S/F/S chains and voltage-biased Josephson sources	Direct voltage bias controls phase dynamics or phase locking	Voltage-driven anomalous-phase dynamics, collective magnetic-mode spectroscopy, and continuously tunable low-noise Josephson voltage generation (Bobkov et al., 2024, Smirr et al., 2024)

Within this diversity, several device architectures recur. JJ-FETs based on InAs near-surface quantum wells use ALD Al$V = (\Phi_0/2\pi)\dot{\varphi}$0O$V = (\Phi_0/2\pi)\dot{\varphi}$1 or HfO$V = (\Phi_0/2\pi)\dot{\varphi}$2 dielectrics followed by Ti/Au gates, closely paralleling III–V transistor processing (Sardashti et al., 2020). Hybrid InAs–EuS–Al nanowires use a spin-orbit-coupled semiconductor core with in-situ epitaxial ferromagnetic-insulator and superconducting shells; in the reported devices, two facets of a hexagonal InAs wire are covered by fully overlapping EuS and Al shells, setting a deterministic structural inversion asymmetry (Telkamp et al., 16 Aug 2025). Gate-defined MATBG junctions are formed entirely inside a single crystal: superconducting, insulating, and metallic regions are selected electrostatically using a graphite bottom gate and local top gates, with weak-link lengths reported as $V = (\Phi_0/2\pi)\dot{\varphi}$3 nm, $V = (\Phi_0/2\pi)\dot{\varphi}$4 nm, and $V = (\Phi_0/2\pi)\dot{\varphi}$5 nm at width $V = (\Phi_0/2\pi)\dot{\varphi}$6m (Vries et al., 2020).

A contrasting fabrication philosophy appears in the Ge quantum-well platform. There, a deep mesa etch removes the epitaxial material except beneath the active VT-JJ device, leaving most of the surrounding circuit on float-zone silicon with microwave loss tangent $V = (\Phi_0/2\pi)\dot{\varphi}$7. The mesa sidewall is tapered by $V = (\Phi_0/2\pi)\dot{\varphi}$8 from normal to allow continuous metal coverage for gates and interconnects (Thompson et al., 26 Jun 2026). All-metal implementations dispense with semiconductors entirely: the Ti interferometer uses a 30-nm-thick superconducting ring interrupted by two Dayem bridges, while the Nb implementation uses a three-dimensional nano-bridge over a vertical SiO$V = (\Phi_0/2\pi)\dot{\varphi}$9 slit with a metallic top gate (Paolucci et al., 2019, Yu et al., 2023).

3. Electrostatic control of critical current, inductance, and the current-phase relation

In the most direct VT-JJ implementations, a gate voltage changes the weak-link carrier density and transparency, which tunes $\Phi_0 = h/2e$0, $\Phi_0 = h/2e$1, and $\Phi_0 = h/2e$2. The clearest circuit-level formulation appears in the JJ-FET random-access quantum memory proposal, where the junction is treated as a gate-tunable inductive element in a $\Phi_0 = h/2e$3 tunable coupling resonator. HFSS simulations there varied $\Phi_0 = h/2e$4 from $\Phi_0 = h/2e$5 pH to $\Phi_0 = h/2e$6 pH; strong coupling to a storage cavity occurred for $\Phi_0 = h/2e$7 in the $\Phi_0 = h/2e$8–$\Phi_0 = h/2e$9 pH range, centered around $I_c$0 pH, while the OFF state was modeled as a $I_c$1 k$I_c$2 resistor that split the resonator into two shorter $I_c$3 cavities at $I_c$4 GHz, far from the $I_c$5–$I_c$6 GHz operating band (Sardashti et al., 2020).

