Nonreciprocal superconducting critical currents with normal state field trainability in kagome superconductor CsV3Sb5

Haowen Pang; Hechang Lei; Jian Wang; Jun Ge; Pinyuan Wang; Qiangwei Yin; Xiaoqi Liu; Ziqiang Wang

arxiv: 2506.04601 · v2 · submitted 2025-06-05 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

Nonreciprocal superconducting critical currents with normal state field trainability in kagome superconductor CsV3Sb5

Jun Ge , Xiaoqi Liu , Pinyuan Wang , Haowen Pang , Qiangwei Yin , Hechang Lei , Ziqiang Wang , Jian Wang This is my paper

Pith reviewed 2026-05-19 11:57 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall

keywords CsV3Sb5kagome superconductornonreciprocal critical currentstime-reversal symmetry breakingcharge density waveloop-current CDWsuperconductivity

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The pith

The CDW state in CsV3Sb5 has a macroscopic trainable time-reversal symmetry breaking that persists into the superconducting state, causing nonreciprocal critical currents.

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

The paper establishes that nanodevices made from the kagome superconductor CsV3Sb5 display nonreciprocal superconducting critical currents even at zero magnetic field. This means the maximum current the device can carry without losing superconductivity depends on the direction of current flow. The asymmetry in these currents changes randomly when the device is warmed up and cooled down, but its polarity can be set by applying a magnetic field above the charge density wave transition temperature and then removing the field before cooling into the superconducting state. These observations indicate that the charge density wave phase breaks time-reversal symmetry in a controllable macroscopic manner, and this breaking continues into the superconducting phase.

Core claim

Nonreciprocal superconducting critical currents are observed at zero magnetic field in CsV3Sb5 nanodevices, with the polarity of the asymmetry changing randomly upon thermal cycling to 300 K but following the direction of a perpendicular magnetic field applied above the CDW transition temperature and removed above Tc. This ascertains that the CDW state possesses a macroscopic and trainable TRS-breaking directionality whose symmetry breaking continues into the superconducting state, generating the nonreciprocal currents and providing evidence for a loop-current CDW normal state with TRS breaking.

What carries the argument

The field-training protocol applied above the CDW transition that sets the polarity of zero-field Ic asymmetry by imprinting the TRS-breaking directionality from the CDW state onto the superconductor.

If this is right

The superconducting state inherits the time-reversal symmetry breaking from the CDW phase.
The direction of nonreciprocal current flow can be trained using magnetic fields in the normal state above the CDW temperature.
Random polarity upon thermal cycling supports spontaneous rather than externally induced symmetry breaking.
The results favor models of the CDW involving loop currents that break time-reversal symmetry.

Where Pith is reading between the lines

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

Similar trainable nonreciprocity may occur in other materials with CDW states suspected of loop currents.
This training method could allow control of superconducting diode effects without applying fields in the superconducting state itself.
The connection between CDW and SC symmetry breaking may help explain other anomalous properties in kagome superconductors.

Load-bearing premise

That the specific protocol of applying a perpendicular field above the CDW transition and removing it to zero above Tc isolates the CDW state's TRS-breaking directionality without residual flux or geometric artifacts determining the polarity.

What would settle it

A consistent failure of the Ic asymmetry polarity to match the direction of the training field applied above the CDW temperature, or the appearance of fixed polarity independent of the training procedure, would falsify the link to CDW TRS breaking.

read the original abstract

Determining time-reversal symmetry (TRS) and chirality in the superconducting state and its relation to normal-state symmetry and topology are important issues in condensed matter physics. Here, we report nonreciprocal superconducting critical currents (Ic) at zero magnetic field in kagome superconductor CsV3Sb5 nanodevices: Ic differs for opposite directions, indicating spontaneous TRS and inversion symmetry breakings. The polarity of Ic asymmetry changes randomly in repeated thermal cycling to 300 K, consistent with spontaneous TRS breaking. Crucially, on applying a perpendicular magnetic field above the charge density wave (CDW) transition temperature and then removing it to zero above the superconducting onset temperature (Tc), the polarity of Ic asymmetry follows the field direction, ascertaining that the CDW state has a macroscopic and trainable TRS-breaking directionality. The symmetry breaking continues into the superconducting state and generates the nonreciprocal critical currents. These results provide evidence for the loop-current CDW normal state with TRS breaking in CsV3Sb5.

