Pith. sign in

REVIEW 4 major objections 4 minor 58 references

By cutting one twisted BSCCO interface into a SQUID, this paper directly measures a π phase difference between the two arms and reads it as evidence for chiral d±id interfacial order, time-reversal symmetry breaking, and Cooper-pair co-tunn

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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2026-08-02 18:21 UTC pith:CJWEACUR

load-bearing objection Genuinely new SQUID geometry on twisted BSCCO gives a phase-sensitive readout; the π-phase interpretation is plausible but lacks controls against trapped flux/vortex artifacts, so the paper deserves a serious but demanding referee. the 4 major comments →

arxiv 2603.12092 v1 pith:CJWEACUR submitted 2026-03-12 cond-mat.supr-con cond-mat.mes-hallcond-mat.str-el

Quantum interference in a twisted high-Tc SQUID senses emergent interfacial order

Amit Basu , Samrat Ash , Ritajit Kundu , Neha Bhatia , Sakshi Nema , Tejaswini Gawade , Khushabu Agrawal , Abhishek Das
show 7 more authors
Joydip Sarkar Amit Shah Ruta Kulkarni Digambar A. Jangade Arijit Kundu A. Thamizhavel Mandar M. Deshmukh
This is my paper
classification cond-mat.supr-con cond-mat.mes-hallcond-mat.str-el PACS 74.50.+r74.72.-h85.25.Dq
keywords twisted BSCCOcuprate SQUIDchiral superconducting ordertime-reversal symmetry breakinganomalous phase differenceCooper-pair co-tunnelingJosephson diodeflux noise
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 tries to establish that the superconducting interface formed by stacking two crystals of BSCCO with a ~45° twist hosts a time-reversal-symmetry-broken chiral (d±id) order, and that this order can be detected directly by cutting the interface into a SQUID. The key observation is an anomalous π phase difference between the two Josephson-junction arms, which the authors interpret as the two arms falling into opposite degenerate minima of the interfacial free energy. They support this with a zero-field diode asymmetry (broken time-reversal symmetry) and a second-harmonic component in the current–phase relation attributed to co-tunneling of Cooper pairs. If correct, this gives a route to probing pairing symmetry at twisted interfaces and a SQUID flux sensor that works near 77 K with noise ~1.5 µΦ₀/√Hz.

Core claim

At a 45° twisted BSCCO interface, Cooper-pair tunneling is suppressed and the interfacial order parameter can choose between two degenerate chiral states with phase α = +π/2 or −π/2 (d+id or d−id, a chiral superconductor with two d-wave components in quadrature). The authors fabricate a SQUID by cutting one twisted region into two arms, so any phase difference between the arms must come from the two arms occupying different chiral minima. Tracking the minima of the dV/dI oscillation as a function of bias current and extrapolating to zero current, they find an intercept of half the oscillation period at zero in-plane field, corresponding to φ₁₂ ≈ π, and an intercept near zero at 10 µT in-plan

What carries the argument

The load-bearing object is the asymmetric SQUID with a corrected phase-sum rule that includes an intrinsic anomalous phase φ₁₂ alongside geometric inductance: φ₁−φ₂+AL_geo I+φ₁₂ = 2πΦ_ext/Φ₀. Because geometric and Josephson inductances are comparable, the authors avoid fitting the full response; instead they track the phase of the dV/dI minima at several bias currents and extrapolate to I=0, which isolates φ₁₂ even when L_geo is not negligible. The interpretation of φ₁₂ relies on the free-energy landscape of a 45° twisted junction, which has two degenerate minima at phase α=±π/2, corresponding to chiral d±id order; two arms of the same interface can occupy the same minimum (φ₁₂=0) or opposit

Load-bearing premise

The central claim rests on the half-period intercept of the dV/dI minima being a genuine intrinsic phase difference rather than a trapped half-flux quantum, a vortex configuration, or a local sign flip of the first-order coupling caused by twist-registry inhomogeneity; the paper does not test this with field-cooling, repeated cooldowns, or imaging.

What would settle it

Cool the SQUID through Tc repeatedly — with in-plane field applied, reversed, and zero — while recording the dV/dI intercept each time; if the π intercept appears whenever a trapped half-flux quantum would be expected and disappears when the loop is imaged to be vortex-free, the intrinsic-chirality interpretation is falsified. A positive control would be a nominally 0° twisted SQUID that never shows the π intercept.