Electrostatic control can also be used to synthesize a desired CPR. In a hybrid InAs/Al circuit containing two series semiconductor weak links, the total element is described as two sinusoidal JJs in series with effective transparency

$I_c$7

Symmetric gating drives $I_c$8, giving $I_c$9 and a strongly anharmonic, sawtooth-like CPR; asymmetric gating reduces the element to a near-sinusoidal weak junction. Experimentally, a desymmetrized arm gave $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$0 and $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$1, whereas a symmetrized arm gave $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$2 and $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$3; the harmonic ratio $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$4 rose toward $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$5 near $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$6, while the model predicted a theoretical maximum $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$7 (Banszerus et al., 2024).

Direct CPR extraction has been carried out in ballistic graphene. In a fully gate-tunable dc SQUID made from hBN-encapsulated graphene JJs contacted by MoRe, one junction was phase-biased by making the SQUID highly asymmetric, allowing direct reconstruction of the weak junction CPR. At $E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$8 mK the CPR was forward skewed, quantified by

$E_J = \Phi_0 I_c/(2\pi) = \hbar I_c/(2e)$9

with average $L_J = \Phi_0/(2\pi I_c \cos \phi)$0 on the p-doped side, average $L_J = \Phi_0/(2\pi I_c \cos \phi)$1 on the n-doped side, and $L_J = \Phi_0/(2\pi I_c \cos \phi)$2 near the Dirac point. Under p-gating, Fabry–Pérot resistance oscillations and CPR skewness oscillated in anti-phase, linking cavity transmission to higher-harmonic content (Nanda et al., 2016).

Planar Ge quantum wells provide a complementary example in which gate tuning is strong but interface transparency remains a central constraint. In a lateral S–Sm–S junction on a deep mesa, the critical current rose with more negative gate voltage to $L_J = \Phi_0/(2\pi I_c \cos \phi)$3 nA at $L_J = \Phi_0/(2\pi I_c \cos \phi)$4 V, while the peak $L_J = \Phi_0/(2\pi I_c \cos \phi)$5 reached $L_J = \Phi_0/(2\pi I_c \cos \phi)$6V. Temperature-dependent fits to a generalized Kulik–Omelyanchuk model yielded interface transparency $L_J = \Phi_0/(2\pi I_c \cos \phi)$7–$L_J = \Phi_0/(2\pi I_c \cos \phi)$8. The lateral gap was $L_J = \Phi_0/(2\pi I_c \cos \phi)$9 nm at the bottom and $\phi = 0$0 nm at the top, while the measured mean free path reached $\phi = 0$1 nm, placing the device in the short, ballistic regime (Thompson et al., 26 Jun 2026).

Voltage control of $\phi = 0$2 has also been integrated directly into qubits. In “gatemonium,” a fluxonium built from planar Al–InAs junctions, a single gate-tunable junction changed the effective Josephson energy from $\phi = 0$3 GHz to $\phi = 0$4 GHz while $\phi = 0$5 and $\phi = 0$6 remained fixed. The fitted effective transparency changed nonmonotonically with gate voltage, taking values $\phi = 0$7, $\phi = 0$8, $\phi = 0$9, and $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$0 across representative bias points, and the qubit could be swept continuously from the heavy regime to the light regime by electrostatic control alone (Strickland et al., 2024).

4. Nonreciprocity, anomalous phase shifts, and voltage-tunable Josephson diodes

A major recent branch of VT-JJ research concerns nonreciprocal supercurrent transport. In hybrid InAs–EuS–Al nanowire junctions, the Josephson diode effect appears inside a hysteretic superconducting window as a function of axial field. After zero-field cooling and magnetization to $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$1 mT, superconductivity turned on near $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$2 mT, the zero-voltage branch reached $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$3 nA at $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$4 mT, and superconductivity disappeared near $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$5 mT on the negative-to-positive sweep. The diode efficiency was defined as

$L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$6

with $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$7 extracted as average switching currents from $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$8 repeated sweeps. At fixed $L_J(V_g) \approx \Phi_0/[2\pi I_c(V_g)]$9 mT and $I_c$0 V, the reported value was $I_c$1; at $I_c$2 V, $I_c$3, consistent with zero. Zero-field operation was established by a controlled demagnetization protocol: after full magnetization at $I_c$4 mT, the field was swept to a negative demagnetizing value $I_c$5, turned off, and superconductivity at $I_c$6 was observed for $I_c$7 roughly between $I_c$8 and $I_c$9 mT, with nonreciprocal supercurrent persisting in that remanent state (Telkamp et al., 16 Aug 2025).

