Asymmetric Dayem Bridges in Superconducting Circuits

• Asymmetric Dayem bridges are superconducting weak links that exhibit nonreciprocal supercurrent due to engineered asymmetry in geometry or interface.
• They utilize varied architectures, including monolithic dc-SQUIDs and planar thin-film implementations, to achieve different current-phase relations and diode effects.
• Experimental studies report rectification efficiencies up to ~27%, highlighting potential applications in superconducting electronics and low-dissipation circuits.

Asymmetric Dayem bridges are superconducting weak links based on narrow constrictions in a continuous superconducting material, operated in a regime where supercurrent transport becomes direction dependent. In the recent literature, the term encompasses several closely related realizations: monolithic dc-SQUIDs containing two nonidentical 3D Dayem nanobridges, planar thin-film bridges with an intentionally asymmetric bridge–lead interface, and metallic Dayem nanobridges whose nonreciprocity emerges under out-of-plane magnetic field from a non-sinusoidal current-phase relation together with field-sensitive phase structure. In all of these cases, the defining observable is an inequality between the positive and negative critical or switching currents, leading to a Josephson diode effect or supercurrent diode effect with reported rectification efficiencies up to $\sim 27\%$ (Greco et al., 2023, Antola et al., 16 Jul 2025, Margineda et al., 2023).

1. Definitions and operational criteria

A Dayem bridge is a superconducting weak link formed by a narrow constriction between larger superconducting electrodes or banks. In the NbRe gate-control study, the devices are explicitly described as having “a Dayem bridge geometry consisting of two large electrodes separated by a narrow constriction (bridge)” (Koch et al., 2023). In the thin-film rectification study, asymmetric Dayem bridges are planar metallic constrictions acting as mesoscopic weak links between wider superconducting banks (Antola et al., 16 Jul 2025). In the monolithic dc-SQUID realization, the weak links are 3D Dayem nanobridges, namely geometric constrictions in a superconducting metal rather than tunnel barriers or hybrid semiconductor links (Greco et al., 2023).

The operational signature of asymmetry is nonreciprocal superconducting transport. In the dc-SQUID formulation, the forward and reverse critical currents are defined as $I_+$ and $I_-$, and rectification is quantified by

$\eta=\frac{I_+ - I_-}{I_+ + I_-}.$

The bridge asymmetry is quantified by

$\alpha=\frac{R_2-R_1}{R_2+R_1}.$

If $|I_+|\neq |I_-|$, the device rectifies supercurrent (Greco et al., 2023). In planar asymmetric weak links, the corresponding quantities are $I_C^+$ and $I_C^-$, with

$\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$

while in Nb Dayem nanobridges the switching-current asymmetry is written as

$$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$

These definitions formalize the same physical criterion: the maximum dissipationless current depends on current direction (Antola et al., 16 Jul 2025, Margineda et al., 2023).

The literature also distinguishes between structural and effective asymmetry. In the planar thin-film case, asymmetry is introduced deliberately through a sharp corner or abrupt geometric defect at one side of the bridge–lead interface (Antola et al., 16 Jul 2025). In the dc-SQUID case, asymmetry is realized by pairing two nonidentical weak links in a single interferometer (Greco et al., 2023). In the Nb nanobridge study, the devices are described as “asymmetric” because the effective superconducting response is nonreciprocal under magnetic field, not because they are lithographically left-right asymmetric in the usual geometric sense (Margineda et al., 2023). This distinction is important because the term does not denote a single geometry class.

2. Device architectures and fabrication modalities

One major realization is the all-metal aluminum dc-SQUID built from asymmetric 3D Dayem nanobridges. The interferometer consists of a thick superconducting Al loop and leads, together with two short, thin Al nanobridges. The structure is patterned by single-step electron-beam lithography on a double-layer PMMA/MMA resist, followed by shadow evaporation in UHV at two angles: a tilted evaporation creates the thin nanowires, and a second evaporation at normal incidence creates the thicker loop and leads. The nanobridges are about 10 nm thick, about 60–70 nm long, and about 70 nm wide, while the loop is about 100 nm thick, square, with edge $I_+$0, and total loop area $I_+$1 (Greco et al., 2023).

