Zero-Field Josephson Diode Fundamentals

• Zero-Field Josephson Diode is a superconducting circuit element that rectifies supercurrent at zero magnetic field by exhibiting nonreciprocal critical currents.
• It quantifies rectification performance using metrics like diode efficiency and switching-current asymmetry derived from detailed current-phase relations.
• The device leverages built-in asymmetries from barrier structure, magnetic order, or spatio-temporal drive, enabling tunable, field-free nonreciprocity in various material platforms.

A zero-field Josephson diode is a Josephson weak link or superconducting circuit element in which the critical supercurrent is nonreciprocal at zero applied magnetic field, so that $I_c^+ \neq |I_c^-|$ and a finite current window exists where one bias direction remains dissipationless while the opposite direction switches to a resistive state. In this sense it is the superconducting analog of a diode, but the relevant transport channel is Cooper-pair tunneling rather than normal-state carrier flow. The defining feature is not merely rectification, but rectification without an external magnetic bias during operation; the required symmetry breaking is instead supplied by barrier asymmetry, internal magnetic order, remanent or trapped magnetic textures, anomalous phase shifts, multiterminal phase biasing, spatio-temporal drive asymmetry, or spontaneous symmetry breaking in correlated junctions (Wu et al., 2021, Golod et al., 2022, Kokkeler et al., 2022, Borgongino et al., 11 Apr 2025, Sun et al., 15 Apr 2026).

1. Definition and observables

In a reciprocal Josephson junction with the standard current-phase relation

$I_J = I_c \sin \phi,$

the switching threshold is symmetric under current reversal, so $I_c^+ = |I_c^-|$ (Wu et al., 2021). A zero-field Josephson diode is identified when this equality fails at $B=0$, producing direction-dependent superconducting-to-resistive switching and, under AC excitation, supercurrent rectification (Wu et al., 2021, Golod et al., 2022).

Several nonequivalent figures of merit are used across the literature. The most common is the diode efficiency

$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$

or the corresponding switching-current form

$$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$

while some works use the asymmetry ratio $\left|\frac{I_{c+}}{I_{c-}}\right|$, the SQUID-based quantity $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$, the material-engineering measure $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$, or, in multiterminal geometries, a diode coefficient $\gamma_d$ defined from current extrema (Golod et al., 2022, Yu et al., 2024, Jeon et al., 27 May 2025, Sahoo et al., 17 Sep 2025).

Quantity	Definition	Typical use
Critical-current asymmetry	$I_J = I_c \sin \phi,$0	Minimal diode criterion
Diode efficiency $I_J = I_c \sin \phi,$1	$I_J = I_c \sin \phi,$2	Junction rectification strength
Switching-current efficiency	$I_J = I_c \sin \phi,$3	Nanowire and switching experiments
Nonreciprocity ratio	$I_J = I_c \sin \phi,$4	Vortex/self-field diodes
SQUID diode efficiency	$I_J = I_c \sin \phi,$5	Asymmetric SQUIDs
Transverse diode coefficient	$I_J = I_c \sin \phi,$6	Multiterminal transverse diode effect

Because conventions differ, direct comparison of efficiencies across platforms requires attention to whether the measured quantity is a static critical current, a switching current, a rectified voltage normalized to an ideal value, or a multiterminal current extremum (Golod et al., 2022, Sahoo et al., 17 Sep 2025).

2. Symmetry structure and current-phase relations

The recurring symmetry principle is that nonreciprocal supercurrent requires the removal of the operations that enforce $I_J = I_c \sin \phi,$7. In many zero-field realizations, this means simultaneous breaking of inversion symmetry and time-reversal symmetry by internal rather than externally applied fields. In a diffusive FIS–TI–FIS junction, time-reversal symmetry is broken by exchange-split superconducting electrodes, while inversion symmetry is broken by transport restricted to the topological-insulator surface; the result is an anomalous phase shift $I_J = I_c \sin \phi,$8 at zero applied field (Kokkeler et al., 2022). In multiferroic NbSe$I_J = I_c \sin \phi,$9/NiI$I_c^+ = |I_c^-|$0/NbSe$I_c^+ = |I_c^-|$1, the barrier’s spiral or helimagnetic order and in-plane ferroelectric polarization provide the required built-in symmetry breaking (Yang et al., 2024). In kagome chiral antiferromagnets, the condition is formulated more specifically: $I_c^+ = |I_c^-|$2, $I_c^+ = |I_c^-|$3, and $I_c^+ = |I_c^-|$4 must all be broken to obtain a field-free diode effect and a $I_c^+ = |I_c^-|$5-junction state (Hou et al., 18 Dec 2025).

