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REVIEW 4 major objections 4 minor 1 cited by

Thermodynamics forbids a perfect equilibrium superconducting diode unless the superconductor sits at an internal phase transition.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-03 14:10 UTC pith:MALLZGZO

load-bearing objection A clean thermodynamic no-go for exact perfect equilibrium diodes, plus a plausible but incompletely proven claim that epsilon→0 requires an internal transition; worth a serious referee after fixing the proof gap and the inconsistent appendix bound. the 4 major comments →

arxiv 2512.21384 v3 pith:MALLZGZO submitted 2025-12-24 cond-mat.supr-con cond-mat.mes-hallcond-mat.str-el

Thermodynamic Constraints on Perfect Equilibrium Superconducting Diodes

Pavan Hosur This is my paper
classification cond-mat.supr-con cond-mat.mes-hallcond-mat.str-el PACS 74.25.Sv74.20.-z74.25.-q
keywords superconducting diode effectdiode efficiencycritical current asymmetrythermodynamic constraintsLandau theoryRemez inequalityinternal phase transitionIsing superconductor
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper derives thermodynamic constraints on how asymmetric a bulk equilibrium superconducting diode can be. The author models the superconductor by a momentum-dependent condensation energy F(q), with supercurrent j(q)=2e∂_qF(q), and shows that a perfect diode (epsilon = 0) is impossible because it would force a discontinuity in the free energy, which an ordinary solid cannot have. Approaching perfect rectification (epsilon→0) is allowed only at the price of a non-analyticity inside the superconducting window, meaning a phase transition between competing superconducting phases. For smooth Landau-type systems far from such criticality, the paper proves a lower bound on epsilon in terms of the polynomial order and the shape of the current profile, explaining the universally modest efficiencies of intrinsic diodes. If correct, a small diode ratio in a clean bulk superconductor becomes a diagnostic of nearby internal structure, and engineered criticality becomes the only intrinsic route to a near-perfect diode.

Core claim

The paper's central claim: the q-dependent condensation free energy F(q) sets the thermodynamic ceiling on diode performance. Since j(q)=2e∂_qF(q), a perfect diode (j≥0 everywhere) would integrate to F(q_c^+)-F(q_c^-)>0, contradicting the continuous endpoints F=0; thus epsilon=0 requires a free-energy discontinuity. Approaching epsilon→0 without a discontinuity forces j(q) to vanish on finite intervals, impossible for analytic j(q) by the identity theorem, so F(q) must be non-analytic inside the superconducting window — an internal phase transition. For finite-order polynomial Landau free energies, the Remez inequality gives epsilon ≥ 1/T_n(1+2θ), so epsilon→0 requires unbounded polynomial o

What carries the argument

The central object is the q-dependent condensation free energy density F(q) of a single bulk superconducting phase, along with the supercurrent j(q)=2e∂_qF(q) it generates. The argument's load-bearing pieces are: (1) continuity of F(q) at the superconducting window's endpoints, where F=0; (2) the identity theorem for analytic functions, which forbids j(q) from vanishing on a finite interval unless it is identically zero; and (3) the Remez–Chebyshev inequality, which bounds the growth of a degree-n polynomial on a long interval given a bound on a subinterval, yielding the diode bound. The exactly solvable Ising-coupled superconductor supplies a concrete F(q) with a cusp at the switch between

Load-bearing premise

The argument rests on a single-mode description in which the diode response of a bulk equilibrium superconductor is fully captured by a momentum-dependent condensation energy F(q) and its critical currents are the extrema of j(q)=2e∂_qF(q) over one bounded superconducting window; if edge depairing, disorder, mesoscopic phase constraints, or an unbounded window actually set the critical currents, the bounds do not apply.

