Gate-Tunable Josephson Diode Effect

• The Gate-Tunable Josephson Diode Effect is the electrically controlled modulation of nonreciprocal supercurrents in Josephson junctions, achieved by breaking inversion and time-reversal symmetry.
• It leverages gate tuning in various architectures—such as semiconductor–superconductor hybrids, SQUID interferometers, and topological nanowires—to adjust chemical potential, spin–orbit coupling, and interference effects.
• Experimental techniques, including current-biased transport measurements and phase-sensitive diagnostics like Shapiro step analysis, quantify diode efficiencies and inform applications in superconducting logic and rectification.

Gate-tunable Josephson diode effect denotes the electrically controllable nonreciprocity of a Josephson junction or Josephson network, in which the maximal dissipationless current depends on current direction and can be modulated by electrostatic gates. In its standard form, the effect is expressed as $I_{c,+}\neq I_{c,-}$, or experimentally as unequal positive and negative switching currents extracted from current-biased transport. Across semiconductor–superconductor hybrids, SQUIDs and multi-terminal interferometers, topological-insulator nanowires, graphene, correlated moiré systems, and field-free magnetic-texture platforms, gate voltages act on chemical potential, transmission, spin–orbit coupling, arm asymmetry, or nonlocal phase-sensitive couplings, thereby tuning both the magnitude and, in many cases, the sign of the diode response (Telkamp et al., 16 Aug 2025, Mazur et al., 2022, Ciaccia et al., 2023, Nikodem et al., 2024).

1. Definition, symmetry conditions, and diode metrics

The Josephson diode effect (JDE) is the directional dependence of the critical supercurrent in a Josephson structure. In the notation used for single junctions, the defining relation is $I_{c,+}\neq I_{c,-}$. Nonreciprocal supercurrent transport requires breaking both inversion symmetry $\mathcal{P}$ and time-reversal symmetry $\mathcal{T}$. In a microscopic description this occurs when the current–phase relation (CPR) ceases to be purely odd in the superconducting phase difference $\varphi$, for example through an anomalous phase shift $\varphi_0$ or higher harmonics,

$$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$

and, in a short-junction Andreev-level picture,

$$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$

Any mechanism that makes the Andreev spectrum asymmetric under $\varphi\to-\varphi$ produces unequal forward and reverse critical currents (Telkamp et al., 16 Aug 2025, Mazur et al., 2022).

Experimental work uses several closely related rectification metrics. A widely used switching-current efficiency is

$$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$

which is equivalent to the standard critical-current expression when retrapping and hysteresis are small. Other studies use $I_{c,+}\neq I_{c,-}$0 with $I_{c,+}\neq I_{c,-}$1, or $I_{c,+}\neq I_{c,-}$2 with $I_{c,+}\neq I_{c,-}$3. A distinct convention appears in the skyrmion-coupled high-$I_{c,+}\neq I_{c,-}$4 proposal,

$I_{c,+}\neq I_{c,-}$5

so numerical efficiencies quoted across the literature are not always directly comparable (Telkamp et al., 16 Aug 2025, Gupta et al., 2022, Hou et al., 10 Mar 2026, Singh et al., 1 Nov 2025).

2. Microscopic mechanisms and the role of electrostatic gating

In Rashba semiconductor Josephson junctions, gate tunability operates by changing the chemical potential, junction transparency, carrier distribution, and effective spin–orbit environment. In short InSb/Al nanowire junctions, Rashba spin–orbit coupling in the proximitized leads breaks inversion symmetry, while a Zeeman field breaks time reversal. The resulting finite-momentum Andreev bound states generate a nonsinusoidal and nonreciprocal CPR, and independent tunnel and super gates can switch the system between a lead-dominated regime with a fixed spin–orbit-field direction and a weak-link-dominated regime with strong gate-sensitive polarity reversals (Mazur et al., 2022). In InAs nanosheet junctions, the back gate tunes the Rashba coefficient and thus the finite-momentum pairing responsible for the anomalous phase shift; the JDE decreases monotonically as $I_{c,+}\neq I_{c,-}$6 is reduced and vanishes around $I_{c,+}\neq I_{c,-}$7 V even while appreciable supercurrent remains, consistent with gate-controlled suppression of Rashba spin–orbit interaction (Yan et al., 26 Jan 2025).

