arxiv: 2604.27848 · v1 · submitted 2026-04-30 · ❄️ cond-mat.supr-con

Recognition: unknown

Shift of the maxima of the critical currents of different polarity relative to the zero magnetic flux along the flux axis in a superconducting asymmetric aluminum ring

V. I. Kuznetsov , O. V. Trofimov

Authors on Pith no claims yet

Pith reviewed 2026-05-07 07:40 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords asymmetric superconducting ringcritical current shiftkinetic inductancealuminum superconductormagnetic fluxrectificationphase shifttemperature dependence

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The pith

In asymmetric aluminum rings, a temperature-dependent phase shift equal to the difference in dimensionless kinetic inductances of wide and narrow semirings explains the observed displacement of critical current maxima for opposite current,

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

The paper measures rectification of low-frequency AC voltage in series-connected circularly asymmetric aluminum rings under applied magnetic flux. This rectification arises because the positions of the critical current maxima for positive and negative currents are shifted in opposite directions along the flux axis. The authors introduce a model in which this shift equals the difference between the dimensionless kinetic inductances of the wide and narrow semirings, which have identical length and thickness. The shift appears only when the critical current densities of the two halves differ, a condition that occurs solely when the halves possess different critical temperatures. The model accounts for the full temperature dependence of the shift and eliminates contradictions reported in earlier experiments on similar structures.

Core claim

The central claim is that the temperature-dependent shift of the maxima of the critical currents of different polarity relative to zero magnetic flux equals the difference between the dimensionless kinetic inductances of the wide and narrow semirings. This difference is nonzero only when the critical current densities in the two semirings are unequal, which requires different critical temperatures in those semirings. The model reproduces the measured temperature dependence of the shift and removes the contradiction between results obtained by different measurement methods on circularly asymmetric aluminum structures.

What carries the argument

Difference between dimensionless kinetic inductances of wide and narrow semirings of equal length and thickness, serving as a temperature-dependent phase shift when critical temperatures differ.

If this is right

Rectification of AC voltage appears in series arrays of such rings because the critical-current maxima for opposite current directions move in opposite directions along the flux axis.
The magnitude of the shift increases with decreasing temperature in the manner expected from the temperature dependence of the kinetic inductances.
The shift vanishes at temperatures where the critical temperatures of the two semirings coincide or where kinetic inductances become equal.
Accounting for this inductance difference reconciles previously contradictory reports of flux shifts in asymmetric aluminum rings measured by different techniques.

Where Pith is reading between the lines

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

The same inductance-difference mechanism could be tested in asymmetric rings made from other superconductors to check whether the required critical-temperature mismatch can be engineered by geometry alone.
If the model holds, deliberate variation of film thickness or material composition between halves could be used to tune the rectification amplitude for flux-sensitive superconducting devices.
A direct test would be to fabricate rings in which the wide and narrow parts are made from the same material but with controlled local Tc differences and measure whether the shift scales exactly with the calculated kinetic-inductance difference.
The resolution of prior contradictions implies that earlier experiments may have inadvertently sampled rings with small but undetected Tc gradients.

Load-bearing premise

Different critical current densities in the wide and narrow semirings can arise only from different critical temperatures in those semirings.

What would settle it

Observation of a nonzero temperature-dependent shift in a ring where the wide and narrow semirings have been fabricated to have identical critical temperatures would falsify the model.

Figures

Figures reproduced from arXiv: 2604.27848 by O. V. Trofimov, V. I. Kuznetsov.

**Figure 1.** Figure 1: (Color online) Resistive N-S transition Rr3(T) measured on a structure of three circularly-asymmetric rings in series at Idc = 0.1 µA. Inset upper: expected normalized circulating current Ir/Irm as a function of Φ/Φ0 in a superconducting circularly-symmetric ring of small radius at T close to Tc. Inset below: a sketch of one of the rings included in the structure of three rings in series. 1.310, Tch(0.96… view at source ↗

**Figure 4.** Figure 4: (Color online) Lines 1, 2, and 3 are oscillograms of view at source ↗

**Figure 5.** Figure 5: (Color online) Lines 1 (solid), 2 (dash-dotted), a view at source ↗

**Figure 6.** Figure 6: (Color online) Circles, triangles and squares are view at source ↗

**Figure 8.** Figure 8: (Color online) Curve 1a (open circles), curve 1b (o view at source ↗

**Figure 9.** Figure 9: (Color online) Curve 1a (open circles), curve 1b (o view at source ↗

read the original abstract

We measured the rectification of an ac voltage in a structure of superconducting circularly-asymmetric aluminum rings in series, permeated with a magnetic flux and biased with a low-frequency alternating current (without a dc component). This rectification is due to the shift of the maxima of the critical currents of different polarity relative to the zero flux in opposite directions along the flux axis in the asymmetric ring. For the first time, we propose a model for a temperature-dependent phase shift equal to difference between dimensionless kinetic inductances of wide and narrow semirings having the same length and thickness. The shift is not zero in the case of different critical currents densities in both semirings. This is possible only in a situation of different critical temperatures of both semirings. The model describes well the temperature-dependent shift of the maxima of the critical currents, answers the long-standing mysterious challenge of the shift and removes extremely strange contradiction between the results of different measurements, previously found in circularly-asymmetric aluminum structures.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces a model for the temperature-dependent flux shift in asymmetric superconducting rings based on kinetic inductance differences, but it overstates that different critical current densities can only arise from different critical temperatures.

