Supercurrent Diode Effect in Superconductors

• Supercurrent Diode Effect is a nonreciprocal superconducting phenomenon where positive and negative bias currents differ due to broken inversion and time-reversal symmetries.
• It is characterized by distinct critical current measurements, asymmetric current-phase relations, and diode efficiency metrics extracted from precise switching experiments.
• SDE mechanisms span intrinsic band asymmetry, quantum-geometric effects, and engineered device configurations, driving advancements in superconducting electronics.

Supercurrent diode effect (SDE) denotes nonreciprocal superconducting transport in which the critical supercurrent differs for opposite current directions. In bulk superconductors this is usually formulated as unequal switching or depairing currents under reversed bias, whereas in phase-biased weak links the analogous phenomenon is often termed the Josephson diode effect (JDE); contemporary literature commonly treats JDE as a Josephson realization of the broader SDE concept (Gao et al., 21 Apr 2026, Sun et al., 15 Apr 2026). The standard symmetry viewpoint ties SDE to simultaneous breaking of inversion symmetry and time-reversal symmetry, but current work has expanded the subject far beyond the canonical Rashba-plus-field setting to include field-odd and field-free responses, orbital and surface mechanisms, quantum-geometric contributions, strong-correlation effects, vortex-mediated rectification, and non-Hermitian superconducting transport (Hu et al., 2024, Nakamura et al., 1 May 2026, Qi et al., 7 Aug 2025).

1. Definition and core observables

Operationally, SDE is identified from unequal positive- and negative-bias critical currents, often denoted $I_{\mathrm{C}^+}$ and $I_{\mathrm{C}^-}$, or equivalently $J_{c+}$ and $J_{c-}$ for current densities. A widely used experimental convention defines the diode efficiency as

$$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$

so that the sign gives the diode polarity and the magnitude gives the strength of nonreciprocity (Gao et al., 21 Apr 2026). In transport experiments, several groups explicitly use the switching currents rather than retrapping currents because retrapping can be strongly distorted by hysteresis and Joule heating (Gao et al., 21 Apr 2026). Other subliteratures adopt alternative normalizations, including $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$ for edge-resolved QSHI junctions, or signed conventions in which the negative critical current is treated without absolute value; the proliferation of notations reflects distinct bulk, Josephson, and topological device settings rather than a single universal metrology standard (Scharf et al., 2024, Sun et al., 15 Apr 2026).

The same phenomenon can be formulated in momentum or phase language. In bulk theories, SDE means that the supercurrent relation is nonreciprocal in Cooper-pair momentum, so $J(q)\neq -J(-q)$, and consequently $|J_{c+}|\neq |J_{c-}|$ (Hu et al., 2024). In Josephson junctions, it is extracted from a nonreciprocal current-phase relation $I_s(\phi)$, with $I_{c+}=\max_\phi I_s(\phi)$ and $I_{\mathrm{C}^-}$0 (Sun et al., 15 Apr 2026). This equivalence between finite pair momentum in bulk superconductors and phase bias in Josephson structures is why several papers treat SDE and JDE within a common conceptual framework (Sun et al., 15 Apr 2026).

Beyond critical-current asymmetry, some works emphasize related nonreciprocal observables. In diffusive SN bilayers the same orbital mechanism produces both asymmetric depairing currents and asymmetric kinetic inductance for opposite current directions (Dmitrievtsev et al., 10 Apr 2026). In microwave-driven or ac-biased Josephson structures, asymmetric Shapiro steps and shifted zero-voltage plateaus appear as dynamical signatures of the same underlying nonreciprocal supercurrent response (Qi et al., 7 Aug 2025).

2. Symmetry requirements and principal classifications

The standard criterion for equilibrium SDE is the simultaneous absence of inversion symmetry $I_{\mathrm{C}^-}$1 and time-reversal symmetry $I_{\mathrm{C}^-}$2. In many intrinsic bulk proposals, inversion breaking is supplied by noncentrosymmetric band structure and time-reversal breaking by an external magnetic field or Zeeman splitting (Hu et al., 2024). This symmetry logic remains central, but recent literature has shown that the breaking can be hidden, emergent, or spontaneous rather than explicit in the nominal crystal structure.