A second recurring motif is that an anomalous phase alone is often insufficient. In the weak-proximity treatment of the FIS–TI system, the current-phase relation acquires a shift $I_c^+ = |I_c^-|$6, but the diode effect appears only after solving the full nonlinear Usadel problem, which restores higher harmonics and makes $I_c^+ = |I_c^-|$7 (Kokkeler et al., 2022). A closely related statement appears in $I_c^+ = |I_c^-|$8-junction and materials-engineered S/F/S analyses, where the shifted first harmonic must be accompanied by nonsinusoidal terms such as

$I_c^+ = |I_c^-|$9

to produce sizable zero-field diode behavior (Bobkov et al., 24 Nov 2025).

Not all zero-field mechanisms are static. A conventional Al-InAs Josephson junction driven by

$B=0$0

develops a diode effect because the biharmonic forcing breaks spatio-temporal symmetries and generates unequal positive and negative current extrema, $B=0$1. Maximum asymmetry occurs at $B=0$2, and $B=0$3 restores reciprocity (Borgongino et al., 11 Apr 2025). This route is conceptually distinct from magnetically prepared devices because the zero-field nonreciprocity is drive-generated rather than encoded in equilibrium materials symmetry.

3. Material platforms and device architectures

Experimental and theoretical work has established that the zero-field Josephson diode is not tied to a single material class. The phenomenon has been reported or proposed in van der Waals tunnel junctions, planar Nb junctions with trapped vortices, diffusive topological-insulator weak links, graphene multiterminal networks, ferromagnetic and multiferroic barriers, semiconductor nanowires, driven conventional junctions, chiral magnets, altermagnets, and strongly correlated junctions (Wu et al., 2021, Golod et al., 2022, Chiles et al., 2022, Yang et al., 2024, Telkamp et al., 16 Aug 2025, Sahoo et al., 17 Sep 2025, Sun et al., 15 Apr 2026).

Platform	Zero-field mechanism	Representative result
NbSe$B=0$4/Nb$B=0$5Br$B=0$6/NbSe$B=0$7	Asymmetric Josephson tunneling from inversion-breaking barrier and interfaces	$B=0$8, rectification ratio $B=0$9 (Wu et al., 2021)
Planar Nb Josephson junctions	Nonuniform-bias self-field plus trapped Abrikosov vortex or antivortex	Nonreciprocity above a factor of 4 at $\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$0, rectification efficiency above 70% and over 80% (Golod et al., 2022)
Graphene Josephson triode	Dissipationless control current breaks time-reversal symmetry operationally	About 80% efficiency; square-wave rectification down to amplitudes as low as 10 nA (Chiles et al., 2022)
NbN/GdN/NbN long junction	Asymmetric injection plus magnetic tunnel barrier	About 23–25% at zero field; enhancement of up to 40%; nearly 28 GHz (Sharma et al., 2023)
NbSe$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$1/NiI$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$2/NbSe$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$3	Multiferroicity plus spin-orbit coupling	$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$4 at zero field; bipolar operation to about $\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$5 mT (Yang et al., 2024)
Al-InAs Josephson junction with biharmonic drive	Broken spatio-temporal symmetries in a conventional junction	Ideal $\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$6 diode efficiency from a few Hz to GHz; robustness up to about 800 mK (Borgongino et al., 11 Apr 2025)
TiN/Al$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$7O$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$8/Hf$\eta=\frac{I_c^+-|I_c^-|}{I_c^+ + |I_c^-|},$9Zr$$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$0O$$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$1/Nb	Coexisting positive and negative Josephson couplings; spontaneous TRSB	Maximum $$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$2 of about 0.39 (Ding et al., 23 Apr 2025)

The earliest explicit field-free realization used a vertical van der Waals NbSe$$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$3/Nb$$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$4Br$$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$5/NbSe$$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$6 junction, where the barrier and interfaces were argued to induce asymmetric Josephson tunneling; half-wave rectification of a square-wave excitation was observed with low switching current density $$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$7, high rectification ratio $$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$8, and robustness of at least $$\eta=\frac{I_{\mathrm{sw}^+}-|I_{\mathrm{sw}^-}|}{I_{\mathrm{sw}^+}+|I_{\mathrm{sw}^-}|}\times 100\%,$$9 cycles (Wu et al., 2021). Another early branch employed conventional planar niobium Josephson junctions, where nonuniform biasing creates a self-field and a trapped Abrikosov vortex shifts the nonreciprocal peak to zero applied field, yielding a diode-with-memory (Golod et al., 2022).