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

If this is right

  • At ~45° twist, the SQUID directly measures an anomalous π phase shift between identical-looking arms of the same interface, giving evidence for chiral (d±id) interfacial order that a single junction cannot provide.
  • The appearance of a second harmonic in the switching-current modulation, increasing as the twist angle approaches 45°, supports co-tunneling of two Cooper pairs as a real transport channel.
  • The zero-field diode asymmetry in the SQUID is consistent with time-reversal symmetry breaking at the twisted interface.
  • The same SQUID geometry works as a low-noise flux sensor near 77 K, with flux noise ~1.5 µΦ₀/√Hz, comparable to established high-Tc SQUID technology.
  • The fabrication and analysis route transfers to other van der Waals superconducting heterostructures, allowing the symmetry of interfacial order to be probed by quantum interference.

Where Pith is reading between the lines

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

  • If the in-plane field toggles the relative chirality by coupling Josephson and Abrikosov vortices, then the SQUID is effectively a field-switchable π–0 phase bit; a direct test is to measure φ₁₂ versus in-plane field magnitude, sweep direction, and cooldown history, which the paper does not report.
  • The unexplained role of the in-plane field raises the possibility that the observed φ₁₂ is domain selection rather than an equilibrium property of the interface; a repeated-cooldown study with imaging (e.g., scanning SQUID or magnetic force microscopy) would distinguish intrinsic chirality from trapped vortex artifacts.
  • The measured field period is ~7 times smaller than the geometric area predicts; modeling this flux focusing could lead to SQUID loops with effective areas far exceeding their physical size, useful for magnetometry.
  • A natural next experiment is a twist-angle series near 45°: the π intercept should disappear or change sharply as the angle moves away from the degeneracy point, which would strengthen the d±id assignment.

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 reports c-axis SQUIDs made from twisted Bi2Sr2CaCu2O8+δ interfaces. The central claim is that a magnetic-field-dependent half-period intercept in the dV/dI modulation (Fig. 3a,b) corresponds to an intrinsic π phase difference between the two Josephson junctions in the SQUID loop, and that this phase difference reflects spontaneous chiral d±id interfacial order in the two arms, with the two arms occupying opposite free-energy minima. The paper also reports higher-harmonic content in the switching-current modulation, time-reversal-symmetry breaking at zero field, and a flux-noise sensitivity of ~1.5 μΦ0/√Hz at 60 K, positioning the device as a high-temperature SQUID sensor.

Significance. If the π-phase interpretation is correct, this is an important advance: a twisted high-Tc interface would provide direct, phase-sensitive evidence for time-reversal-symmetry-broken chiral superconductivity, a quantity inaccessible to the single-junction experiments of previous twisted-BSCCO work. The use of the Wollman et al. extrapolation protocol [34] is a strength, as is the multi-device approach and the explicit appeal to an external free-energy theory (Can et al. [7]) rather than a fit to the present data. The additional sensor demonstration is a useful practical contribution. However, the central phase claim rests on a small number of assumptions that are not all tested, and the reported controls are incomplete. The paper is technically interesting and potentially significant, but the evidence as presented does not yet uniquely establish the chiral-domains interpretation.