What would settle it

Measure epsilon in a clean, uniform, single-phase bulk superconductor with no junctions and no drive while independently verifying F(q) is analytic (e.g., no specific-heat anomaly inside the superconducting window). Observing epsilon = 0 or epsilon below 1/T_n(1+2θ) for the independently measured polynomial order n and positive-current fraction θ would falsify the claimed bound. Alternatively, tuning through a suspected continuous internal transition and finding that epsilon does not vanish as r→r_c would falsify the critical-scaling claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Bulk equilibrium superconductors without an internal transition cannot be perfect diodes: the diode ratio epsilon is bounded away from zero by the polynomial-order and current-shape bound, making modest observed efficiencies the generic expectation.
  • A small epsilon in a nominally intrinsic device is itself diagnostic: it implies either an extrinsic cause (geometry, inhomogeneity, junction/proximity physics) or proximity to an internal transition between competing superconducting phases.
  • The route to a near-perfect equilibrium diode is to engineer competing superconducting states with distinct Cooper-pair momenta; the number of competing branches must grow logarithmically with 1/epsilon.
  • Near a continuous internal transition, epsilon vanishes as |r-r_c|^x, and the exponent x is not an independent quantity but is determined by the conventional critical exponents of the softest branch — a testable universal scaling.
  • Josephson and proximity systems that report high efficiencies are not counterexamples; they operate under phase constraints, metastable switching, or external drive, and the equilibrium thermodynamic bounds do not apply to them.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same analytic-continuation logic likely applies to any equilibrium rectification governed by a scalar potential (e.g., thermal or spin diodes): perfect one-way transport would require a broken free-energy surface, so near-perfect rectification may always sit next to an internal instability.
  • The Remez bound suggests a measurable diagnostic for junction devices: in a Josephson junction, epsilon should be bounded by the harmonic content of the current-phase relation, so a junction reporting a very low epsilon must either have many harmonics or be operating outside the single-mode equilibrium description — a useful test for reported Josephson diodes.
  • If low epsilon is a softness diagnostic, then intrinsic materials with known soft modes (nematic fluctuations, low-frequency phonons, nearly competing orders) should show systematically lower epsilon than rigid superconductors; a survey of published diode efficiencies could test this without new experiments.
  • One experimental strategy follows directly: tune a clean superconductor through an internal transition with magnetic field or strain, and monitor epsilon; the predicted power-law collapse to zero, with an exponent matching known critical exponents, would confirm the mechanism, while saturation would bound its validity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The manuscript argues that, for a bulk equilibrium superconductor whose diode response is captured by a Cooper-pair-momentum-dependent condensation energy F(q), the diode asymmetry ε = |I_c^-/I_c^+| obeys universal thermodynamic constraints. It proves that exact ε = 0 is impossible for continuous F, claims that ε → 0 requires a non-analyticity of F inside the superconducting window (an internal phase transition), and derives a Remez/Chebyshev lower bound on ε for finite-order polynomial Landau theories. An exactly solvable Ising-coupled superconductor model is presented as an explicit realization, together with a critical-scaling exponent x.

Significance. The ε = 0 impossibility argument is compact and, under the stated definitions, correct; it provides a clean conceptual reason why a finite critical current in one direction forces some negative supercurrent in the other if F is continuous. The Ising toy model is a useful explicit construction, and the paper's classification of intrinsic versus Josephson/proximity/non-equilibrium routes is helpful. However, the central asymptotic claim — that ε → 0 necessarily requires an internal phase transition — is false as stated. A simple one-parameter family of analytic polynomial free energies with a fixed, bounded superconducting window achieves ε → 0 with no internal non-analyticity. The Remez bound for fixed polynomial degree may be correct after repairing the derivation, but it does not support the advertised conclusion.