A second realization uses planar aluminum thin films in an effectively two-dimensional limit. The devices are fabricated in a 14 nm-thick Al film for which $I_+$2, with estimated $I_+$3 nm, $I_+$4 nm, and Pearl length $I_+$5. The principal geometry has bridge width $I_+$6 nm $I_+$7 and length $I_+$8 nm $I_+$9, while a second family uses $I_-$0 nm to probe confinement effects. Asymmetry is introduced at one side of the bridge–lead interface by a right-angled connection or by a sharper $I_-$1 defect (Antola et al., 16 Jul 2025).

The Nb Dayem nanobridge study examines two geometries fabricated by single-step e-beam lithography, sputtered Nb, and lift-off, with a thin Ti adhesion layer. The short bridge has roughly $I_-$2 nm, $I_-$3 nm, and $I_-$4 nm. The long bridge is a quasi-1D nanowire with roughly $I_-$5, $I_-$6 nm, and $I_-$7 nm (Margineda et al., 2023).

An adjacent but distinct architecture is the gated NbRe Dayem bridge. These are top-down dry-etched nanobridges made from sputtered NbRe on $I_-$8, with bridge width 50–80 nm, length 175–220 nm, and a gate electrode 50–300 nm away on only one side of the constriction. The fabrication chemistry varies across devices, including Ar/Cl$I_-$9, Ar only, Ar/SF$\eta=\frac{I_+ - I_-}{I_+ + I_-}.$0, and Al hard mask plus Ar/CF$\eta=\frac{I_+ - I_-}{I_+ + I_-}.$1. The strongest experimental result is that gate-controlled supercurrent appears only for devices etched with Ar/Cl$\eta=\frac{I_+ - I_-}{I_+ + I_-}.$2 (Koch et al., 2023).

Not all Dayem-bridge platforms in the literature are asymmetric in design. Neon-focused-ion-beam-fabricated Nb Dayem bridges terminating a $\eta=\frac{I_+ - I_-}{I_+ + I_-}.$3 coplanar-waveguide resonator are incorporated in a SQUID loop with two bridges of width around 50 nm, but the work does not report a deliberately asymmetric bridge geometry or asymmetry-driven rectification (Potter et al., 2020). Similarly, NbRe Dayem bridges with dimensions such as $\eta=\frac{I_+ - I_-}{I_+ + I_-}.$4–200 nm, $\eta=\frac{I_+ - I_-}{I_+ + I_-}.$5–80 nm, and $\eta=\frac{I_+ - I_-}{I_+ + I_-}.$6–30 nm are studied primarily for high critical temperature, high normal-state resistance, high kinetic inductance, and high critical magnetic field, not for asymmetry (Battisti et al., 2023).

3. Symmetry breaking, current crowding, and nonlinear phase transport

The central theoretical requirement for a Josephson or supercurrent diode effect is simultaneous breaking of spatial inversion symmetry and time-reversal symmetry. In the monolithic dc-SQUID, spatial inversion symmetry is broken by bridge asymmetry, $\eta=\frac{I_+ - I_-}{I_+ + I_-}.$7, while time-reversal symmetry is broken by magnetic flux through the loop. The total current is

$\eta=\frac{I_+ - I_-}{I_+ + I_-}.$8

and the phase drops satisfy

$\eta=\frac{I_+ - I_-}{I_+ + I_-}.$9

In the $\alpha=\frac{R_2-R_1}{R_2+R_1}.$0 limit this simplifies to

$\alpha=\frac{R_2-R_1}{R_2+R_1}.$1

A key result is that large rectification does not require large loop inductance (Greco et al., 2023).