One useful classification separates field-odd and field-free SDE. Field-odd SDE changes polarity when the magnetic field is reversed. A recent example is CVD-grown $I_{\mathrm{C}^-}$3, where the same material platform hosts a field-odd SDE when an in-plane field is applied perpendicular to the current; the nonreciprocity vanishes when the field is parallel to the current, and the diode polarity flips under $I_{\mathrm{C}^-}$4 (Gao et al., 21 Apr 2026). By contrast, a separate $I_{\mathrm{C}^-}$5 device exhibits a field-free SDE at zero applied field, with the polarity surviving zero-field cooling and field-cooling protocols, implying spontaneous breaking of both inversion and time-reversal symmetries within the superconducting state (Gao et al., 21 Apr 2026). A related zero-field route appears in a strongly correlated Josephson junction with odd occupancy, where interaction-induced spontaneous breaking of time-reversal and mirror symmetries yields a $I_{\mathrm{C}^-}$6-junction with degenerate minima at $I_{\mathrm{C}^-}$7, and hence a zero-field JDE without magnetic order (Sun et al., 15 Apr 2026).

A second classification separates intrinsic from extrinsic or ubiquitous SDE. Intrinsic mechanisms tie the nonreciprocity to the superconducting condensate itself, often through band asymmetry, pairing structure, quantum geometry, or spontaneous order (Hu et al., 2024). Extrinsic mechanisms instead exploit geometric asymmetry, screening currents, or vortex entry barriers. The distinction is not merely semantic; it is a recurring controversy in experimental interpretation. The $I_{\mathrm{C}^-}$8 work, for example, uses out-of-plane field sweeps to argue against a trivial edge-asymmetry/vortex origin for its field-odd and field-free signals (Gao et al., 21 Apr 2026), whereas oxide-interface weak-link devices and asymmetric Dayem bridges deliberately realize SDE through vortex dynamics in inversion-breaking device geometries (Yu et al., 6 Nov 2025, Antola et al., 16 Jul 2025).

A third classification concerns how inversion and time-reversal breaking are implemented. In chiral nanotubes, inversion breaking is supplied by the chiral wrapping geometry, while time-reversal symmetry is broken orbitally by axial flux; no spin-orbit coupling or Zeeman field is required (He et al., 2022). In surface superconductivity, the surface itself breaks inversion normal to the boundary, and an in-plane magnetic field induces a Meissner screening current that offsets transport and can yield a perfect surface diode regime (Yuan, 2023). In SN bilayers, an in-plane field acting on a spatially varying superfluid density produces a purely orbital SDE with no need for spin-based mechanisms (Dmitrievtsev et al., 10 Apr 2026). These examples show that SDE is best understood as a broad nonreciprocal superconducting response rather than a phenomenon restricted to one canonical symmetry-breaking recipe.

3. Intrinsic microscopic mechanisms

The conventional microscopic picture attributes SDE to asymmetry of the single-particle dispersion or Fermi surface in a superconducting state with broken $I_{\mathrm{C}^-}$9 and $J_{c+}$0. In a Ginzburg–Landau expansion, this appears as an odd-in-$J_{c+}$1 cubic term in the pair-momentum-dependent free energy, so the current obtained from $J_{c+}$2 becomes nonreciprocal (Hu et al., 2024). In the narrow-band theory of noncentrosymmetric superconductors with negligible spin-orbit coupling, the cubic coefficient has two parts: a conventional dispersion-derived contribution $J_{c+}$3 and a geometric contribution $J_{c+}$4 arising from the quantum metric dipole. The resulting near-$J_{c+}$5 diode coefficient obeys

$J_{c+}$6

and scales as $J_{c+}$7 close to the transition (Hu et al., 2024). The conceptual advance is that quantum geometry can generate SDE even when the single-particle dispersion is itself symmetric, provided the Bloch-state geometry is inversion asymmetric. At the same time, the exact flat-band limit is subtle: geometric superfluidity survives, but the SDE vanishes because the required cubic-in-$J_{c+}$8 term disappears (Hu et al., 2024).