Subsequent work broadened the platform set. A graphene Josephson triode demonstrated that a three-terminal network can realize field-free nonreciprocal supercurrents because a control branch remains superconducting while reconfiguring the phase landscape of the measured branch (Chiles et al., 2022). Long NbN/GdN/NbN junctions showed that geometric asymmetry and a magnetic tunnel barrier can produce zero-field switching-current rectification in a sputter-deposited architecture (Sharma et al., 2023). Multiferroic NbSe$\left|\frac{I_{c+}}{I_{c-}}\right|$0/NiI$\left|\frac{I_{c+}}{I_{c-}}\right|$1/NbSe$\left|\frac{I_{c+}}{I_{c-}}\right|$2 extended the concept to field-resilient operation under bipolar stray fields (Yang et al., 2024). More recent proposals and experiments add altermagnets, rare-earth intermetallic magnets, chiral kagome antiferromagnets, Cr$\left|\frac{I_{c+}}{I_{c-}}\right|$3NbS$\left|\frac{I_{c+}}{I_{c-}}\right|$4 helimagnets, and strongly correlated odd-parity junctions as further routes to field-free or nominally field-free diode physics (Sahoo et al., 17 Sep 2025, Bobkov et al., 24 Nov 2025, Beach et al., 1 Dec 2025, Hou et al., 18 Dec 2025, Sun et al., 15 Apr 2026).

4. Reconfigurability, polarity control, and memory

One of the central developments in the field is that zero-field nonreciprocity is often tunable rather than fixed. In the biharmonic-drive junction, the phase shift $\left|\frac{I_{c+}}{I_{c-}}\right|$5 is the primary control parameter: $\left|\frac{I_{c+}}{I_{c-}}\right|$6 gives maximal asymmetry and can enable ideal diode behavior, while $\left|\frac{I_{c+}}{I_{c-}}\right|$7 restores a reciprocal response. The ratio $\left|\frac{I_{c+}}{I_{c-}}\right|$8 is another tuning knob, with maximum operation reported near $\left|\frac{I_{c+}}{I_{c-}}\right|$9 (Borgongino et al., 11 Apr 2025).

In planar niobium diodes with vortex control, polarity can be reversed either by changing from a vortex to an antivortex or by switching between left-corner and right-corner bias injection. The same device can also be toggled between a reciprocal state with no trapped vortex and a nonreciprocal state with a trapped vortex or antivortex. The persistent zero-field states are described as “0” for the reciprocal state and “$n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$0” or “$n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$1” for the two diode polarities, which is why the platform was presented as a superconducting diode-with-memory (Golod et al., 2022).

Electrostatic control is prominent in hybrid semiconductor devices. In InAs nanowires coated with EuS and Al shells, the zero-field diode efficiency depends strongly on back-gate voltage: at $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$2 V the distributions of $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$3 and $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$4 are clearly separated, giving about $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$5, whereas at $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$6 V the efficiency is about $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$7, consistent with zero. Zero-field operation is obtained after a demagnetization procedure, with superconductivity recovered at $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$8 for demagnetization fields roughly between $n_c=\frac{I_c^+ - I_c^-}{I_c^+ + I_c^-}$9 and $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$0 mT (Telkamp et al., 16 Aug 2025).

Materials engineering provides a second route to polarity control. In lateral Nb junctions on proximity-magnetized Pt, Ta, W, or Pd atop YIG, the zero-field diode efficiency and sign depend on the proximity layer. Pt-based devices serve as a benchmark, Ta yields a similar magnitude but opposite polarity, W yields a much smaller diode efficiency, and Pd yields a large diode efficiency with the same polarity as Pt. SQUID interferometry directly extracts a nonvolatile anomalous phase shift $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$1, with representative values $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$2 for Pt, $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$3 for Ta, $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$4 for W, and $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$5 for Pd (Jeon et al., 27 May 2025).

Magnetization-controlled nonvolatility appears in multilayers and magnetic tunnel barriers as well. In $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$6, the zero-field superconducting diode polarity is written by the remanent magnetization direction of the Co layers (Narita et al., 2022). In NbN/GdN/NbN, minor-loop field cycling changes the micromagnetic structure of GdN and boosts the efficiency by up to 40% (Sharma et al., 2023). A distinct, more spontaneous form of polarity selection is proposed in strongly correlated junctions with odd electron number, where the zero-field $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$7-junction chooses one of two degenerate minima at $Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$8; repeated superconducting transitions can then cause the sign to switch randomly (Sun et al., 15 Apr 2026).