For the 3D Dayem nanobridges, the nonlinearity of the current-phase relation is essential. The bridges are short metallic weak links whose Josephson transport is governed by a strongly nonlinear current-phase relation, and for short diffusive bridges with $\alpha=\frac{R_2-R_1}{R_2+R_1}.$2 the current-phase relation is approximated by the Kulik–Omelyanchuk KO-1 form. With $\alpha=\frac{R_2-R_1}{R_2+R_1}.$3 nm and $\alpha=\frac{R_2-R_1}{R_2+R_1}.$4 nm, the bridges lie in the short/intermediate weak-link regime where KO-1 remains applicable. The paper emphasizes that their current-phase relation contains significant higher-harmonic content, and that this higher-harmonic content alone can generate rectification in the asymmetric SQUID without the need for sizable screening current caused by a finite loop inductance (Greco et al., 2023).

In the planar thin-film bridges, the asymmetry mechanism is different. A perpendicular magnetic field induces screening currents in the superconducting banks, while the transport current crowds at the geometric defect. Depending on bias polarity relative to field direction, the screening current either adds to or subtracts from the transport current at the defect, so the maximum local current density becomes polarity dependent. Because switching is triggered where the current density is largest, the positive and negative critical currents differ. The effect is odd in field, with $\alpha=\frac{R_2-R_1}{R_2+R_1}.$5, and the low-field response is approximately linear because the screening current is approximately linear in $\alpha=\frac{R_2-R_1}{R_2+R_1}.$6 (Antola et al., 16 Jul 2025).

The Nb Dayem nanobridge study argues against a primary explanation based on Meissner currents or self-field effects. The dimensions satisfy $\alpha=\frac{R_2-R_1}{R_2+R_1}.$7, with $\alpha=\frac{R_2-R_1}{R_2+R_1}.$8 nm, so the field penetrates essentially uniformly and magnetic screening is weak or absent. The proposed mechanisms instead rely on a non-sinusoidal current-phase relation plus an inversion-symmetry breaker. Two models are advanced. In Model I, vortex phase winding enters through a spatially varying phase

$\alpha=\frac{R_2-R_1}{R_2+R_1}.$9

with rectification sign reversal arising from competition between vortex winding and vector-potential phase bias. In Model II, the current-phase relation acquires an anomalous phase-shift term,

$|I_+|\neq |I_-|$0

corresponding to a $|I_+|\neq |I_-|$1-junction scenario compatible with anisotropic spin-orbit interactions (Margineda et al., 2023).

A plausible implication is that “asymmetric Dayem bridge” physics spans at least two nonidentical nonreciprocity mechanisms: one dominated by interference between unequal nonlinear weak links in a loop, and another dominated by streamline distortion and local current-density enhancement in an open bridge geometry. The supplied literature treats both as valid diode platforms, but not as the same microscopic system.

4. Experimental phenomenology and parameter regimes

In the monolithic Al dc-SQUID, a perfectly symmetric device with $|I_+|\neq |I_-|$2 shows no diode effect because $|I_+|\neq |I_-|$3 and $|I_+|\neq |I_-|$4 overlap. As $|I_+|\neq |I_-|$5 increases, rectification appears and grows, the flux value at which maximum rectification occurs shifts away from $|I_+|\neq |I_-|$6, and the effect is strongest for intermediate asymmetry. The theoretical calculations show maximum rectification near $|I_+|\neq |I_-|$7, with maximum theoretical $|I_+|\neq |I_-|$8 in the zero-inductance model, while rectification vanishes again for very large asymmetry $|I_+|\neq |I_-|$9. Experimentally, the device achieves a maximum rectification efficiency of about $I_C^+$0, operates from 30 mK to 800 mK, and shows only weak temperature dependence of $I_C^+$1, even though the critical currents decrease with increasing temperature. The temperature dependence follows the KO-1 form well with fitting parameters including $I_C^+$2 K, bridge resistance $I_C^+$3, and asymmetry $I_C^+$4. The real device has a small but finite inductance of about $I_C^+$5 pH, which can slightly enhance rectification and improve agreement with experiment near integer flux values, but is not essential to the effect (Greco et al., 2023).