A complementary mechanism arises in interferometers, where the diode effect is not a property of an individual junction but of flux-biased interference between nonlinear CPRs. In proximitized InAs supercurrent interferometers, two high-transmission Josephson junctions form a SQUID whose total CPR,

$I_{c,+}\neq I_{c,-}$8

becomes nonreciprocal when finite flux bias and arm asymmetry cause higher harmonics to interfere differently for positive and negative current directions. Gates tune the effective transmissions and critical currents of the two arms, giving a flux- and gate-tunable diode with butterfly-like efficiency maps (Ciaccia et al., 2023). In InSb nanosheet interferometers, local back gates independently control the two arms, and fractional Shapiro steps directly track flux-enhanced second-harmonic content near half-integer flux quanta, tying gate tunability to the harmonic decomposition of the CPR rather than to a purely $I_{c,+}\neq I_{c,-}$9-junction mechanism (Wu et al., 19 Feb 2025). In double-loop SQUIDs, series pairs of gate-tunable junctions in each branch synthesize effective branch transparencies $\mathcal{P}$0, allowing separate control of CPR amplitude and harmonic content in three interfering branches (Gibbons et al., 16 Dec 2025).

Gate control can also act nonlocally. In nanowire-based Andreev molecules, the left-junction CPR depends on the phase of a coherently coupled right junction, and local as well as nonlocal gates tune the hybridized Andreev spectrum. The JDE follows from phase-coherent competition between double elastic cotunneling and double-crossed Andreev reflection; gates modulate the coupling strengths and produce a central-peak structure in diode efficiency near symmetric tuning of the two junctions (Zhu et al., 19 Aug 2025).

3. Experimental platforms and quantitative regimes

Semiconductor nanowire devices provided some of the clearest early demonstrations of strong electrostatic control. In short InSb/Al nanowire junctions, the gate-tunable diode efficiency reaches $\mathcal{P}$1 at $\mathcal{P}$2 mT, with a threshold at $\mathcal{P}$3 V and a reproducible angle of maximal response $\mathcal{P}$4–$\mathcal{P}$5, interpreted as the spin–orbit-field direction in the proximitized leads (Mazur et al., 2022). In InAs nanosheet Josephson junctions, representative values at $\mathcal{P}$6 V and $\mathcal{P}$7 mT are $\mathcal{P}$8 nA, $\mathcal{P}$9 nA, $\mathcal{T}$0, and retrapping efficiency $\mathcal{T}$1, with the angular dependence peaking for in-plane field perpendicular to the bias current and nearly vanishing for the parallel orientation (Yan et al., 26 Jan 2025).

Interferometric architectures reach substantially larger efficiencies. In a proximitized InAs 2DEG SQUID, gate control tunes the diode efficiency from zero up to about $\mathcal{T}$2, close to the approximately $\mathcal{T}$3 theoretical ceiling discussed for a two-junction interferometer with highly transmitting channels (Ciaccia et al., 2023). In a three-terminal InAs quantum-well device, the synthetic multi-terminal CPR yields $\mathcal{T}$4 in one device and $\mathcal{T}$5 in another, with polarity switchable both by a small out-of-plane magnetic field and by electrostatic gates (Gupta et al., 2022). In a gate-tunable double-loop SQUID, optimized Josephson-energy tuning produces $\mathcal{T}$6 between approximately $\mathcal{T}$7 and $\mathcal{T}$8, and the authors report diode efficiency exceeding $\mathcal{T}$9 (Gibbons et al., 16 Dec 2025).

Topological and correlated platforms extend gate tunability into regimes where nonreciprocity is intertwined with topology or strongly inhomogeneous supercurrent flow. A side-contacted BiSbTeSe$\varphi$0 nanowire junction behaves as an intrinsic nano-SQUID formed by top and bottom TI surfaces; with axial flux and gate-induced arm asymmetry, the measured efficiency reaches $\varphi$1, and both the sign and magnitude of $\varphi$2 are tunable by $\varphi$3 and $\varphi$4 (Nikodem et al., 2024). In Cd$\varphi$5As$\varphi$6 nanowire junctions, the JDE is strongly gate-tunable and highly anisotropic; $\varphi$7 and $\varphi$8 peak near $\varphi$9 V, and temperature anomalies around $\varphi_0$0 K are interpreted as evidence for multiple transport channels, with inferred characteristic fields $\varphi_0$1 mT for surface states and $\varphi_0$2 mT for bulk states (Hou et al., 10 Mar 2026). In graphene-based theoretical work, magnetochiral anisotropy yields a diode efficiency from zero up to approximately $\varphi_0$3, with a sign reversal when electrostatic doping switches from $\varphi_0$4-type to $\varphi_0$5-type (Huang, 2023).