major comments (4)
  1. [Constraints on ε, after Eq. (4)] The central claim that ε → 0 requires non-analyticity is refuted by an explicit family within the paper's own framework. For odd k, define F_k(q) = q^{k+1} - q on q ∈ [0,1], with F_k(q) > 0 outside this interval. For q ∈ (0,1), F_k(q) < 0 and F_k(0) = F_k(1) = 0. The supercurrent is j_k(q) = (k+1)q^k - 1, so j_c^- = 1 and j_c^+ = k, giving ε = 1/k → 0 as k → ∞. Each F_k is a polynomial, hence analytic, and has a single minimum; there is no internal phase transition. The proof's inference that 'the negative segments of j_λ(q) vanish in the limit' is false: the negative segment has depth O(1), and ε → 0 occurs because the positive critical current diverges. Without an unstated bound on j_c^+, the conclusion does not follow.
  2. [Constraints on ε, identity-theorem paragraph] The identity-theorem argument is not a rigorous proof: it assumes a fixed, bounded superconducting window and convergence in a function space, neither of which is specified. The paper's own Ising model, Eqs. (9)-(11), has ε → 0 with γ_±, K_- → 0, which sends q_c^- → -∞; the interval is not fixed, and the text never flags this degeneracy. A complete proof must control endpoint motion and specify the sense in which F_λ tends to F_{λ0}. The current manuscript leaves this load-bearing step at the level of a sketch.
  3. [Appendix A, Eq. (A10)] The appendix's bound 1/T_n(1+2θ) is inconsistent with Eq. (5) of the main text, 1/T_n((1+θ)/(1-θ)). Under the affine map (A5) that sends a negative-current interval to length 2, the full momentum window maps to [−1, (1+θ)/(1-θ)], so (1+2θ) appears to be a typo. Moreover, the derivation assumes I_- can be mapped to a single interval E of length 2, while the text explicitly states that these intervals need not be contiguous. For a polynomial of degree n the negative set can have several components; the bound must account for the length of the largest usable component. As written, the quantitative bound is not derived from the stated assumptions.
  4. [Critical scaling, Eq. (14)] In the Ising model, Eq. (11) shows that j_c^- = max(γ_-, sqrt(γ_-^2 + 2K_- F_0)) has no dependence on γ_+, and j_c^+ remains finite if K_+ is not tuned. Therefore, under the scaling in Eq. (13), the exponent should be x = min(a_-, b/2), not min(a_+, a_-, b/2). The extension of this Ising scaling form to generic continuous internal transitions is asserted without derivation, so the claim that x is locked to conventional critical exponents is not supported.
minor comments (4)
  1. [Eq. (4)] There is a convention/dimension mismatch: with j = 2e ∂_q F, the integral should read (1/2e) ∫ j dq, not (1/2e) ∫ dq/(2π) j(q). The factor 2π does not affect the argument, but it should be corrected.
  2. [Abstract versus body] The abstract states that Josephson systems obey analogous bounds set by finite harmonic content of the current-phase relation, but the body states that Josephson devices evade the bounds because they are far from the thermodynamic limit. No derivation of a Josephson bound is given in the text or appendices.
  3. [Fig. 1, left panel] The label 'perfect diode without fine-tuning' is misleading: the proof shows exact ε = 0 is impossible for any continuous F, not merely 'without fine-tuning.'
  4. [Eq. (6) and Appendix A] The definition of θ as 'range of q over which j(q)>0' is ambiguous if the positive-current set has multiple components; it should be the total length. The appendix's statement that intervals need not be contiguous makes this ambiguity relevant to the Remez argument.

Circularity Check

0 steps flagged

No significant circularity: the thermodynamic bounds are derived from explicit assumptions (continuity, analyticity, polynomial Landau form) and the Ising model is solved directly; the sole author self-citation is a non-load-bearing classification example.

