Superconducting Diode Effect (SDE) Overview

• The superconducting diode effect is defined as a phenomenon where a superconductor conducts without resistance in one direction while exhibiting resistance in the opposite direction due to broken symmetry.
• Key mechanisms include finite-momentum Cooper pairing, asymmetric vortex dynamics, and anomalous current–phase relations, which lead to measurable differences in critical currents and rectification efficiencies.
• Applications span low-power cryoelectronics, superconducting memory, and quantum computation, with performance tunable via magnetic fields, strain, and engineered device geometries.

The superconducting diode effect (SDE) is the phenomenon whereby a superconductor supports dissipationless electrical transport (zero resistance) for current in one direction but not in the opposite direction, thus mimicking the unidirectional response of a conventional diode yet retaining superconductivity’s defining absence of resistance. This effect, of central interest in low-dissipation electronics, is intimately tied to symmetry breaking—specifically, the breaking of inversion and/or time-reversal symmetry—and is realized via a variety of microscopic and device-scale mechanisms. The SDE has attracted significant attention due to its implications for electronics, quantum computation, and the fundamental physics of unconventional superconducting states.

1. Fundamental Symmetry Principles and Physical Mechanisms

The SDE fundamentally requires the breaking of spatial inversion symmetry; time-reversal symmetry breaking is also present in most realizations but, under certain conditions, can be circumvented via strain-induced polarization or extrinsic device effects.

Theoretical mechanisms giving rise to SDE include:

• Finite-momentum Cooper pairing: In noncentrosymmetric superconductors with Rashba-type spin-orbit coupling and either Zeeman splitting or internal magnetization, the superconducting order parameter acquires a finite center-of-mass momentum $q$. The GL free energy density expansion,

$$f(\Delta, q) = \alpha(q)\Delta^2 + \frac{\beta(q)}{2}\Delta^4,$$

with odd powers in $q$ induced by symmetry breaking, yields $j(q) \neq -j(-q)$. Consequently, critical currents differ in opposite directions (Daido et al., 2021).

• Asymmetric vortex dynamics: In type-II superconductors with engineered pinning landscapes that lack inversion symmetry (e.g., conformal nanohole arrays), vortices experience direction-dependent entry barriers and pinning forces, yielding nonreciprocal dissipation at the vortex-flow transition (Lyu et al., 2021).
• Anomalous current–phase relations in Josephson junctions: Rashba SOC and Zeeman coupling in Josephson devices introduce $\varphi_0$-shifts and additional harmonics (e.g., $\sin 2\varphi$) in the CPR. Asymmetric CPR directly enables different positive and negative critical currents (Ma et al., 17 Feb 2025).
• Field-free SDE via extrinsic effects: Device geometry (e.g., asymmetric contacts) and strong thermoelectric response can mimic inversion symmetry breaking, resulting in field-free SDE without intrinsic material asymmetry (Nagata et al., 3 Sep 2024).

The SDE is thus broadly classifiable as intrinsic (arising from bulk or interface electronic structure) or extrinsic (originating from sample geometry or non-equilibrium effects).

2. Material Platforms and Symmetry Engineering

SDE has been realized and/or predicted in a variety of superconducting systems, with key features summarized below:

Platform	Symmetry-Breaking Mechanism	Notable Features
Noncentrosymmetric multilayers Nb/V/Co/V/Ta	Artificial stacking, magnetic exchange field	Field-free, tunable via magnetization, non-volatile polarity
Rashba/Ising 2D superconductors (Bankier et al., 19 Mar 2025)	SOC (Rashba, Ising), in-plane field	Strong SDE efficiency when Ising SOC dominates
Patterned films (conformal nanoholes) (Lyu et al., 2021)	Nanoengineered pinning, broken inversion	Giant millivolt-scale rectification, tuneable morphology
Strained van der Waals/trigonal SCs [PbTaSe₂, FTS]	Strain-induced electric polarization	Field-free or B-even SDE, amplified by local stress (Liu et al., 12 Jun 2024, Dong et al., 1 Oct 2025)
FeSe (asymmetric geometry) (Nagata et al., 3 Sep 2024)	Geometrical asymmetry + thermoelectricity	Field-free, geometry-dependent SDE
Quantum spin Hall JJ (Scharf et al., 12 Jun 2024)	Out-of-plane field, edge asymmetry	SDE linked to helical edge modes, universal Q-factor
2D Shiba lattices (Bhowmik et al., 14 Aug 2025)	Conical spin texture (atomic design)	Field-free SDE, directionally tunable efficiency
Double quantum dot + 3 SC leads (Takeuchi et al., 28 Dec 2024)	Phase-controlled molecular Andreev spectrum	Dirac cones in phase space, $>30\%$ SDE efficiency

Control of SDE often hinges on precise manipulation of physical or device symmetries (e.g., stacking order, pinning potential, magnetic anisotropy, lattice strain, edge transport properties), as well as tuning by external fields, gating, or electrostatic doping.

3. Experimental Signatures, Measurement Methodologies, and Quantitative Metrics

Experimental observation of SDE involves clear markers:

• Asymmetric critical currents: A difference $\Delta I_c = I_{c+} - I_{c-}$ observed through DC I–V measurements. SDE efficiency is often quantified as

$$\eta = \frac{I_{c+} - |I_{c-}|}{I_{c+} + |I_{c-}|} \in [0,1].$$

Millivolt-scale rectification reported in conformal-nanohole MoGe (Lyu et al., 2021); 30% efficiency in double quantum dot models (Takeuchi et al., 28 Dec 2024); $>$40% in 2D Shiba lattices (Bhowmik et al., 14 Aug 2025); $>$50% in Pt/Co/Nb heterostructures (Li et al., 21 Jun 2025).

• Second-harmonic detection: In the TAFF or fluctuation regime, $R_{2\omega}$ or $V_{2\omega}$ measurements reveal nonlinear, symmetry-breaking components in voltage response near the superconducting transition or at the SDE onset (Dong et al., 1 Oct 2025, Liu et al., 12 Jun 2024).
• Magnetic field dependence: SDE polarity and amplitude can be tuned or even reversed by applied magnetic field, as in [Nb/V/Co/V/Ta] multilayers (Narita et al., 2022) or in the sign-reversal phenomena reported in Rashba–Zeeman models (Daido et al., 2021) or with controlled disorder (Ikeda et al., 2022).
• Device and geometry dependence: SDE vanishes in symmetric device geometries or with negligible thermoelectric response (FeSe vs. NbN); strain and local stress are critical for enhancing the effect in FTS and PbTaSe₂ (Liu et al., 12 Jun 2024, Dong et al., 1 Oct 2025).
• Shapiro steps and AC bias: Asymmetry in the size or position of Shapiro steps under microwave drive provides a direct probe of SDE in Josephson circuits, including in non-Hermitian systems (Qi et al., 7 Aug 2025).

Controlled disorder, sample thickness, and exposure to strain or local geometric modification strongly modulate the SDE and have been leveraged both for probing underlying mechanisms and for enhancing device functionality.

4. Theoretical Models and Formulae

Several theoretical frameworks have been used to analyze and predict the SDE:

• Ginzburg–Landau and TDGL theory: Expansion of the free energy in terms of order parameter gradients (and including odd powers as induced by broken symmetries); e.g.,

$$\frac{\partial \psi}{\partial t} = (\nabla - iA)^2 \psi + \alpha(1-T)\psi - |\psi|^2\psi + \chi(r,t)$$

and associated heat transfer equations to incorporate Joule heating and flux-flow transitions (Lyu et al., 2021).