The field-free nanowire diode is interpreted phenomenologically through the combined effects of structural inversion asymmetry, exchange-induced spin splitting, and multidomain magnetization textures. The generic CPR used for interpretation,

$I_s = I_c \sin \varphi$00

makes explicit that both an anomalous phase shift $I_s = I_c \sin \varphi$01 and higher harmonics can produce $I_s = I_c \sin \varphi$02. Near the coercive field, EuS domains with size $I_s = I_c \sin \varphi$03 reduce the effective exchange splitting averaged over the Cooper-pair size, allowing superconductivity to re-emerge. A common misconception is that “field-free” here means absence of magnetic preparation; the reported zero-field operation instead depends on a remanent magnetization state prepared by a prior demagnetization sequence (Telkamp et al., 16 Aug 2025).

In MATBG, gate-defined adjacent JJs display a different form of voltage-tunable diode physics. There, the diode efficiency is written in the supporting analysis as

$I_s = I_c \sin \varphi$04

and both $I_s = I_c \sin \varphi$05 and its polarity can be tuned by gate voltage. Near interference minima, one polarity’s critical current can be strongly suppressed relative to the other, driving $I_s = I_c \sin \varphi$06 to large values; near symmetric lobes, $I_s = I_c \sin \varphi$07. The reported mechanism is a combination of large kinetic inductance and nonuniform supercurrent density $I_s = I_c \sin \varphi$08, with gate tuning acting through the filling-dependent superfluid density, effective inductance, and phase landscape. Despite their proximity, two adjacent JJs showed different interference patterns and different diode behavior, attributed to microscopic inhomogeneities such as local twist-angle variations and strain (Rothstein et al., 17 Oct 2025).

More general theoretical frameworks place these experiments within a broader class of anomalous-phase VT-JJs. For planar Al–InAs Josephson junctions with time-dependent Rashba SOC and an in-plane Zeeman field, the anomalous phase scales as $I_s = I_c \sin \varphi$09, while voltage control of $I_s = I_c \sin \varphi$10 can move the energy minimum among $I_s = I_c \sin \varphi$11, $I_s = I_c \sin \varphi$12, and $I_s = I_c \sin \varphi$13 states or realize diode-like CPRs with finite $I_s = I_c \sin \varphi$14. In the representative InAs–Al parameter set $I_s = I_c \sin \varphi$15A, $I_s = I_c \sin \varphi$16, and $I_s = I_c \sin \varphi$17 fF, the plasma frequency is $I_s = I_c \sin \varphi$18 GHz, and simulated phase transitions under $I_s = I_c \sin \varphi$19–$I_s = I_c \sin \varphi$20 GHz SOC ramps could complete about an order of magnitude faster than the gate-modulation rate (Monroe et al., 2022). In $I_s = I_c \sin \varphi$21-S/F/S chains, a direct voltage bias tunes the Josephson frequency $I_s = I_c \sin \varphi$22; once $I_s = I_c \sin \varphi$23 crosses a magnetic eigenfrequency, the conventional AC Josephson regime becomes unstable and new beat-dominated or multi-harmonic dynamical states emerge, giving IV-characteristics that serve as fingerprints of magnetoelectric coupling (Bobkov et al., 2024).