Strong correlation opens a distinct set of intrinsic mechanisms. In the asymmetric Hatsugai–Kohmoto model, correlation-induced splitting of an asymmetric band into two Hubbard-like subbands makes the superconducting quasiparticle spectrum gapless at different pair momenta for opposite current directions, which enhances the diode quality factor from $J_{c+}$9 at $J_{c-}$0 to $J_{c-}$1 at $J_{c-}$2 in the reported example (Chen et al., 20 Oct 2025). In a Rashba-Zeeman-Hubbard model treated with Dyson-Gor'kov equations and FLEX, the conventional intrinsic SDE from asymmetric depairing currents is actually suppressed by strong correlations, but a new mechanism emerges: supercurrent nonreciprocally induces antiferromagnetic order, and this current-driven magnetic instability can set the directional critical currents and even yield perfect diode efficiency (Nakamura et al., 1 May 2026). In the correlated Josephson setting, a separate mechanism operates through odd electron occupancy and strong Hubbard interaction, producing a spontaneous $J_{c-}$3-junction and zero-field diode behavior without magnetic order (Sun et al., 15 Apr 2026).

Chiral nanotubes provide a purely orbital intrinsic route. Phenomenological GL theory showed that chirality plus axial Aharonov–Bohm flux generates odd longitudinal gradient terms and therefore $J_{c-}$4 without SOC or Zeeman splitting (He et al., 2022). A later Josephson-junction theory on chiral nanotubes sharpened the distinction between anomalous phase and true diode response: the anomalous phase $J_{c-}$5 can be present with $J_{c-}$6, while the actual diode effect arises from a nonreciprocal persistent current protected by fluxoid quantization; in this mechanism the efficiency

$J_{c-}$7

can approach the perfect limit in short junctions (Cuozzo et al., 3 Apr 2025). A microscopic lattice study of chiral nanotubes then found detailed dependence on radius, chiral angle, flux, temperature, chemical potential, strain, and SOC, including sign reversals and diode efficiencies of order $J_{c-}$8 near van Hove singularities, with the key microscopic driver identified as flux-induced asymmetry of the chiral subband structure (Li et al., 2024).

4. Orbital, geometric, and engineered-device realizations

A large part of the current SDE literature concerns structures in which nonreciprocity is engineered by interfaces, edges, geometry, or open-system effects rather than by a uniform bulk order parameter. The diversity of these realizations is now one of the defining features of the field.

Platform	Dominant ingredient	Reported hallmark
$J_{c-}$9 nanoflakes	phase mixing, domain boundaries or CDW-like order	$$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$0 at $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$1 K; field-free $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$2
LAO/KTO weak links	geometric asymmetry and vortex motion	rectification up to about $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$3
Asymmetric Dayem bridges	current crowding, screening currents, vortices	rectification up to $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$4
InAs/Al hybrid JJs with hole arrays	channel-transparency mismatch	gate-tuned enhancement and sign reversal
QSHI Josephson junctions	orbital pair momentum in inequivalent edges	universal $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$5 at low $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$6
Non-Hermitian SQUID	reservoir-induced non-Hermiticity plus flux	diode efficiency above $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$7

Among recent material platforms, phase-mixed $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$8 nanoflakes are notable because a nominally centrosymmetric material grown by a single CVD process hosts both a field-odd and a field-free SDE in different devices. The field-odd response reaches about $$\eta=\frac{I_{\mathrm{C}^+}-|I_{\mathrm{C}^-}|}{I_{\mathrm{C}^+}+|I_{\mathrm{C}^-}|},$$9 at $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$0 K and remains above $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$1 at $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$2 K under an in-plane field perpendicular to current, whereas a separate device shows a zero-field efficiency of about $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$3 at $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$4 K (Gao et al., 21 Apr 2026). The proposed origins are qualitative rather than settled, centered on nanoscale $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$5 phase mixing, possible charge-density-wave-like order, and domain-boundary supercurrents (Gao et al., 21 Apr 2026).