4. Field-free and zero-field gate-tunable diodes

A central development is the transition from field-assisted to field-free operation. In hybrid InAs nanowire junctions with epitaxial EuS and Al shells, a Josephson weak link of length $\varphi_0$6 nm exhibits a hysteretic superconducting window near the EuS coercive field. Within that window, the switching-current asymmetry is gate-tunable: at $\varphi_0$7 V and $\varphi_0$8 mT, switching-current histograms yield $\varphi_0$9, whereas at $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$0 V they nearly overlap, giving $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$1. After magnetization at $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$2 mT and a controlled demagnetization sweep to $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$3, superconductivity reappears at $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$4 for $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$5 mT, and the field-free diode remains gate-tunable at zero field (Telkamp et al., 16 Aug 2025). This zero-field operation does not imply absence of magnetism; it is sustained by remanent EuS magnetization and domain structure.

Several theoretical studies generalize field-free gate control beyond remanent ferromagnetism. In singlet-superconductor/altermagnet/triplet-superconductor junctions, the altermagnet breaks time-reversal symmetry without net magnetization, and a gate potential in the altermagnetic region can both modulate the magnitude of the diode effect and reverse its sign; efficiencies up to approximately $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$6 are reported in the calculated parameter space (Sharma et al., 26 Feb 2025). In a skyrmion-coupled $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$7-wave planar junction, the spatially varying exchange field of a Néel-type skyrmion crystal, together with Rashba SOC and $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$8-wave anisotropy, generates a field-free diode with $$I(\varphi)=I_1\sin(\varphi-\varphi_0)+I_2\sin(2\varphi)+\cdots,$$9–$$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$0 near $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$1 meV, $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$2 meV, $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$3 meV, and $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$4 nm (Singh et al., 1 Nov 2025). In planar unconventional-superconductor heterostructures with $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$5 or $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$6 pairing, breaking a $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$7-rotation symmetry by lobe misalignment permits a large field-free JDE even without spin–orbit coupling, and gate voltage, junction length, and orientation angles control both the magnitude and sign of the diode quality factor (Vakili et al., 2024).

Field-effect proposals based on asymmetric spin–momentum-locking states formulate the same idea more abstractly: electrostatic gates create finite-momentum Cooper pairs, producing an effective Doppler shift $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$8 and a gate-controlled $$I(\varphi)=\frac{2e}{\hbar}\sum_n \frac{\partial E_n(\varphi)}{\partial \varphi}.$$9 shift. In the single-channel limit the predicted maximal efficiency is about $\varphi\to-\varphi$0, while two-edge interference in a topological quantum spin Hall realization can enhance the total efficiency to approximately $\varphi\to-\varphi$1 (Fu et al., 2022).

5. Measurement protocols and diagnostic signatures

Most experimental demonstrations rely on repeated current-biased $\varphi\to-\varphi$2–$\varphi\to-\varphi$3 sweeps and statistical extraction of switching currents. In the EuS/Al–InAs field-free nanowire diode, sweeps were repeated up to $\varphi\to-\varphi$4 times at $\varphi\to-\varphi$5 mK to construct histograms of $\varphi\to-\varphi$6 (Telkamp et al., 16 Aug 2025). In the InSb/Al nanowire study, the authors used fast switching detection and histograms of $\varphi\to-\varphi$7 switching events for each polarity, enabling direct comparisons of $\varphi\to-\varphi$8 and $\varphi\to-\varphi$9 as functions of field angle, field magnitude, and gate settings (Mazur et al., 2022). In InAs nanosheet junctions, up to $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$0 switching and retrapping events were recorded to resolve small diode efficiencies and their angular dependence (Yan et al., 26 Jan 2025).

Because the JDE is tied to higher harmonics and anomalous phase shifts in the CPR, phase-sensitive and microwave diagnostics are especially informative. In InSb nanosheet interferometers, half-integer Shapiro steps at $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$1 GHz provide direct evidence for a second-harmonic contribution, and these fractional steps are strongly enhanced near half-integer flux quanta where the effective first harmonic cancels (Wu et al., 19 Feb 2025). In Andreev molecules, differential-resistance maps versus bias current and magnetic flux show oscillatory crossings of $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$2 and $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$3 twice per flux period, directly visualizing polarity reversals driven by nonlocal phase tuning (Zhu et al., 19 Aug 2025). In the TI nanowire nano-SQUID, time-domain rectification under a sinusoidal current of amplitude approximately $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$4 $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$5A demonstrates one-polarity rectification at one axial field and the opposite polarity at another (Nikodem et al., 2024).