5. Circuit architectures, memories, qubits, and voltage sources

Voltage tunability has been pursued not only at the single-junction level but also as a circuit-design principle. In the random-access quantum-memory proposal based on Al/InAs JJ-FETs, the VT-JJ is placed at the current antinode of a $I_s = I_c \sin \varphi$24 tunable coupling resonator that mediates interaction between a transmission feedline and a high-$I_s = I_c \sin \varphi$25 $I_s = I_c \sin \varphi$26 storage cavity. The four-device array in the HFSS model used storage cavity frequencies of $I_s = I_c \sin \varphi$27, $I_s = I_c \sin \varphi$28, $I_s = I_c \sin \varphi$29, and $I_s = I_c \sin \varphi$30 GHz. ON operation corresponded to $I_s = I_c \sin \varphi$31 pH in the strong-coupling window, while OFF operation corresponded to full depletion modeled as a resistor $I_s = I_c \sin \varphi$32 k$I_s = I_c \sin \varphi$33. Write and read were implemented conceptually by short DC gate pulses that temporarily turned the JJ-FET ON for a swap operation, then returned it to OFF for isolation. Multi-chip integration by indium bump bonding to a silicon or PCB/laminate interposer was discussed, with connectivity up to $I_s = I_c \sin \varphi$34 chips noted (Sardashti et al., 2020).

The gatemonium architecture shows that VT-JJs can be used to tune the effective mass of the fluxonium phase particle rather than merely switch a coupler. Device A employed $I_s = I_c \sin \varphi$35 planar Al–InAs JJs in the array, with $I_s = I_c \sin \varphi$36 GHz and $I_s = I_c \sin \varphi$37 GHz; Device B used $I_s = I_c \sin \varphi$38, with $I_s = I_c \sin \varphi$39 GHz and $I_s = I_c \sin \varphi$40 GHz. Two-tone spectroscopy resolved fluxon and plasmon branches across heavy, intermediate, and light regimes. Near half flux in one heavy-regime fit, the minimum $I_s = I_c \sin \varphi$41 reached about $I_s = I_c \sin \varphi$42 MHz. Time-domain characterization in Device B at $I_s = I_c \sin \varphi$43 gave $I_s = I_c \sin \varphi$44 ns and $I_s = I_c \sin \varphi$45 ns, with the authors inferring $I_s = I_c \sin \varphi$46 for the inductive loss channel under the stated assumptions (Strickland et al., 2024).

The Ge quantum-well platform addresses a different bottleneck: integration of VT-JJs into low-microwave-loss superconducting circuits. By leaving only the active device on the heterostructure and placing the rest of the circuit directly on float-zone silicon, the deep-mesa approach is intended to reduce dielectric participation from semiconductor and buffer layers. Using the measured $I_s = I_c \sin \varphi$47 range of $I_s = I_c \sin \varphi$48–$I_s = I_c \sin \varphi$49 nA and $I_s = I_c \sin \varphi$50 MHz in a transmon estimate, the reported range corresponds to gate-tunable qubit frequencies of $I_s = I_c \sin \varphi$51–$I_s = I_c \sin \varphi$52 GHz with $I_s = I_c \sin \varphi$53–$I_s = I_c \sin \varphi$54 (Thompson et al., 26 Jun 2026).

A distinct but related development is the tunable Josephson voltage source. Here the tunable quantity is not $I_s = I_c \sin \varphi$55 or $I_s = I_c \sin \varphi$56 but the DC voltage itself, set by analog control of the microwave frequency while the source remains phase-locked on a Shapiro step. The demonstrated operating range was approximately $I_s = I_c \sin \varphi$57–$I_s = I_c \sin \varphi$58V, with the source able to supply over $I_s = I_c \sin \varphi$59 nA to a cryogenic load and measured RMS voltage noise at the load of $I_s = I_c \sin \varphi$60 pV. Concrete first-step voltages included $I_s = I_c \sin \varphi$61V at $I_s = I_c \sin \varphi$62 GHz, $I_s = I_c \sin \varphi$63V at $I_s = I_c \sin \varphi$64 GHz, and $I_s = I_c \sin \varphi$65V at $I_s = I_c \sin \varphi$66 GHz (Smirr et al., 2024).