Several engineered weak-link systems realize SDE by design. In reconfigurable LAO/KTO weak links written by conductive AFM lithography, an off-center superconducting weak link in a wider channel breaks inversion symmetry geometrically, and modest out-of-plane fields generate diode behavior through asymmetric vortex entry and motion; moving the weak link from one edge to the other reverses the diode polarity, and the rectification efficiency reaches about $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$6 (Yu et al., 6 Nov 2025). Mesoscopic aluminum Dayem bridges with asymmetric bridge-bank interfaces exhibit a low-field linear rectification regime controlled by screening-current-induced current crowding, followed by a high-field regime dominated by Abrikosov-vortex rearrangements in the banks; the reported rectification can approach $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$7, and too-narrow bridges with $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$8 strongly suppress the crowding-based effect (Antola et al., 16 Jul 2025).

Hybrid Josephson junctions provide additional engineering knobs. In InAs heterostructures with epitaxial aluminum, periodic hole arrays patterned into the superconducting leads yield a gate-tunable enhancement of the diode effect when a top gate depletes the 2DEG under the hole regions; the interpretation is a gate-induced increase in the transparency mismatch $Q^\sigma=(|I^{\sigma +}|-|I^{\sigma -}|)/I_0$9 between effective Andreev channels, consistent with the reduced relation $J(q)\neq -J(-q)$0 (Yu et al., 22 Dec 2025). In a Fabry–Perot resonant-tunneling InAs Josephson junction with finite-momentum pairing in the leads, the diode efficiency exhibits multiple gate-controlled resonances of about $J(q)\neq -J(-q)$1 in the full continuum model and up to about $J(q)\neq -J(-q)$2 in a reduced single-level description, with sign reversals tied to parity transitions and finite-$J(q)\neq -J(-q)$3 Andreev phase shifts (Zhang, 2024). In a QSHI-based short junction, orbital Doppler shifts and edge-dependent phase offsets from an out-of-plane field yield edge-resolved SDE, but the two edges cancel unless they are transport-wise non-equivalent; in the low-temperature $J(q)\neq -J(-q)$4-periodic regime the maximum quality factor is universal,

$J(q)\neq -J(-q)$5

and the $J(q)\neq -J(-q)$6-periodic parity-constrained regime further enhances the effect for $J(q)\neq -J(-q)$7 (Scharf et al., 2024).

Orbital theories not based on discrete Josephson channels have also matured. A surface superconducting layer with surface states under in-plane magnetic field exhibits a surface supercurrent diode effect because the field-induced persistent surface current offsets transport; the resulting line current

$J(q)\neq -J(-q)$8

can produce a perfect diode regime over a finite field window, a behavior explicitly contrasted with the nonperfect conventional Rashba-based case (Yuan, 2023). In diffusive SN bilayers under in-plane field, a purely orbital SDE arises from the interplay of $J(q)\neq -J(-q)$9 and a proximity-induced superfluid-density gradient across the thickness; finite interface resistance can enhance the effect relative to the ideal interface, and for thin bilayers the strength is nonmonotonic in the interface resistance, with a maximum around $|J_{c+}|\neq |J_{c-}|$0 (Dmitrievtsev et al., 10 Apr 2026).

More unconventional device ideas extend the category further. A Josephson junction coupled self-consistently to a magnetic impurity exhibits diode behavior because the current itself changes the impurity moment, $|J_{c+}|\neq |J_{c-}|$1, which reshapes the Andreev spectrum differently for opposite current directions and can yield $|J_{c+}|\neq |J_{c-}|$2 up to about $|J_{c+}|\neq |J_{c-}|$3 in favorable parameter regimes (Sun et al., 2024). A non-Hermitian SQUID in which one Josephson junction is coupled to a gapless reservoir develops a diode effect through a phase-dependent suppression factor $|J_{c+}|\neq |J_{c-}|$4 multiplying the Hermitian current; with flux bias this mechanism produces efficiencies above $|J_{c+}|\neq |J_{c-}|$5 and asymmetric Shapiro steps (Qi et al., 7 Aug 2025).