major comments (4)
  1. [§'Now we try to understand...', Fig. 3(a,b), Eq. (2)] The load-bearing identification of the half-period intercept with an intrinsic φ12=π is underdetermined. Eq. (2) is modulo 2π, so the same observed intercept would result from a trapped half-flux quantum, an Abrikosov vortex in or near the SQUID loop, a flux-focusing offset, or a field-history-dependent shift of the SQUID transfer function. The manuscript reports no field-cooling, repeated-cooldown, or imaging controls that would exclude these alternatives. The authors themselves state that the role of the in-plane field is 'not well understood' and invoke coupling of Josephson and Abrikosov vortices as the proposed mechanism; that very mechanism provides a concrete alternative route to a half-period shift without chiral interfacial order. Because the π state appears at in-plane field 0 μT and the 0 state at 10 μT, a field-dependent vortex reconfiguration is the most economical alternati
  2. [Methods: twist-angle accuracy; Fig. 3(c,d)] The two SQUID arms are cut from the same twisted region, but the argument that their interfacial phases must be identical assumes a uniform local twist angle/registry across the junction area. The fabrication method states an alignment accuracy of only 0.5°. Near 45°, the first-order d-wave Josephson coupling vanishes and changes sign with the sign of θ−45°. Local registry variations on the scale of the two arms could therefore produce opposite signs of the residual first-order coupling and a π phase difference without any chiral pairing. The paper does not characterize the local twist-angle homogeneity or demonstrate that first-order coupling is negligible in both arms. The cited inhomogeneity-induced TRS-breaking scenario (Yuan et al. [50]) makes this more than a pedantic concern, and it must be experimentally or theoretically excluded before the π intercept can be uniquely attributed
  3. [Fig. 3(a,b) and SI 14 / Extended Data Fig. 2] The intercept analysis that supports φ12≈π is presented with no statistical uncertainty. The bottom panels of Fig. 3 show a linear extrapolation of phase minima versus bias current, but no error bars, number of independent sweeps, or goodness-of-fit are given. The claim that one intercept is 'close to half-integer' and the other 'approximately zero' requires a quantitative statement of the uncertainty in the extracted phase. Without this, the reader cannot judge whether the difference between 0 and π is statistically significant, especially because the data are sparse and the period is large (~25 μT). The phase statistics in Extended Data Fig. 2 are helpful but are not enough; a per-device fit with errors and repeated cooldowns is needed.
  4. ['The 0° control is only for diode; not phase'] The nominally 0° twisted SQUID is used as a control for the diode effect at zero field, but the same device is not subjected to the Wollman-type phase-intercept protocol. A 0° or non-twisted c-axis SQUID fabricated and measured with the identical in-plane-field history would provide the essential control: if a half-period intercept also appears in a junction where chiral d±id order is not expected, the present interpretation would be falsified. As reported, the paper does not include this control, and therefore the central claim lacks a baseline measurement against the same trapped-flux/vortex artifacts.
minor comments (4)
  1. [Fig. 5 and Extended Data Fig. 1] The flux-noise value is reported as ~1.5 μΦ0/√Hz at 60 K in the text, but Extended Data Fig. 1's table lists the same device at 77 K. Please clarify the measurement temperature and, if both numbers exist, show both consistently.
  2. [Eq. (2) and Methods] The definition of the parameter A in Eq. (2) is postponed to the Methods section. For readability, define A in the main text where Eq. (2) is introduced, or provide a pointer to the derivation at first use.
  3. [Fig. 3 caption] The caption appears to label the in-plane field values inconsistently with the main text: the text says Fig. 3(a) is taken at 10 μT in-plane and Fig. 3(b) at 0 μT, but the caption lists 'B=0 μT in-plane' next to panel (a) and 'B=10 μT in-plane' next to panel (b). Please correct this to avoid reader confusion.
  4. [General] The switching-current modulation period is ~7 times smaller than the geometric area predicts; the manuscript attributes this to flux focusing and Meissner screening (SI 7). Because the phase-intercept analysis assumes a particular relation between applied field and enclosed flux, it would help to explicitly state how this area-enhancement uncertainty propagates into the φ12 extraction.

Circularity Check

0 steps flagged

No significant circularity: the phi12 extraction is a direct phase-sensitive measurement and the chiral interpretation leans on external theory, not on self-cited inputs.

full rationale

The paper's derivation chain is self-contained with respect to the circularity patterns enumerated. The anomalous phase difference phi12 is introduced as an unknown term in Eq. 2 and then extracted from the intercept of the linear extrapolation of dV/dI phase-minima positions versus bias current, following the independent Wollman et al. protocol [34]; this is a measurement, not a fit of the target conclusion. The identification of phi12 ~ pi with opposite chiral minima is supplied by Can et al.'s Landau-Ginzburg free-energy analysis (external theory, not author-derived) and by Zhao et al.'s independent experiment, while the same-versus-opposite minima assignment is read from the data. Self-citations enter only in peripheral roles: [12] for the field-tunable diode effect and for a speculative flux-focusing possibility that the paper itself labels 'not well understood at this point,' and [41] for a fabrication detail; neither is load-bearing for the central phase claim, and [12] is an independent published experiment. The admitted limitations (in-plane-field mechanism 'not well understood'; domains 'cannot discern using SQUIDs in the present work') are empirical underdetermination, not circularity: alternative explanations such as trapped half-flux quanta or vortex configurations would call for scientific controls, but their absence does not make the paper's derivation equivalent to its inputs. No equation is defined in terms of the quantity it purports to predict, and no fitted parameter is renamed as a prediction. Hence score 0.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 1 invented entities

The measurement is direct and the interpretation leans on external theory and independent prior experiments, so the circularity burden is low. The main ledger additions are the phenomenological flux-focusing enhancement (which enters the φ12 normalization), the unmodeled in-plane-field switching mechanism, and the assumed domain configuration of opposite chirality in the two arms.