In the planar asymmetric thin-film bridges, the low-field regime is separated from a vortex-dominated high-field regime by a threshold $I_C^+$6 mT. For $I_C^+$7, the rectification efficiency $I_C^+$8 grows linearly with measured slope

$I_C^+$9

and the maxima of $I_C^-$0 and $I_C^-$1 are shifted to opposite finite fields, roughly $I_C^-$2 mT. For $I_C^-$3, the critical current becomes irregular, develops jumps and dips, and the rectification efficiency can reach about $I_C^-$4, but it oscillates quasi-periodically and changes sign several times. Time-dependent Ginzburg–Landau simulations reproduce the essential phenomenology and yield a linear low-field slope

$I_C^-$5

Sharper defects enhance rectification, with the $I_C^-$6 defect giving

$I_C^-$7

whereas in the narrower $I_C^-$8 nm bridges rectification is strongly suppressed up to

$I_C^-$9

These observations are interpreted in terms of current crowding at low field and vortex entry and rearrangement in the superconducting banks at higher field (Antola et al., 16 Jul 2025).

In the Nb nanobridges, the short bridge measured at 300 mK shows a rectification maximum at

$\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$0

a sign reversal at

$\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$1

and a maximum rectification efficiency of about $\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$2. Temperature dependence is weak up to about $\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$3, after which $\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$4, $\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$5, $\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$6, and the field sensitivity decrease. The field-to-rectification transfer slope

$\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$7

reaches $\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$8 near $\eta=\frac{I_C^+-I_C^-}{I_C^++I_C^-},$9 K. The long bridge measured at 50 mK shows sign reversal at $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$0, maximum rectification around $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$1, and several additional sign changes at higher field, with maximum $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$2 at $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$3 K. The zero-field switching current follows the Bardeen-like form

$$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$4

with approximate fit parameters $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$5, $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$6 for the short bridge and $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$7, $$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$8 for the long bridge (Margineda et al., 2023).

A recurrent conclusion across these experiments is that the field value at which rectification is strongest need not coincide with the field value at which the polarity reverses. This is stated explicitly in the Nb nanobridge work and is consistent with the separate low-field and vortex-dominated regimes reported for planar asymmetric bridges (Margineda et al., 2023, Antola et al., 16 Jul 2025).

5. Gate asymmetry, material dependence, and non-asymmetric comparators

One-sided electrostatic control introduces a different asymmetry class. In dry-etched NbRe Dayem bridges, the gate electrode is placed on only one side of the constriction, producing a natural geometry for asymmetric gate effects in the supercurrent response. The material is non-centrosymmetric NbRe, with strong spin-orbit coupling and possible unconventional superconducting order parameter in bulk single crystals. The paper does not prove a microscopic mechanism from non-centrosymmetry alone, but argues that the lack of inversion symmetry together with strong disorder and spin-orbit coupling may make NbRe more susceptible to gate-induced changes in superconductivity than centrosymmetric Nb or NbN, and explicitly states that ad hoc theory would be needed to quantify the role of these properties (Koch et al., 2023).

The experimental evidence for gate-controlled supercurrent is highly fabrication dependent. Devices D1–D3, etched with Ar/Cl$$\Delta I_{sw}=I_{sw}^+ - |I_{sw}^-|, \qquad \eta=\frac{I_{sw}^+ - |I_{sw}^-|}{I_{sw}^+ + |I_{sw}^-|}.$$9, show gate-controlled supercurrent, whereas devices fabricated with other etch gases show no gate-controlled supercurrent up to 100 V, even when they have smaller gate distance and larger leakage current. For D1, $I_+$00 and gate-controlled supercurrent is observed from 1.9 K to 5.8 K below $I_+$01 K. For D3, $I_+$02 and $I_+$03. The paper concludes that surface modification during etching is crucial, proposing that Cl$I_+$04 reacting with Re may form rhenium chlorides or halides with magnetic properties, possibly assisting gate-controlled surface depairing (Koch et al., 2023).