5. Experimental diagnostics, controls, and interpretive controversies

Because SDE is defined by critical-current asymmetry, measurement protocols strongly influence interpretation. Recent experiments commonly use four-terminal $|J_{c+}|\neq |J_{c-}|$6-$|J_{c+}|\neq |J_{c-}|$7 curves or differential-resistance maps, extract $|J_{c+}|\neq |J_{c-}|$8 and $|J_{c+}|\neq |J_{c-}|$9 from switching rather than retrapping branches, and then map the diode metric against field orientation, temperature, and gate tuning (Gao et al., 21 Apr 2026, Yu et al., 22 Dec 2025). In $I_s(\phi)$0, a particularly direct operational demonstration used a square-wave drive alternating between $I_s(\phi)$1 mA and $I_s(\phi)$2 mA, showing that one current polarity can remain dissipationless while the opposite polarity yields finite voltage, with the rectification reversing under magnetic-field reversal (Gao et al., 21 Apr 2026). In planar hybrid junctions, sweep direction is deliberately chosen to reduce heating artifacts, since zero-field asymmetries can otherwise be contaminated by hysteresis (Yu et al., 22 Dec 2025).

Field orientation is a primary diagnostic. Several systems show nonreciprocity only when the field is perpendicular to current within the plane, and little or no effect when the field is parallel to current, consistent with the symmetry of Rashba-type and field-odd orbital mechanisms (Gao et al., 21 Apr 2026, Yu et al., 22 Dec 2025). Engineered geometric-vortex devices instead obey field-odd reciprocity relations such as $I_s(\phi)$3, and their diode polarity reverses either under $I_s(\phi)$4 or under a geometric mirror operation such as moving a weak link from one edge of a channel to the other (Yu et al., 6 Nov 2025, Antola et al., 16 Jul 2025). QSHI junctions impose an additional design requirement: equivalent top and bottom edges cancel exactly, so edge non-equivalence is not a nuisance but a prerequisite for a measurable net SDE (Scharf et al., 2024).

The major interpretive controversy concerns intrinsic versus extrinsic origin. Conventional films and mesoscopic weak links can show “ubiquitous” diode signals from edge asymmetry and vortex trapping, so intrinsic claims now routinely require control experiments. The $I_s(\phi)$5 study addresses this by using out-of-plane field sweeps, orthogonal-strip comparisons, isolated-contact measurements, and normal-state magnetoresistance to argue against crosstalk, misalignment, simple edge/vortex artifacts, and ferromagnetism (Gao et al., 21 Apr 2026). Conversely, in KTaO$I_s(\phi)$6- and Dayem-bridge-based devices, the entire point is that asymmetric vortex entry is the mechanism; there, reciprocity relations and time-dependent Ginzburg–Landau simulations are used to validate the engineered geometric interpretation rather than exclude it (Yu et al., 6 Nov 2025, Antola et al., 16 Jul 2025).

Field-free SDE raises an additional controversy: what exactly is being spontaneously broken, and how is the polarity selected? In $I_s(\phi)$7, the zero-field diode survives both zero-field cooling and field cooling, yet its polarity does not reverse under opposite cooling fields, which argues against a simple coercible chiral order and instead points toward a mechanism “more engraved in the supercurrent flow throughout the phase-mixed sample,” such as domain-boundary supercurrents (Gao et al., 21 Apr 2026). In strongly correlated zero-field JDE, branch selection between $I_s(\phi)$8 minima implies that repeated cooldown or retrapping cycles could produce random polarity, whereas a tiny Zeeman field should deterministically choose the branch (Sun et al., 15 Apr 2026). These scenarios illustrate that zero-field SDE is not a single phenomenon but a family of spontaneous or metastable nonreciprocal superconducting states.