5. Dynamical models and microscopic interpretations

The resistively and capacitively shunted junction framework remains a common language for describing zero-field diode dynamics. In the biharmonic-drive realization, the phase obeys

$Q_{H_0H=0}=\frac{\Delta I_c}{I_{\mathrm{avg}}}$9

so the superconducting phase behaves as a particle in a tilted washboard potential. In the adiabatic limit,

$\gamma_d$0

the direction-dependent critical currents become

$\gamma_d$1

The ideal-diode condition follows when one current direction is fully suppressed; for the biharmonic drive this occurs at $\gamma_d$2 with $\gamma_d$3 (Borgongino et al., 11 Apr 2025).

A different washboard mechanism is developed for TiN/Al$\gamma_d$4O$\gamma_d$5/Hf$\gamma_d$6Zr$\gamma_d$7O$\gamma_d$8/Nb tunnel junctions. There the effective Josephson potential is written as

$\gamma_d$9

where $I_J = I_c \sin \phi,$00 is the average positive Josephson coupling and $I_J = I_c \sin \phi,$01 arises from the inhomogeneous coexistence of positive direct tunneling and negative indirect tunneling through localized states. The $I_J = I_c \sin \phi,$02 term produces a double-minimum washboard potential and spontaneous time-reversal-symmetry breaking at nominally zero field (Ding et al., 23 Apr 2025).

The anomalous-phase viewpoint is especially important in diffusive and magnetic weak links. In FIS–TI–FIS junctions, the weak-proximity solution yields a $I_J = I_c \sin \phi,$03-shifted current-phase relation and shows that the relevant phase shift derives from interference between even-frequency singlet and odd-frequency triplet components, but the diode effect itself requires the nonlinear regime where higher harmonics survive (Kokkeler et al., 2022). In S/F/S junctions through thin films of $I_J = I_c \sin \phi,$04, first-principles plus BdG calculations show a pronounced $I_J = I_c \sin \phi,$05 of order unity and a diode efficiency $I_J = I_c \sin \phi,$06, with strong control by in-plane magnetization orientation (Bobkov et al., 24 Nov 2025).

A more radical interpretation replaces externally imposed symmetry breaking by many-body spontaneous symmetry breaking. In the Hubbard-$I_J = I_c \sin \phi,$07 model with odd total electron number, strong correlations induce a $I_J = I_c \sin \phi,$08-junction whose Josephson energy has two equal minima at $I_J = I_c \sin \phi,$09, thereby breaking time-reversal and mirror symmetries spontaneously and producing zero-field $I_J = I_c \sin \phi,$10 without magnetic order (Sun et al., 15 Apr 2026). This suggests that zero-field diode behavior need not always be traced to an explicit magnetic texture or externally prepared remanent state.

6. Performance regimes and functional scope

Reported zero-field diode efficiencies span a wide range, reflecting different definitions and operating modes. Experiments include about $I_J = I_c \sin \phi,$11 in multiferroic NbSe$I_J = I_c \sin \phi,$12/NiI$I_J = I_c \sin \phi,$13/NbSe$I_J = I_c \sin \phi,$14 at zero field (Yang et al., 2024), about $I_J = I_c \sin \phi,$15 in a Cd$I_J = I_c \sin \phi,$16As$I_J = I_c \sin \phi,$17-mediated asymmetric SQUID at $I_J = I_c \sin \phi,$18 (Yu et al., 2024), about $I_J = I_c \sin \phi,$19 zero-field asymmetry and up to $I_J = I_c \sin \phi,$20 in Cr$I_J = I_c \sin \phi,$21NbS$I_J = I_c \sin \phi,$22 helimagnet junctions (Beach et al., 1 Dec 2025), about 23–25% in long NbN/GdN/NbN junctions with boosts up to 40% via micromagnetic tuning (Sharma et al., 2023), about 17% in Ta/YIG-based proximity diodes and about 15% in Pd/YIG-based devices (Jeon et al., 27 May 2025), above 70% and in the best cases over 80% for zero-field vortex-assisted niobium diodes (Golod et al., 2022), about 80% in the graphene Josephson triode with the abstract also describing efficiencies upwards of 90% (Chiles et al., 2022), about 0.39 in the CMOS-compatible HZO tunnel junction (Ding et al., 23 Apr 2025), and ideal $I_J = I_c \sin \phi,$23 in the biharmonic-drive conventional junction (Borgongino et al., 11 Apr 2025).