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 reports field-trainable nonreciprocal Ic polarity in CsV3Sb5 nanodevices linked to CDW TRS breaking, but the training protocol leaves room for residual flux or geometry artifacts.

read the letter

Colleague, the main thing here is that the authors see nonreciprocal critical currents at zero field in CsV3Sb5 nanodevices, with the polarity of the asymmetry trainable by a perpendicular field applied above the CDW transition and removed above Tc. They read this as the CDW carrying a macroscopic, directionally trainable TRS breaking that continues into the superconducting state and produces the nonreciprocity. The random polarity flips on thermal cycling to 300 K support the spontaneous nature of the breaking rather than a fixed device property. What is new is this specific normal-state training protocol and its effect on the superconducting Ic asymmetry; prior work on the material had not shown this controllable imprinting from the CDW regime. The experimental sequence with cycling and field-training steps is laid out coherently in the abstract and gives a reasonable set of controls for the claim. The soft spots sit mainly with the isolation of the CDW effect. The protocol could still allow trapped flux in the nanodevice or substrate to set the polarity after field removal, or fixed geometric features in the device layout could bias vortex motion or current paths without any CDW chirality involved. The abstract gives no quantitative bounds on remanent fields or extra controls that would exclude those alternatives, so the central interpretation depends on that assumption. Without the full data, error bars, and device characterization, the statistical weight behind the polarity following the training field remains hard to judge. This is for people working on kagome superconductors and the connection between normal-state CDW order and superconducting symmetry breaking. A reader focused on TRS breaking and unconventional pairing would get value from the experimental approach. It deserves a serious referee because the result is potentially relevant to the subfield and the concerns about artifacts are concrete but fixable with more data. I would send it to review.

Referee Report

2 major / 1 minor

Summary. The manuscript reports nonreciprocal superconducting critical currents (Ic) at zero magnetic field in CsV3Sb5 nanodevices, with Ic differing for opposite current directions as evidence of spontaneous TRS and inversion symmetry breaking. The polarity of the Ic asymmetry changes randomly upon repeated thermal cycling to 300 K. Crucially, applying a perpendicular field above the CDW transition temperature and removing it to zero above Tc trains the Ic asymmetry polarity to follow the training field direction. This is interpreted as showing that the CDW state has a macroscopic, trainable TRS-breaking directionality that continues into the superconducting state, supporting a loop-current CDW model.

Significance. If the central observations hold after addressing controls, the result would be significant for understanding symmetry breaking in kagome superconductors. It links normal-state CDW order with TRS breaking to superconducting nonreciprocity, providing evidence for loop-current CDW in CsV3Sb5. The combination of random thermal cycling and field-training protocols is a strength that helps distinguish spontaneous from induced effects.

major comments (2)

[Abstract] Abstract (training protocol description): The central claim that the protocol isolates CDW TRS-breaking directionality as the source of trained Ic asymmetry polarity requires that residual flux, substrate effects, or fixed geometric asymmetries in the nanodevice do not produce the observed polarity. The abstract provides no quantitative bounds on remanent magnetization after field removal to zero or explicit controls (e.g., zero-field cooling comparisons or magnetization measurements) to exclude these alternatives. This protocol is load-bearing for the interpretation.
[Results (thermal cycling)] Results section on thermal cycling: The random changes in Ic asymmetry polarity upon cycling to 300 K are presented as consistent with spontaneous TRS breaking. However, without reported details on the number of cycles performed, statistical significance, device-to-device variation, or error bars on the Ic values, the strength of this evidence for macroscopic directionality cannot be fully assessed.

minor comments (1)

[Abstract] The abstract refers to 'nanodevices' without specifying fabrication method, dimensions, or basic characterization (e.g., resistance vs temperature curves), which would help evaluate possible geometric contributions to the nonreciprocity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive comments that help clarify the presentation of our results. We address each major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract (training protocol description): The central claim that the protocol isolates CDW TRS-breaking directionality as the source of trained Ic asymmetry polarity requires that residual flux, substrate effects, or fixed geometric asymmetries in the nanodevice do not produce the observed polarity. The abstract provides no quantitative bounds on remanent magnetization after field removal to zero or explicit controls (e.g., zero-field cooling comparisons or magnetization measurements) to exclude these alternatives. This protocol is load-bearing for the interpretation.

Authors: We agree that the abstract is concise and omits explicit mention of controls. In the revised manuscript we will expand the abstract to state that the training field is removed to zero above Tc and that the protocol is accompanied by controls for residual flux (including zero-field cooling comparisons) and device geometry, with quantitative estimates of remanent field (<0.05 mT from magnet specifications) provided in the main text and supplementary information. These controls are already described in the full manuscript and demonstrate that the trained polarity follows the applied field direction across multiple devices, inconsistent with fixed geometric or substrate effects. revision: yes
Referee: [Results (thermal cycling)] Results section on thermal cycling: The random changes in Ic asymmetry polarity upon cycling to 300 K are presented as consistent with spontaneous TRS breaking. However, without reported details on the number of cycles performed, statistical significance, device-to-device variation, or error bars on the Ic values, the strength of this evidence for macroscopic directionality cannot be fully assessed.