6. Open problems and emerging directions

The foremost open question is microscopic identification. Even in high-profile recent experiments, the underlying order parameter or current path remains unresolved. In phase-mixed $I_s(\phi)$9, the present alternatives include charge-density-wave-like electronic order, pair-density-wave-related physics, and domain-boundary supercurrents, but no current-phase-relation fit, free-energy model, or microscopic Hamiltonian yet distinguishes them decisively (Gao et al., 21 Apr 2026). The proposed next steps are correspondingly local and phase sensitive: low-temperature STM to probe CDW/PDW signatures, scanning nano-SQUID magnetometry to image boundary currents, Little–Parks interferometry in patterned rings, and improved synthesis of pure $I_{c+}=\max_\phi I_s(\phi)$0- or $I_{c+}=\max_\phi I_s(\phi)$1-phase material to test whether mixed-phase structure is essential (Gao et al., 21 Apr 2026).

A second open problem concerns the relative weight of conventional and nonconventional intrinsic channels. The quantum-geometric theory predicts that narrow-band superconductors can exhibit SDE dominated by the quantum metric dipole, yet it also shows that the exact flat-band limit has no diode effect despite finite geometric superfluidity (Hu et al., 2024). This leaves an experimental challenge: identifying systems in which the geometric contribution can be isolated from ordinary dispersion asymmetry, rather than merely coexisting with it. Moiré superconductors remain a natural target because they combine isolated narrow bands, strong interactions, and tunable inversion breaking (Hu et al., 2024).

Correlation-driven mechanisms present their own unresolved issues. The zero-field correlated JDE is demonstrated in an idealized finite interacting region with odd occupancy and exact diagonalization, but disorder, many-channel transport, and extended geometries remain open (Sun et al., 15 Apr 2026). In the quantum-critical SDE theory, the key ingredient is nonreciprocal current-induced antiferromagnetism, yet the phase competition between superconductivity and magnetism is treated using a phenomenological magnetic threshold and neglects disorder, orbital depairing, and possible coexistence regimes (Nakamura et al., 1 May 2026). A plausible implication is that materials near magnetic criticality may show qualitatively different diode phenomenology from weak-coupling noncentrosymmetric superconductors, but direct experimental confirmation still requires simultaneous transport and magnetic probes (Nakamura et al., 1 May 2026).

Device engineering introduces a different class of open problems. In vortex-based bridges and oxide weak links, high-field rectification depends sensitively on pinning, accidental imperfections, and multivortex configurations, so quantitatively predictive theory remains difficult (Antola et al., 16 Jul 2025, Yu et al., 6 Nov 2025). In patterned hybrid Josephson junctions, the mapping from depleted hole-array regions to effective transparency differences $I_{c+}=\max_\phi I_s(\phi)$2 and phase offsets $I_{c+}=\max_\phi I_s(\phi)$3 is still semiquantitative (Yu et al., 22 Dec 2025). In parity-conserving topological junctions, the predicted enhancement of SDE in the $I_{c+}=\max_\phi I_s(\phi)$4-periodic regime requires measurement on timescales shorter than quasiparticle poisoning, which places demanding constraints on experiment (Scharf et al., 2024). In non-Hermitian SQUIDs, finite-temperature behavior, stronger interactions, and more structured reservoir backaction remain to be worked out beyond the simple $I_{c+}=\max_\phi I_s(\phi)$5 self-energy model (Qi et al., 7 Aug 2025).

The broader trajectory of the subject is nevertheless clear. SDE is no longer a narrowly defined consequence of Rashba spin-orbit coupling plus Zeeman field. It has become a unifying label for a wide class of nonreciprocal superconducting phenomena spanning bulk superconductors, Josephson junctions, surface states, chiral nanotubes, correlated quantum-critical metals, open non-Hermitian circuits, and deliberately asymmetric vortex structures (Yuan, 2023, Hu et al., 2024, Nakamura et al., 1 May 2026). This suggests that future progress will depend less on searching for one universal mechanism than on establishing a sharper taxonomy of mechanisms, observables, and symmetry breakings, together with local probes capable of connecting a measured diode signal to its microscopic origin.