full rationale

The paper's derivation chain is self-contained rather than circular. The exact-epsilon=0 prohibition follows from the integral identity F(q_c^+)-F(q_c^-)=∫j dq/(2e), which is a direct mathematical consequence of j=2e∂_q F together with the assumed boundary condition F(q_c^±)=0; it is not a fitted parameter renamed as a prediction. The epsilon→0-nonanalyticity argument is a proof by contradiction using the identity theorem for analytic functions inside the superconducting window; although a rigorous gap exists concerning domain expansion and vanishing measure of the negative-current segments (e.g., in the paper's own Ising model q_c^-→−∞ as epsilon→0), that is a correctness/rigor concern, not a reduction of the conclusion to its assumptions. The quantitative Landau bound is explicitly derived in Appendix A from the stated polynomial assumption via the Remez inequality, and the discrepancy between main-text Eq. (5) and Appendix Eq. (A10) is an algebraic inconsistency rather than a circular step. No experimental data are fitted, no parameter is tuned to reproduce the claimed scaling, and the Ising model is exactly solved to illustrate the mechanism. The only self-citation, Ref. [28], is cited merely as an example of a proximity-based route that evades the bounds; it does not support the core thermodynamic argument. Thus the central results have independent content and are not equivalent to their inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 1 invented entities

The central claim rests on (1) the single-mode F(q) description with extrema-of-current critical currents, (2) boundedness and continuity of the superconducting window, (3) the finite-degree polynomial model class for the quantitative bound, and (4) standard analytic-function and polynomial inequalities. The toy-model parameters are illustrative, not fitted. No new physical entities are posited.

free parameters (2)
  • Landau truncation order n = unspecified (free integer)
    The bound ε ≥ 1/T_n((1+θ)/(1−θ)) depends on the polynomial degree n of j(q); n is not fixed by physics and the paper treats n→∞ as the only route to ε→0 (Eqs. (5)-(7)). Not fitted to data, but the strength of the claimed constraint hinges on it.
  • Ising toy-model parameters (K₊, K₋, γ₊, γ₋, F₀) = Fig. 2: F₀=1, K₊=1, K₋=3×10⁻³, γ₊=γ₋=0.01 (near-perfect regime); K₋=0.7, γ₊=0.8, γ₋=0.35 (generic regime)
    Hand-chosen toy-model values that realize ε≈3×10⁻³. Illustrative only, not fitted to experiment, and not load-bearing for the general thermodynamic claims.
axioms (6)
  • domain assumption F(q) is continuous and vanishes at both edges of a single bounded superconducting window (q_c⁻, q_c⁺).
    Enters the ε=0 impossibility proof and the Remez bound; §'Constraints on ε'. Violated in the model's own ε→0 limit, where q_c⁻→−∞.
  • domain assumption Critical currents are the extrema of j(q)=2e∂_qF(q).
    Eqs. (2)-(3); assumes a single-mode q-space description with no edge, vortex, disorder, or mesoscopic effects setting the critical current.
  • domain assumption Zeroth-order (discontinuous) phase transitions cannot occur in local extensive solids.
    Used to exclude the only escape from the ε=0 contradiction; §'Constraints on ε'.
  • standard math Identity theorem: an analytic j(q) that vanishes on a finite segment vanishes identically.
    Core of the claim that ε→0 forces non-analyticity of F(q); §'Constraints on ε'.
  • standard math Remez inequality and the Chebyshev extremal-growth property for polynomials.
    Basis of the quantitative lower bound; Appendix A.
  • ad hoc to paper F(q) can be modeled as a finite-degree polynomial over the entire superconducting window (q_c⁻, q_c⁺).
    Load-bearing modeling step for the Remez bound. A Taylor expansion truncated at order n need not converge over the full window, and n is unspecified; the bound is conditional on this model class.
invented entities (1)
  • Internal Ising variable σ in the toy model no independent evidence
    purpose: Produces the cusp in F(q) that realizes ε→0 in an exactly solvable model (Eqs. (8)-(9)).
    Explicitly a toy-model device; not claimed to exist in any real material, and no mapping to a concrete microscopic degree of freedom is given.