Frequency and temperature windows are equally diverse. The biharmonic-drive device operates from 100 Hz and 1 kHz through 700 MHz up to a few GHz, with the effect stated to work from a few Hz to GHz in the adiabatic regime, while Shapiro steps persist up to 900 mK and diode or rectification functionality to about 800 mK (Borgongino et al., 11 Apr 2025). The long NbN/GdN/NbN platform reports an operating frequency of nearly 28 GHz and maintains clear zero-field efficiency from the lowest temperatures up to at least 4.2 K (Sharma et al., 2023). The original NbSe$I_J = I_c \sin \phi,$24/Nb$I_J = I_c \sin \phi,$25Br$I_J = I_c \sin \phi,$26/NbSe$I_J = I_c \sin \phi,$27 junction exhibits ideal half-wave rectification at 0.9 K and still rectifies at 3.86 K, albeit with punch-through errors (Wu et al., 2021). The graphene triode was studied from 60 mK to 1.9 K, with hysteresis disappearing between about 0.5 K and 1 K depending on gate voltage (Chiles et al., 2022).

Field resilience is a distinct performance category. The multiferroic NiI$I_J = I_c \sin \phi,$28 junction maintains the same diode polarity over a bipolar in-plane field range from $I_J = I_c \sin \phi,$29 mT to $I_J = I_c \sin \phi,$30 mT and a large operating window extending to about $I_J = I_c \sin \phi,$31 mT, which is highlighted as beyond industrial standards for field tolerance (Yang et al., 2024). This is qualitatively different from platforms whose zero-field operation depends on a prepared remanent or vortex state and may be more sensitive to magnetic history (Golod et al., 2022, Telkamp et al., 16 Aug 2025).

The application space described in the literature includes superconducting logic gates, ultra-fast switches, dynamic half-wave supercurrent rectifiers, on-chip cryogenic power electronics, in-memory superconducting computing, quantum-circuit-compatible rectifiers, nonvolatile memory, and phase-bias elements (Golod et al., 2022, Chiles et al., 2022, Yang et al., 2024, Borgongino et al., 11 Apr 2025, Jeon et al., 27 May 2025, Ding et al., 23 Apr 2025). This suggests that the field’s practical significance lies not only in dissipationless rectification but in programmable nonreciprocity integrated with memory and phase control.

7. Conceptual distinctions and recurrent misconceptions

A common ambiguity concerns the meaning of “zero field.” In some platforms, zero-field operation means that no external magnetic field is present during readout even though the device relies on an internally prepared state, such as a trapped Abrikosov vortex, remanent ferromagnetic or ferrimagnetic order, or a demagnetized multidomain configuration (Golod et al., 2022, Narita et al., 2022, Jeon et al., 27 May 2025, Telkamp et al., 16 Aug 2025). In other platforms, the effect is field-free in a stronger sense because the nonreciprocity is attributed to intrinsic inversion breaking, multiferroicity, anomalous phase structure, spatio-temporal driving, or spontaneous many-body symmetry breaking rather than to magnetic state preparation (Wu et al., 2021, Kokkeler et al., 2022, Yang et al., 2024, Borgongino et al., 11 Apr 2025, Sun et al., 15 Apr 2026). The literature therefore uses “zero-field” for both prepared and intrinsically field-free cases; the distinction is physically important.

A second misconception is that any anomalous junction with $I_J = I_c \sin \phi,$32 is automatically a Josephson diode. The diffusive FIS–TI analysis makes the opposite point explicitly: a pure $I_J = I_c \sin \phi,$33 current-phase relation still has equal positive and negative critical currents, and diode behavior requires sufficiently nonsinusoidal current-phase structure (Kokkeler et al., 2022). This is consistent with the two-harmonic CPR fits used in rare-earth intermetallic S/F/S theory and with effective $I_J = I_c \sin \phi,$34 terms in tunnel junctions with spontaneous TRSB (Bobkov et al., 24 Nov 2025, Ding et al., 23 Apr 2025).

A third distinction is between genuine zero-field and merely low-field or field-orientation-controlled Josephson diodes. A short superconductor–semiconductor nanowire junction with Rashba SOC and homogeneous Zeeman field can host Andreev- and Majorana-enhanced diode effects, but that system does not realize a true field-free diode: the effect requires a nonzero Zeeman component parallel to the SOC axis, and it disappears at $I_J = I_c \sin \phi,$35 (Mondal et al., 11 Mar 2025). By contrast, proposed altermagnetic transverse Josephson diodes and kagome chiral antiferromagnet junctions aim to obtain nonreciprocity without any external magnetic field by using internally broken symmetries in multiterminal or spin-orbit-coupled antiferromagnetic geometries (Sahoo et al., 17 Sep 2025, Hou et al., 18 Dec 2025).

Taken together, these distinctions show that the zero-field Josephson diode is not a single mechanism but a family of nonreciprocal superconducting states and devices united by one criterion—$I_J = I_c \sin \phi,$36 at zero applied field—and differentiated by how that asymmetry is generated, stabilized, tuned, and exploited.