Temperature dependence has become a diagnostic of mechanism rather than merely a degradation channel. In Cd$$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$6As$$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$7 nanowire junctions, $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$8 is fitted by a two-channel Eilenberger model yielding $$\eta=\frac{I_{\mathrm{SW}^+}-|I_{\mathrm{SW}^-}|}{I_{\mathrm{SW}^+}+|I_{\mathrm{SW}^-}|}\times100\%,$$9 nm and $I_{c,+}\neq I_{c,-}$00 nm, while a pronounced peak in $I_{c,+}\neq I_{c,-}$01 near $I_{c,+}\neq I_{c,-}$02 K is interpreted as enhanced surface-state contribution to the JDE (Hou et al., 10 Mar 2026). In MATBG gate-defined junctions, extraction of $I_{c,+}\neq I_{c,-}$03 in thermally rounded regimes required an Ivanchenko–Zil’berman treatment rather than a simple switching-threshold criterion, underscoring that diode metrics can depend on the dynamical regime of the junction (Rothstein et al., 17 Oct 2025).

6. Limitations, interpretations, and applications

A persistent interpretive issue is that many reported diode metrics are extracted from switching currents rather than true equilibrium critical currents. The EuS/Al–InAs single-junction diode explicitly notes that the absolute switching currents are only a few nA and that the $I_{c,+}\neq I_{c,-}$04–$I_{c,+}\neq I_{c,-}$05 curves are hysteretic, so $I_{c,+}\neq I_{c,-}$06 is defined from switching rather than from an equilibrium $I_{c,+}\neq I_{c,-}$07 (Telkamp et al., 16 Aug 2025). Similar care is required in nanosheet devices where retrapping asymmetries and self-heating are present, and in MATBG where different damping regimes require different extraction models (Yan et al., 26 Jan 2025, Rothstein et al., 17 Oct 2025). A second common misconception is that field-free JDE must be “magnet-free.” In practice, zero-field operation often relies on remanent magnetization, internal magnetic textures, or intrinsically time-reversal-breaking order parameters rather than on the absence of magnetic symmetry breaking (Telkamp et al., 16 Aug 2025, Singh et al., 1 Nov 2025, Vakili et al., 2024).

Another important distinction concerns where the gate acts. In some systems the dominant control variable is the weak-link transparency; in others it is the proximitized leads, arm asymmetry in a SQUID, nonlocal phase coupling in an Andreev molecule, or the relative weight of bulk and surface channels in a topological material (Mazur et al., 2022, Ciaccia et al., 2023, Zhu et al., 19 Aug 2025, Hou et al., 10 Mar 2026). This suggests that “gate-tunable Josephson diode effect” is not a single mechanism but a family of electrically reconfigurable nonreciprocal superconducting phenomena.

Applications proposed across the literature are consistent with this diversity. A voltage-tunable field-free single junction can serve as a low-loss superconducting rectifier and phase battery, or as a building block for logic, memory, and neuromorphic circuits (Telkamp et al., 16 Aug 2025). Gate- and flux-tunable interferometers have been discussed as rectifiers, direction-selective circuit elements, Josephson field-effect transistors, gyrators, circulators, and components of phase-sensitive readout architectures (Mazur et al., 2022, Ciaccia et al., 2023). In topological and multi-terminal devices, the same control knobs that generate nonreciprocity also reshape Andreev spectra and topological phase structure, suggesting a dual use as both circuit elements and probes of hidden symmetry breaking or topological superconductivity (Nikodem et al., 2024, Gupta et al., 2022, Hou et al., 10 Mar 2026).

The field now spans compact single-junction diodes, engineered interferometric diodes, nonlocal Andreev-molecule diodes, and theoretically proposed magnetic-texture or altermagnetic field-free diodes. What unifies these realizations is not a single material class but a common operational principle: electrostatic gates reshape the CPR by tuning $I_{c,+}\neq I_{c,-}$08, $I_{c,+}\neq I_{c,-}$09, transmission, phase offsets, or channel interference, thereby providing an experimental handle on nonreciprocal superconducting transport that is both diagnostically sensitive and technologically reconfigurable.