By contrast, several Dayem-bridge studies in the supplied corpus are explicitly not asymmetry studies. The Nb Dayem-bridge resonator work reports a quarter-wavelength coplanar-waveguide resonator terminated by a SQUID loop containing two Dayem bridges of width around 50 nm. The bridges behave as nonlinear Josephson inductors, yielding flux tunability and intrinsic quality factor exceeding 10,000 at 300 mK up to local fields of at least 60 mT, but the paper does not analyze unequal bridge widths, different critical currents in the two arms, intentional left-right asymmetry, or diode-like response (Potter et al., 2020). Likewise, the high-impedance NbRe bridge study does not mention asymmetric Dayem bridges, left-right asymmetry, asymmetric current-phase relation, rectification, or asymmetry-induced diode effects (Battisti et al., 2023).

A common misconception is therefore that any Dayem-bridge weak link under field is automatically an asymmetric Dayem bridge. The comparative literature does not support that usage. Some platforms are best understood as flux-tunable nonlinear inductors or high-kinetic-inductance nanoconstrictions rather than asymmetry-driven nonreciprocal elements (Potter et al., 2020, Battisti et al., 2023).

6. Applications, scaling, and unresolved issues

The all-Al asymmetric dc-SQUID is presented as a practical Josephson diode because it is monolithic, all-Al, based on conventional fabrication, compatible with Al and Nb superconducting electronics, and potentially extendable to higher-$I_+$05 materials such as V or Pb. Its major scaling advantage is that the diode effect does not rely on large loop inductance, so downsizing is not limited by the geometrical constraints of the superconducting ring. The work identifies it as promising for nonreciprocal superconducting electronics, superconducting logic, and on-chip low-dissipation circuit elements (Greco et al., 2023).

The planar asymmetric weak-link work frames mesoscopic Dayem bridges as a flexible platform for designing and controlling superconducting diode functionalities. The design lessons are explicit: sharper defects enhance rectification, wider bridges are better for crowding-induced supercurrent diode effect, and vortex control in the banks is a major avenue for optimization. A promising design strategy is to engineer the leads so that vortices are deterministically placed or pinned, thereby making the diode response more controllable (Antola et al., 16 Jul 2025).

The Nb Dayem nanobridge work emphasizes ease of fabrication, tunable sign of supercurrent rectification, and large efficiency in a single all-metallic platform. Because the bridges are too small for strong screening and because sign reversal occurs without reversing the field polarity, the work leaves the microscopic origin open between vortex phase winding, anomalous phase shift compatible with anisotropic spin-orbit interactions, and coexistence of both mechanisms (Margineda et al., 2023). This suggests that “asymmetric Dayem bridge” behavior can emerge even when lithographic left-right asymmetry is not the primary design feature, provided the weak-link current-phase relation contains sufficiently strong higher harmonics and the field couples to an internal phase texture.

NbRe broadens the material landscape in a different direction. High-impedance NbRe Dayem bridges show $I_+$06 K for Nb$I_+$07Re$I_+$08 and $I_+$09 K for Nb$I_+$10Re$I_+$11, normal-state resistances up to $I_+$12, switching figures of merit up to $I_+$13 mV, kinetic inductance per square up to $I_+$14 pH, and sizable switching current at $I_+$15 T. The paper argues that these properties are relevant for superinductors, fluxonium qubits, high Q-factor resonators, radiation sensors, superconductive oscillating circuits, high inductance memory elements, superconducting gate-tunable transistors, cryotrons, nanocryotrons, shift registers, memories, superconducting logic, and high-field quantum platforms (Battisti et al., 2023). A plausible implication is that, if asymmetry were deliberately introduced into this NbRe materials platform, both current distribution and field response would become important design degrees of freedom; the paper itself, however, does not test that hypothesis.

Taken together, the literature establishes asymmetric Dayem bridges as a family of all-metallic weak-link devices in which nonreciprocity can be produced by unequal junction parameters, geometric streamline control, one-sided electrostatic perturbation, or field-coupled internal phase structure. The unifying theme is not a single geometry, but the controlled conversion of a Dayem bridge from a symmetric superconducting constriction into a direction-selective element.