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read the original abstract

Superconducting diodes promise dissipationless rectification, yet equilibrium platforms without engineered junctions typically exhibit modest efficiencies. We identify a general thermodynamic origin of this behavior that is largely independent of microscopic details. Denoting $\epsilon = |I_c^-/I_c^+|$, where $I_c^\pm$ are critical currents in opposite directions with $|I_c^+|>|I_c^-|$ by convention, we show that an exact perfect equilibrium diode ($\epsilon=0$) is forbidden by continuity of the free energy. Asymptotically perfect behavior $\epsilon\to0$ is possible within a global equilibrium description, but requires free-energy singularities to enable softening of the unfavorable current-carrying branch. We demonstrate this explicitly in an exactly solvable Ising superconductor model. For smooth single-branch superconductors, standard finite-order polynomial Landau theory yields finite lower bounds on $\epsilon$, while Josephson systems obey analogous bounds set by finite harmonic content of the current-phase relation. The high efficiencies often reported in Josephson platforms arise because such devices commonly operate under phase constraints, metastable switching, or external drive, thereby evading unconstrained equilibrium limits. Thus, our results provide a unified framework for interpreting diode efficiencies across superconducting platforms.

Figures

Figures reproduced from arXiv: 2512.21384 by Pavan Hosur.

Figure 1
Figure 1. Figure 1: (left). Such zeroth order phase transitions have in￾deed been found or proposed in some systems that violate conventional thermodynamics via nonlocal interactions [11], absence of ergodicity [12], or involvement of gravity [13–24]. In intrinsic superconductors that respect local￾ity and have extensive energy and entropy, F(q) must be continuous, so such phase transitions and hence ϵ = 0 are impossible. Nex… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum Landscape of Superconducting Diodes

    cond-mat.supr-con 2026-04 unverdicted novelty 3.0

    Superconducting diodes can provide built-in nonlinearity, nonreciprocity, and quantum features to support scalable, integrated superconducting quantum circuits with improved thermal compatibility.

Reference graph

Works this paper leans on

48 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [1]

    J. Ma, R. Zhan, and X. Lin, Superconducting diode effects: Mechanisms, materials and applica- tions, Advanced Physics Research4, 2400180 (2025), https://advanced.onlinelibrary.wiley.com/doi/pdf/10.1002/apxr.202400180

    doi:10.1002/apxr.202400180 2025

  2. [2]

    Nadeem, M

    M. Nadeem, M. S. Fuhrer, and X. Wang, The super- conducting diode effect, Nature Reviews Physics5, 558 (2023)

    2023

  3. [3]

    Bauriedl, C

    L. Bauriedl, C. B¨ auml, L. Fuchs, C. Baumgartner, N. Paulik, J. M. Bauer, K.-Q. Lin, J. M. Lupton, T. Taniguchi, K. Watanabe, C. Strunk, and N. Paradiso, Supercurrent diode effect and magnetochiral anisotropy in few-layer nbse2, Nature Communications13, 4266 (2022)

    2022

  4. [4]

    B. Pal, A. Chakraborty, P. K. Sivakumar, M. Davydova, A. K. Gopi, A. K. Pandeya, J. A. Krieger, Y. Zhang, M. Date, S. Ju, N. Yuan, N. B. M. Schr¨ oter, L. Fu, and S. S. P. Parkin, Josephson diode effect from cooper pair momentum in a topological semimetal, Nature Physics 10.1038/s41567-022-01699-5 (2022)

    work page doi:10.1038/s41567-022-01699-5 2022

  5. [5]

    Tanaka, B

    Y. Tanaka, B. Lu, and N. Nagaosa, Theory of giant diode effect ind-wave superconductor junctions on the sur- face of a topological insulator, Phys. Rev. B106, 214524 (2022)

    2022

  6. [6]

    J.-X. Lin, P. Siriviboon, H. D. Scammell, S. Liu, D. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, M. S. Scheurer, and J. I. A. Li, Zero-field superconducting diode effect in small-twist-angle trilayer graphene, Na- ture Physics18, 1221 (2022)

    2022

  7. [7]