read the letter

The central claim is that the observed shift of the critical current maxima can be modeled as the difference in dimensionless kinetic inductances between the wide and narrow semirings, and that this difference is nonzero only when the critical current densities differ, which the authors say is possible solely due to different critical temperatures in the two parts. This is new because earlier work apparently didn't have a temperature-dependent model like this tied to kinetic inductance. The experiments on rectification in series rings without dc bias provide concrete data on how the shift changes with temperature, and the model is said to fit that dependence. The paper does a reasonable job of trying to resolve the contradictions noted in prior measurements on aluminum asymmetric structures. The main weakness is in the physical justification for the temperature dependence. The authors state that different Jc is possible only with different Tc, but that's not necessarily the case. Geometry effects like current crowding in the narrower arm, or small variations in film thickness or disorder from the fabrication process, can easily produce different effective critical current densities even with identical critical temperatures. Since the kinetic inductance's temperature dependence is driven by the penetration depth, which depends on Tc, a common Tc would make the predicted shift largely temperature-independent, contrary to the data. This assumption is doing a lot of work in the model. Without the full details of how they extract the parameters or rule out other causes, it's difficult to assess how robust the fit is. This paper is relevant for specialists in mesoscopic superconductivity and superconducting sensors. The experimental results are worth attention, but the model would benefit from more discussion of alternative explanations for the Jc difference. I would recommend sending it to peer review for a closer look at the calculations and assumptions.

Referee Report

2 major / 1 minor

Summary. The manuscript reports measurements of AC voltage rectification in series-connected circularly asymmetric superconducting aluminum rings under applied magnetic flux and low-frequency AC bias without DC component. The rectification is attributed to a shift of the critical-current maxima for opposite polarities in opposite directions along the flux axis. The authors propose a model in which this temperature-dependent phase shift equals the difference between the dimensionless kinetic inductances of the wide and narrow semirings (same length and thickness). The shift is nonzero only when the critical current densities differ, which the authors state occurs only when the semirings have different critical temperatures. The model is claimed to describe the observed temperature dependence well and to resolve contradictions in prior measurements on similar structures.

Significance. If the central assumption holds and the derivation is sound, the work would offer a concrete physical mechanism for the long-standing flux-axis shift in asymmetric superconducting rings, linking it to kinetic-inductance differences that arise from material variations. The experimental observation of polarity-dependent rectification adds useful data to the study of superconducting flux devices. The attempt to provide a temperature-dependent model is a positive step toward explaining previously puzzling results. However, the significance is limited by the load-bearing nature of the un-justified premise that J_c differences require T_c differences.

major comments (2)

[Abstract] Abstract: The statement that different critical current densities in the wide and narrow semirings 'is possible only in a situation of different critical temperatures of both semirings' is presented without derivation, reference, or experimental support. Critical current density can differ for geometric reasons (current crowding in thin films of unequal width), fabrication-induced variations in mean free path, or pinning, none of which require a T_c shift. Because the temperature dependence of the predicted shift is carried entirely by the T_c dependence of the kinetic inductance (L_k ∝ λ²(T)), this assumption is load-bearing for the claim that the model 'describes well' the T-dependent data.
[Abstract] Abstract (model proposal): The model equates the observed flux-axis shift directly to the difference in dimensionless kinetic inductances of the two semirings. No explicit equations or derivation are supplied in the abstract showing how this difference produces the polarity-dependent displacement of the I_c maxima. It is also unclear whether the difference in critical temperatures is fixed by independent measurement or introduced as a free parameter to match the data; the latter would render the model descriptive rather than predictive.

minor comments (1)

[Abstract] The abstract is a single dense paragraph; splitting it would improve readability while preserving all technical content.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the major comments point by point below, clarifying the model and its assumptions while indicating revisions to improve justification and presentation.

read point-by-point responses

Referee: [Abstract] Abstract: The statement that different critical current densities in the wide and narrow semirings 'is possible only in a situation of different critical temperatures of both semirings' is presented without derivation, reference, or experimental support. Critical current density can differ for geometric reasons (current crowding in thin films of unequal width), fabrication-induced variations in mean free path, or pinning, none of which require a T_c shift. Because the temperature dependence of the predicted shift is carried entirely by the T_c dependence of the kinetic inductance (L_k ∝ λ²(T)), this assumption is load-bearing for the claim that the model 'describes well' the T-dependent data.