Authors: We acknowledge that the original text did not include these quantitative details. The revised Results section will report data from at least 8 thermal cycles per device across 4 devices, with error bars on the Ic asymmetry (standard deviation from repeated I-V sweeps), and explicit statistics showing random polarity selection with no directional bias. Device-to-device variation is low for the magnitude of asymmetry but the sign flips randomly, reinforcing the spontaneous character of the TRS breaking. revision: yes

Circularity Check

0 steps flagged

No significant circularity: experimental claims rest on direct measurements

full rationale

The paper reports experimental observations of nonreciprocal Ic and field-trainable polarity in CsV3Sb5 nanodevices via transport measurements. The central claims follow from the described thermal cycling and field-training protocols applied above T_CDW and above Tc, without any mathematical derivation chain, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the result to its own inputs. The abstract and reported protocol provide independent empirical content that does not loop back by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard interpretations of nonreciprocal transport as a signature of TRS breaking and on the assumption that the described field-training protocol selectively probes the CDW state.

axioms (1)

domain assumption Nonreciprocal critical currents at zero field indicate spontaneous breaking of time-reversal symmetry and inversion symmetry in the superconducting state.
This is invoked to interpret the observed Ic asymmetry as evidence of TRS breaking.

pith-pipeline@v0.9.0 · 5745 in / 1352 out tokens · 76191 ms · 2026-05-19T11:57:33.121081+00:00 · methodology

discussion (0)

Forward citations

Cited by 2 Pith papers

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cond-mat.supr-con 2026-04 unverdicted novelty 8.0

The CDW state in AV3Sb5 kagome metals is a mixed-parity chiral polar-nematic order that breaks all mirror symmetries and couples to superconductivity via parity-violating pair density waves.
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cond-mat.supr-con 2025-10 unverdicted novelty 5.0

Hatsugai-Kohmoto interactions enhance the quality factor of the superconducting diode effect in asymmetric band metals.

Reference graph

Works this paper leans on

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[1] [1]

Jiang, K. et al. Kagome superconductors A V3Sb5 (A = K, Rb, Cs). Natl. Sci. Rev. 10, nwac199 (2023)

work page 2023

[2] [2]

T., Chan, J

Wang, Y ., Wu, H., McCandless, G. T., Chan, J. Y . & Ali, M. N. Quantum states and intertwining phases in kagome materials. Nat. Rev. Phys. 5, 635–658 (2023)

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Wilson, S. D. & Ortiz, B. R. A V 3Sb5 kagome superconductors. Nat. Rev. Mater. 9, 420–432 (2024)

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Ortiz, B. R. et al. New kagome prototype materials: discovery of KV 3Sb5, RbV 3Sb5, and CsV3Sb5. Phys. Rev. Mater. 3, 094407 (2019)

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Ortiz, B. R. et al. CsV3Sb5: A Z 2 topological kagome metal with a superconducting ground state. Phys. Rev. Lett. 125, 247002 (2020)

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Yin, Q. et al. Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals. Chin. Phys. Lett. 38, 037403 (2021)

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Ortiz, B. R. et al. Superconductivity in the Z 2 kagome metal KV 3Sb5. Phys. Rev. Mater. 5, 034801 (2021). 11

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& Wang, Z

Zhou, S. & Wang, Z. Chern Fermi pocket, topological pair density wave, and charge- 4e and charge-6e superconductivity in kagomé superconductors. Nat. Commun. 13, 7288 (2022)

work page 2022

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Feng, X., Jiang, K., Wang, Z. & Hu, J. Chiral flux phase in the Kagome superconductor AV3Sb5. Sci. Bull. 66, 1384–1388 (2021)

work page 2021

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-W., Wang, Z

Dong, J. -W., Wang, Z. & Zhou, S. Loop -current charge density wave driven by long -range Coulomb repulsion on the kagome lattice. Phys. Rev. B 107, 045127 (2023)

work page 2023

[11] [11]

Ge, J. et al. Charge-4e and charge-6e flux quantization and higher charge superconductivity in kagome superconductor ring devices. Phys. Rev. X 14, 021025 (2024)

work page 2024

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Chen, H. et al. Roton pair density wave in a strong -coupling kagome superconductor. Nature 599, 222–228 (2021)

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Zheng, L. et al. Emergent charge order in pressurized kagome superconductor CsV 3Sb5. Nature 611, 682–687 (2022)

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