    Y. Hou, F. Nichele, H. Chi, A. Lodesani, Y. Wu, M. F. Ritter, D. Z. Haxell, M. Davydova, S. Ili´ c, O. Glezakou- Elbert, A. Varambally, F. S. Bergeret, A. Kamra, L. Fu, P. A. Lee, and J. S. Moodera, Ubiquitous superconduct- ing diode effect in superconductor thin films, Phys. Rev. Lett.131, 027001 (2023)

    2023

  8. [8]

    Castellani, O

    M. Castellani, O. Medeiros, A. Buzzi, R. A. Foster, M. Colangelo, and K. K. Berggren, A superconduct- ing full-wave bridge rectifier (2025), arXiv:2406.12175 [physics.app-ph]

    Pith/arXiv arXiv 2025

  9. [9]

    Ingla-Ayn´ es, Y

    J. Ingla-Ayn´ es, Y. Hou, S. Wang, E.-D. Chu, O. A. Mukhanov, P. Wei, and J. S. Moodera, Highly Effi- cient Superconducting Diodes and Rectifiers for Quan- tum Circuitry, arXiv e-prints , arXiv:2406.12012 (2024), arXiv:2406.12012 [cond-mat.supr-con]

    Pith/arXiv arXiv 2024

  10. [10]

    Chiles, E

    J. Chiles, E. G. Arnault, C.-C. Chen, T. F. Q. Lar- son, L. Zhao, K. Watanabe, T. Taniguchi, F. Amet, and G. Finkelstein, Nonreciprocal supercurrents in a field-free graphene josephson triode, Nano Letters23, 5257 (2023)

    2023

  11. [11]

    V. P. Maslov, Zeroth-order phase transitions, Mathemat- ical Notes76, 697 (2004)

    2004

  12. [12]

    Hou, Zeroth order phase transition induced by er- godicity breaking in a mean-field system, The European Physical Journal B94, 6 (2021)

    J.-X. Hou, Zeroth order phase transition induced by er- godicity breaking in a mean-field system, The European Physical Journal B94, 6 (2021)

    2021

  13. [13]

    Altamirano, D

    N. Altamirano, D. Kubizˇ n´ ak, R. B. Mann, and Z. Sherkatghanad, Kerr-ads analogue of triple point and solid/liquid/gas phase transition, Classical and Quantum Gravity31, 042001 (2014)

    2014

  14. [14]

    Altamirano, D

    N. Altamirano, D. Kubizˇ n´ ak, and R. B. Mann, Reentrant phase transitions in rotating anti–de sitter black holes, Phys. Rev. D88, 101502 (2013)

    2013

  15. [15]

    Altamirano, D

    N. Altamirano, D. Kubizˇ n´ ak, R. B. Mann, and Z. Sherkatghanad, Thermodynamics of rotating black holes and black rings: Phase transitions and thermody- namic volume, Galaxies2, 89 (2014)

    2014

  16. [16]

    S.-W. Wei, P. Cheng, and Y.-X. Liu, Analytical and exact critical phenomena ofd-dimensional singly spinning kerr- ads black holes, Phys. Rev. D93, 084015 (2016)

    2016

  17. [17]

    A. M. Frassino, D. Kubizˇ n´ ak, R. B. Mann, and F. Simovic, Multiple reentrant phase transitions and triple points in lovelock thermodynamics, Journal of High Energy Physics2014, 80 (2014). 6

    2014

  18. [18]

    D.-C. Zou, Y. Liu, and B. Wang, Critical behavior of charged gauss-bonnet-ads black holes in the grand canon- ical ensemble, Phys. Rev. D90, 044063 (2014)

    2014

  19. [19]

    M. B. Jahani Poshteh, B. Mirza, and Z. Sherkatghanad, Phase transition, critical behavior, and critical exponents of myers-perry black holes, Phys. Rev. D88, 024005 (2013)

    2013

  20. [20]

    R. A. Hennigar and R. B. Mann, Reentrant phase transi- tions and van der waals behaviour for hairy black holes, Entropy17, 8056 (2015)

    2015

  21. [21]