• Microscopic BdG and mean-field treatments: For Rashba–Zeeman systems, intrinsic SDE is linked to helical superconductivity and finite-momentum pairing, with critical currents defined as extrema of $j_s(q)$; sign reversals are predicted upon tuning $h_v$ (valley splitting field) or magnetic field (Daido et al., 2021, Zhuang et al., 1 Jan 2025).
• Heterostructure modeling (S/F/TI, nanowires, Shiba lattices): Incorporating spin–orbit, exchange, geometric, or topological features; use of quasiclassical Green’s functions and self-consistent BdG simulations to extract critical currents and diode coefficients (Karabassov et al., 2023, Bhowmik et al., 14 Aug 2025).
• Device-level models (double quantum dots, non-Hermitian SQUIDs): Andreev bound state engineering, Dirac cone spectra in phase space, and non-Hermitian Fermi–Dirac distributions for decoherence-influenced transport (Takeuchi et al., 28 Dec 2024, Qi et al., 7 Aug 2025).

Disorder generally suppresses absolute critical current but can enhance the diode quality factor by reducing the denominator of $\eta$ more rapidly than the numerator (Ikeda et al., 2022).

5. Technological Implications, Integration, and Application Landscape

SDE platforms are suited for ultralow-power logic, superconducting memory, nonvolatile switching, and quantum information architectures. Key properties enabling integration include:

• Field-free operation: Achievable via intrinsic material asymmetry, strain, or device engineering; simplifies design for scalable circuits (Narita et al., 2022, Li et al., 21 Jun 2025, Dong et al., 1 Oct 2025).
• Non-volatility and tunability: Polarity switching via magnetization (e.g., in multilayers), or via strain and gating in device-scale platforms (Narita et al., 2022, Liu et al., 12 Jun 2024).
• High rectification efficiency: Record values $\sim$50% for field-free designs, with potential for 100% in valley-polarized ferromagnetic superconductors as predicted theoretically (Zhuang et al., 1 Jan 2025).
• Robustness and scalability: Compatibility with microfabrication (e.g., Pt/Co/Nb, NbTiN/MgO heterostructures) and potential for CMOS integration (Li et al., 21 Jun 2025, Yang et al., 31 Aug 2025).

Potential challenges persist in separating intrinsic SDE from extrinsic rectification effects and engineering robust, high-Tc, or device-optimized material systems for operation above cryogenic temperatures.

6. Emerging Directions and Outstanding Questions

Open topics in SDE research include:

• Unified description of SDE regimes: Integration of intrinsic and extrinsic mechanisms, and development of predictive multi-scale theory encompassing disorder, vortex physics, and device-level nonequilibrium (Nadeem et al., 2023, Ma et al., 17 Feb 2025).
• Role of strong correlations and topology: SDE serves as a probe for symmetry-breaking superconducting states (FFLO, chiral, helical, topological), including possible interface phenomena and mixed-parity/multiphase order (Shaffer et al., 20 Jun 2024, Mao et al., 2023).
• Programmable and parity-protected SDE: Use of ground-state parity (4$\pi$ periodicity), Dirac cone engineering (double quantum dot), and control over topological edge states expand device possibilities (Scharf et al., 12 Jun 2024, Takeuchi et al., 28 Dec 2024).
• Non-Hermitian superconductivity: Coupling to reservoirs and decoherence leads to new forms of SDE, measurable by asymmetric Shapiro response (Qi et al., 7 Aug 2025).
• Straintronics and flexoelectric control: Strain engineering via substrate selection or mechanical design offers an alternative route to SDE, broadening the accessible material palette (Liu et al., 12 Jun 2024, Yang et al., 31 Aug 2025).
• Application-tailored SDE optimization: Material optimization (e.g., high-Tc, large SOC, robust pinning) and integration for cryogenic logic, quantum interconnects, and superconducting spintronics remain under active development.

Further comparative and systematic studies, especially in devices with clean isolation of symmetry-breaking mechanisms, are anticipated to clarify universal versus system-specific aspects of the SDE and accelerate its adoption in practical cryoelectronic devices.