6. Limitations, unresolved mechanisms, and research frontiers

The central limitations of VT-JJs are now highly platform-dependent. In semiconductor hybrids, microwave loss and interface transparency remain persistent concerns. The Ge quantum-well work makes this especially explicit: although the junction length is short and ballistic, the measured $I_s = I_c \sin \varphi$67V is about $I_s = I_c \sin \varphi$68 smaller than the Ambegaokar–Baratoff estimate $I_s = I_c \sin \varphi$69V for Al with $I_s = I_c \sin \varphi$70eV, and the extracted transparency $I_s = I_c \sin \varphi$71–$I_s = I_c \sin \varphi$72 is attributed to the finite $I_s = I_c \sin \varphi$73 nm top spacer (Thompson et al., 26 Jun 2026). In the QuMem proposal, dielectric losses and TLS from gate dielectrics are explicitly identified as a trade-off of gate control, even though the absence of flux-bias lines is presented as a scalability advantage (Sardashti et al., 2020).

In materials with strong correlation or moiré inhomogeneity, reproducibility is a central issue. Gate-defined MATBG junctions showed irregular magnetic interference patterns that the authors attributed to disorder and twist-angle inhomogeneity, rather than to a clean Fraunhofer geometry (Vries et al., 2020). In the later MATBG diode study, adjacent junctions in the same flake exhibited different interference envelopes and different diode behavior, again attributed to local twist-angle and strain variations that reshape $I_s = I_c \sin \varphi$74, $I_s = I_c \sin \varphi$75, and $I_s = I_c \sin \varphi$76 (Rothstein et al., 17 Oct 2025).

For nonreciprocal nanowire devices, the main text establishes reproducibility across measurement cycles but does not address long-term or thermal-cycle stability of the remanent zero-field state. The same work also reports no microwave response or Shapiro-step probes, and it does not extract explicit parameters such as $I_s = I_c \sin \varphi$77, $I_s = I_c \sin \varphi$78, $I_s = I_c \sin \varphi$79, or channel transparency from Hamiltonian fits (Telkamp et al., 16 Aug 2025). In gatemonium, the Josephson energy drifts in time, with qubit frequency wandering by $I_s = I_c \sin \varphi$80 MHz over $I_s = I_c \sin \varphi$81 minutes, attributed to $I_s = I_c \sin \varphi$82-type charge noise on the gate, and present coherence is limited primarily by inductive loss in thin Al films and the array superinductor rather than by the existence of voltage tunability itself (Strickland et al., 2024).

The most explicit conceptual controversy concerns all-metal VT-JJs. In the titanium interferometer, gate bias suppresses the switching current and shifts the interference pattern, yet the normal-state transport remains unchanged and the field effect is nearly symmetric in gate polarity. The accompanying model therefore invokes gate-induced phase fluctuations on a single junction rather than simple charge depletion (Paolucci et al., 2019). In the 3D Nb nano-bridge devices, $I_s = I_c \sin \varphi$83 can be tuned to zero by gate voltage up to $I_s = I_c \sin \varphi$84 K while $I_s = I_c \sin \varphi$85 remains fixed at $I_s = I_c \sin \varphi$86 K and $I_s = I_c \sin \varphi$87 remains constant; the proposed mechanisms discussed by the authors include a field-induced weakening of superconductivity, coherent excitations analogous to a Sauter–Schwinger effect in a BCS superconductor, high-energy carrier or phonon injection, and vortex surface-barrier modulation (Yu et al., 2023). No single microscopic explanation is established across the metallic literature.

A plausible implication is that VT-JJs have moved beyond proof-of-principle questions about whether voltage control is possible, and are now increasingly constrained by interface engineering, microwave-loss participation, noise, and deliberate control of symmetry breaking. The published record already supports several distinct mature functions—tunable inductors, field-free Josephson diodes, harmonic-engineered CPR elements, gate-defined correlated-state junctions, tunable fluxonium qubits, and ultra-low-noise Josephson voltage sources—but each function places different demands on transparency, dielectric quality, magnetic texture control, or spectral stability (Sardashti et al., 2020, Telkamp et al., 16 Aug 2025, Yu et al., 2023, Strickland et al., 2024).