    Gunasekaran, D

    S. Gunasekaran, D. Kubizˇ n´ ak, and R. B. Mann, Ex- tended phase space thermodynamics for charged and ro- tating black holes and born-infeld vacuum polarization, Journal of High Energy Physics2012, 110 (2012)

    2012

  22. [22]

    Kubizˇ n´ ak and F

    D. Kubizˇ n´ ak and F. Simovic, Thermodynamics of hori- zons: de sitter black holes and reentrant phase transi- tions, Classical and Quantum Gravity33, 245001 (2016)

    2016

  23. [23]

    Dehyadegari, A

    A. Dehyadegari, A. Sheykhi, and A. Montakhab, Novel phase transition in charged dilaton black holes, Phys. Rev. D96, 084012 (2017)

    2017

  24. [24]

    Dehyadegari and A

    A. Dehyadegari and A. Sheykhi, Reentrant phase tran- sition of born-infeld-ads black holes, Phys. Rev. D98, 024011 (2018)

    2018

  25. [25]

    Shaffer, D

    D. Shaffer, D. V. Chichinadze, and A. Levchenko, Super- conducting diode effect in multiphase superconductors, Phys. Rev. B110, 184509 (2024)

    2024

  26. [26]

    Chakraborty and A

    D. Chakraborty and A. M. Black-Schaffer, Perfect super- conducting diode effect in altermagnets, Phys. Rev. Lett. 135, 026001 (2025)

    2025

  27. [27]

    N. F. Q. Yuan and L. Fu, Supercurrent diode effect and finite-momentum superconductors, Proceedings of the National Academy of Sciences119, e2119548119 (2022), https://www.pnas.org/doi/pdf/10.1073/pnas.2119548119

    doi:10.1073/pnas.2119548119 2022

  28. [28]

    Hosur and D

    P. Hosur and D. Palacios, Proximity-induced equilib- rium supercurrent and perfect superconducting diode ef- fect due to band asymmetry, Phys. Rev. B108, 094513 (2023)

    2023

  29. [29]

    L. D. Anh, K. Ishihara, T. Hotta, K. Inagaki, H. Maki, T. Saeki, M. Kobayashi, and M. Tanaka, Large supercon- ducting diode effect in ion-beam patterned sn-based su- perconductor nanowire/topological dirac semimetal pla- nar heterostructures, Nature Communications15, 8014 (2024)

    2024

  30. [30]

    Davydova, S

    M. Davydova, S. Prembabu, and L. Fu, Universal joseph- son diode effect, Science Advances8, eabo0309 (2022), https://www.science.org/doi/pdf/10.1126/sciadv.abo0309

    doi:10.1126/sciadv.abo0309 2022

  31. [31]

    R. S. Souto, M. Leijnse, and C. Schrade, Josephson diode effect in supercurrent interferometers, Phys. Rev. Lett. 129, 267702 (2022)

    2022

  32. [32]

    Turini, S

    B. Turini, S. Salimian, M. Carrega, A. Iorio, E. Stram- bini, F. Giazotto, V. Zannier, L. Sorba, and S. Heun, Josephson diode effect in high-mobility insb nanoflags, Nano Letters22, 8502 (2022)

    2022

  33. [33]

    Soori, Josephson diode effect in junctions of super- conductors with band asymmetric metals, Journal of Physics: Condensed Matter36, 335303 (2024)

    A. Soori, Josephson diode effect in junctions of super- conductors with band asymmetric metals, Journal of Physics: Condensed Matter36, 335303 (2024)

    2024

  34. [34]

    Hu, Z.-T

    J.-X. Hu, Z.-T. Sun, Y.-M. Xie, and K. T. Law, Joseph- son diode effect induced by valley polarization in twisted bilayer graphene, Phys. Rev. Lett.130, 266003 (2023)

    2023

  35. [35]

    Cheng and Q.-F

    Q. Cheng and Q.-F. Sun, Josephson diode based on con- ventional superconductors and a chiral quantum dot, Phys. Rev. B107, 184511 (2023)