free parameters (3)
  • Effective flux-focusing area enhancement (~7×) = ~7 (observed period ≈ Φ0/A_geo / 7)
    The observed modulation period is ~7× smaller than Φ0/A_geo (Fig. 2a,d; Table V in SI 7). This field-to-flux conversion enters both the L_J slope extraction and the normalization of the φ12 intercept (Φext/Φperiod), yet the enhancement is not computed from first principles in the main text; it is attributed to Meissner/flux-focusing effects discussed only in SI 7.
  • In-plane-field chirality-switch threshold = switches between in-plane field 0 and 10 μT
    The in-plane field value at which the two arms go from φ12 ≈ 0 to φ12 ≈ π is read directly from the data (Fig. 3a,b; Extended Data Fig. 2). The mechanism (flux focusing coupling Josephson and Abrikosov vortices) is acknowledged as 'not well understood,' so the switching condition functions as a free control in the interpretation rather than a predicted quantity.
  • Co-tunneling fraction in simulated CPR (SI 10) = not stated in main text
    The theoretical reproduction of the SQUID response in SI 10 presumably tunes the weight of the second-harmonic (sin 2φ) CPR term to match the observed modulation; the main text references the simulation but does not report its parameters, so this weight is effectively a fitted quantity in the interpretation of the higher-harmonic signature.
axioms (6)
  • domain assumption BSCCO has a d-wave order parameter; at 45° twist the first-order Cooper-pair tunneling is suppressed and the interface free energy has two degenerate minima (α = ±π/2, a chiral d±id state), per Can et al. [7].
    This theory is the interpretive lens for the measured φ12 ≈ π as opposite-chirality domains (Fig. 3c,d; §'Now we try to understand our experimental observation...').
  • domain assumption The Wollman et al. dV/dI-minima-intercept technique (ref. 34) isolates the intrinsic phase difference φ12 by linear extrapolation of minima positions to zero bias current.
    The analysis of Fig. 3 assumes the minima positions vary linearly with bias (slope set by A L_geo I) and that the intercept is φ12, valid for sinusoidal, copy-similar CPRs; the paper's own claim of strong second-harmonic content is in tension with this assumption and is not tested in the main text.
  • ad hoc to paper The two SQUID arms, cut from the same twisted region, can spontaneously occupy different free-energy minima (opposite chirality).
    Required for φ12 = π. The final paragraph admits 'complex scenarios involving domains [54] that we cannot discern using SQUIDs in the present work,' so the domain configuration is assumed rather than evidenced.
  • ad hoc to paper An in-plane magnetic field modifies the free-energy landscape of the two junctions differently (via flux focusing and coupling of Josephson and Abrikosov vortices).
    Invoked to explain why sweeping the in-plane field switches between φ12 ≈ 0 and π. The authors state the role of the in-plane field 'is not well understood at this point,' so this is an ad hoc supporting premise.
  • domain assumption Cryogenic exfoliation preserves oxygen stoichiometry and a pristine twisted interface (Zhao et al. [11]).
    The validity of all transport conclusions depends on the interface being the clean, stoichiometric junction described by the cryo-exfoliation method (Methods; ref. 11).
  • domain assumption Co-tunneling of two Cooper pairs contributes a sin(2φ) term to the CPR (Can et al. [7], Tummuru et al. [51], Yuan et al. [50]).
    Used to interpret the FFT second-harmonic amplitude ratio A2/A1 and its temperature dependence as evidence for 4e co-tunneling (Fig. 4c,d).
invented entities (1)
  • Emergent chiral (d±id) interfacial superconducting order with junction phase α at the ±π/2 free-energy minima independent evidence
    purpose: Provides the physical origin of the measured φ12 ≈ π and of the zero-field TRS-breaking asymmetry in the SQUID.
    Predicted by Can et al. [7]; prior single-junction signatures in Zhao et al. [11] are consistent. The paper's falsifiable handle is the half-period intercept plus ~4–8% zero-field diode asymmetry, but alternative explanations (trapped half-flux vortex, twist-angle sign flip) are not excluded, so independent support is partial.

pith-pipeline@v1.3.0-alltime-deepseek · 17522 in / 29733 out tokens · 283444 ms · 2026-08-02T18:21:52.509372+00:00 · methodology

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read the original abstract

Engineering artificial systems by twisting and stacking van der Waals materials has proven to be an excellent platform for exploring emergent quantum phenomena that can be significantly different from the constituents. Recent advances in the fabrication of high-quality twisted interfaces provide a unique opportunity to study the little-explored interfacial superconducting order in twisted cuprate superconductors. In our work, we fabricate superconducting quantum interference devices (SQUID) that utilize the twisted interface of $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$, a high-Tc cuprate superconductor. By measuring the magnetic field modulation of switching current and differential resistance, we find a $\mathrm{\pi}$ phase difference between the two Josephson junction arms of the SQUID reflecting chiral superconducting order -- a crucial aspect inaccessible to single Josephson junction devices of the past. Our observations also indicate co-tunneling of the Cooper pairs and a time-reversal symmetry-broken emergent superconducting order. Additionally, these SQUIDs are well suited for use as state-of-the-art flux sensors close to 77 K, achieving a flux noise sensitivity of $\sim$1.5 $\mathrm{\mu\Phi_0/\sqrt{Hz}}$. Stabilizing new superconducting orders using twisted interfaces and probing them using quantum interference opens new avenues to understanding the microscopic origin of unconventional superconductors. Our SQUID architecture is suitable for investigating the charge transport mechanisms and the symmetry of superconducting order at the interfaces of other systems, reflecting the broad applicability beyond cuprate superconductors.

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