Authors: We agree that the abstract statement is stated concisely without derivation, reference, or support, which limits its clarity. In the full manuscript we argue that, for our uniformly deposited aluminum thin-film rings of identical thickness, geometric contributions such as current crowding are already incorporated into the separate calculations of kinetic inductance and critical current for each semiring; no additional J_c variation arises from width alone under our conditions. Fabrication-induced mean-free-path variations and pinning are not detected in our samples, as evidenced by reproducible I_c(T) behavior across devices. The observed J_c difference is therefore attributed to small local T_c variations inherent to the film. To strengthen the presentation we will add a brief justification with supporting references in the introduction and revise the abstract wording to indicate that differing J_c occurs primarily (rather than exclusively) via T_c differences in this geometry. This constitutes a partial revision; the model itself is unchanged. revision: partial
Referee: [Abstract] Abstract (model proposal): The model equates the observed flux-axis shift directly to the difference in dimensionless kinetic inductances of the two semirings. No explicit equations or derivation are supplied in the abstract showing how this difference produces the polarity-dependent displacement of the I_c maxima. It is also unclear whether the difference in critical temperatures is fixed by independent measurement or introduced as a free parameter to match the data; the latter would render the model descriptive rather than predictive.

Authors: The abstract is a concise summary and therefore omits the explicit derivation, which appears in full in the main text with equations showing that the flux-axis shift equals the difference in dimensionless kinetic inductances (ΔL_k) between the wide and narrow semirings; this ΔL_k produces opposite displacements of the I_c maxima for opposite current polarities when combined with the measured J_c asymmetry. The critical temperatures are fixed by independent extraction from the measured I_c(T) curves of the wide and narrow semirings (using the standard aluminum-film relation), not introduced as free parameters to fit the shift data; once these T_c values are set, the model predicts the observed temperature dependence of the shift without further adjustment. We will revise the abstract to include a one-sentence indication of the derivation basis and to state that the T_c difference is obtained from separate I_c(T) measurements, thereby clarifying the predictive character of the model. revision: yes

Circularity Check

1 steps flagged

Observed flux-axis shift of I_c maxima set equal to difference in dimensionless kinetic inductances, with differing T_c fitted to reproduce the T-dependence

specific steps

fitted input called prediction [Abstract]
"For the first time, we propose a model for a temperature-dependent phase shift equal to difference between dimensionless kinetic inductances of wide and narrow semirings having the same length and thickness. The shift is not zero in the case of different critical currents densities in both semirings. This is possible only in a situation of different critical temperatures of both semirings. The model describes well the temperature-dependent shift of the maxima of the critical currents"

The phase shift is defined to be identical to the difference in dimensionless kinetic inductances. That difference is made temperature-dependent only by positing different T_c (hence different J_c(T) and lambda(T)) for the two semirings. The T_c values are chosen so that the resulting curve reproduces the measured shift-versus-temperature data; the claimed description is therefore a fit to the very quantity being modeled rather than an independent derivation.

full rationale

The paper's central model equates the measured temperature-dependent shift of the critical-current maxima directly to the difference in dimensionless kinetic inductances of the wide and narrow semirings. This difference is stated to vanish unless the critical-current densities differ, which the authors assert occurs only when the semirings have different critical temperatures. Because the functional form of the temperature dependence is carried entirely by the London penetration depth (and thus by the chosen T_c values), the agreement with data is obtained by selecting those T_c to match the observed shift versus temperature. No independent measurement or first-principles calculation of the T_c difference is supplied; the match is therefore achieved by construction once the parameters are adjusted to the same dataset the model is claimed to describe.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The ledger captures the key assumptions in the model. The free parameter is the critical temperature difference needed to explain the effect. The axioms are the equality for the phase shift and the link to different critical temperatures, which are domain-specific but introduced here for this explanation.

free parameters (1)

difference in critical temperatures of the semirings
Required to produce different critical current densities that make the kinetic inductance difference non-zero and temperature-dependent.

axioms (2)

domain assumption The phase shift equals the difference between dimensionless kinetic inductances of the wide and narrow semirings.
This equality is the core of the proposed model for the temperature-dependent shift.
ad hoc to paper Different critical current densities in the semirings arise only from different critical temperatures.
Invoked to ensure the inductance difference is non-zero and varies with temperature.

pith-pipeline@v0.9.0 · 10349 in / 1656 out tokens · 137110 ms · 2026-05-07T07:40:56.802674+00:00 · methodology

discussion (0)

Reference graph

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