    2023

  36. [36]

    A. Soori, Josephson diode effect in one-dimensional quan- tum wires connected to superconductors with mixed singlet-triplet pairing, arXiv e-prints , arXiv:2409.02794 (2024), arXiv:2409.02794 [cond-mat.supr-con]

    Pith/arXiv arXiv 2024

  37. [37]

    Ghosh, V

    S. Ghosh, V. Patil, A. Basu, Kuldeep, A. Dutta, D. A. Jangade, R. Kulkarni, A. Thamizhavel, J. F. Steiner, F. von Oppen, and M. M. Deshmukh, High-temperature josephson diode, Nature Materials23, 612 (2024)

    2024

  38. [38]

    Jeon, J.-K

    K.-R. Jeon, J.-K. Kim, J. Yoon, J.-C. Jeon, H. Han, A. Cottet, T. Kontos, and S. S. P. Parkin, Zero-field polarity-reversible josephson supercurrent diodes enabled by a proximity-magnetized pt barrier, Nature Materials 21, 1008 (2022)

    2022

  39. [39]

    Zhang, Y

    Y. Zhang, Y. Gu, P. Li, J. Hu, and K. Jiang, General the- ory of josephson diodes, Phys. Rev. X12, 041013 (2022)

    2022

  40. [40]

    Debnath and P

    D. Debnath and P. Dutta, Gate-tunable josephson diode effect in rashba spin-orbit coupled quantum dot junc- tions, Phys. Rev. B109, 174511 (2024)

    2024

  41. [41]

    H. Wu, Y. Wang, Y. Xu, P. K. Sivakumar, C. Pasco, U. Filippozzi, S. S. P. Parkin, Y.-J. Zeng, T. McQueen, and M. N. Ali, The field-free josephson diode in a van der waals heterostructure, Nature604, 653 (2022)

    2022

  42. [42]

    Diez-Merida, A

    J. Diez-Merida, A. Diez-Carlon, S. Y. Yang, Y. M. Xie, X. J. Gao, K. Watanabe, T. Taniguchi, X. Lu, K. T. Law, and D. K. Efetov, Magnetic josephson junctions and superconducting diodes in magic angle twisted bilayer graphene (2021)

    2021

  43. [43]

    Baumgartner, L

    C. Baumgartner, L. Fuchs, A. Costa, S. Reinhardt, S. Gronin, G. C. Gardner, T. Lindemann, M. J. Manfra, P. E. Faria Junior, D. Kochan, J. Fabian, N. Paradiso, and C. Strunk, Supercurrent rectification and magne- tochiral effects in symmetric Josephson junctions, Nature Nanotechnology17, 39 (2022)

    2022

  44. [44]

    Daido and Y

    A. Daido and Y. Yanase, Unidirectional Superconduc- tivity and Diode Effect Induced by Dissipation, arXiv e-prints , arXiv:2310.02539 (2023), arXiv:2310.02539 [cond-mat.supr-con]

    Pith/arXiv arXiv 2023

  45. [45]

    J. Qi, M. Lu, J. Liu, C.-Z. Chen, and X. C. Xie, Non- hermitian superconducting diode effect, Phys. Rev. B 112, L060502 (2025)

    2025

  46. [46]

    Banerjee and M

    S. Banerjee and M. S. Scheurer, Dissipation-enhanced nonreciprocal superconductivity: Application to multi- valley superconductors, Phys. Rev. Appl.24, L031004 (2025)

    2025

  47. [47]

    M. Mori, W. Koshibae, and S. Maekawa, Josephson diode effect via a non-equilibrium rashba system (2025), arXiv:2501.05671 [cond-mat.supr-con]

    Pith/arXiv arXiv 2025

  48. [48]

    Shaffer, S

    D. Shaffer, S. Li, J. Hasan, M. Titov, and A. Levchenko, Josephson diode effect from nonequilibrium current in a superconducting interferometer, Phys. Rev. B112, 094509 (2025)

    2025