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arxiv: 2605.16943 · v1 · pith:3CSDW6Y2new · submitted 2026-05-16 · ❄️ cond-mat.supr-con

Nonreciprocal impurity scattering as a probe for pairing symmetries in kagome superconductors

Hong-Min Jiang , Hao Du , Shun-Li Yu This is my paper

Pith reviewed 2026-05-19 18:57 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords kagome superconductorspairing symmetrytime-reversal symmetry breakingYu-Shiba-Rusinov statesimpurity scatteringscanning tunneling microscopynonreciprocal scattering
0
0 comments X

The pith

Two magnetic impurities produce distinct spectral patterns that identify time-reversal symmetry breaking in kagome superconductor pairings.

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

The paper establishes that local density of states measurements around two magnetic impurities can differentiate between conventional s-wave and time-reversal symmetry breaking d plus id pairings in kagome superconductors. For s-wave, time-reversal symmetry causes equivalent scattering in forward and backward directions for any impurity placement, resulting in the near disappearance of a pair of Yu-Shiba-Rusinov states along the line between them. For the d plus id case, this equivalence and state disappearance is limited to inversion-symmetric configurations only. These differences are detectable via scanning tunneling microscopy and provide a probe for pairing symmetry that avoids issues with sublattice interference and charge-density-wave entanglement.

Core claim

Using representative models of on-site s-wave and TRSB d_x2-y2 + i d_xy-wave pairings, the authors demonstrate that while single magnetic impurities yield similar LDOS for both, two impurities lead to distinct patterns. Time-reversal symmetry in s-wave pairing enforces equivalent forward and backward scattering for all configurations, causing YSR state pair disappearance along the impurity connecting line. In the TRSB pairing, this holds only for inversion-symmetric configurations.

What carries the argument

Nonreciprocal impurity scattering arising from broken time-reversal symmetry, manifested in the configuration-dependent equivalence of scattering directions between two magnetic impurities.

If this is right

  • Distinct LDOS patterns from two impurities are resolvable in STM experiments for different pairings.
  • Provides a direct method to discriminate TRSB and non-TRSB superconducting pairing symmetries in kagome materials.
  • Offers an alternative probe of superconducting nonreciprocity that circumvents ambiguities in conventional critical current techniques.
  • Addresses ambiguities from sublattice interference and CDW entanglement with superconductivity.

Where Pith is reading between the lines

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

  • This approach may help resolve pairing symmetry questions in other vanadium-based or kagome systems.
  • Could be tested by varying impurity distances and positions in actual STM experiments.
  • Implies that nonreciprocity in scattering can serve as a general signature of TRSB in superconductors.
  • Extensions might include considering non-magnetic impurities or lattice effects for more realistic models.

Load-bearing premise

The on-site s-wave and d plus id pairings are representative of the pairings in the actual kagome materials, and magnetic exchange dominates the impurity scattering.

What would settle it

STM observation of whether YSR state pairs disappear for all two-impurity configurations or only for inversion-symmetric ones would confirm or refute the distinction between the pairings.

Figures

Figures reproduced from arXiv: 2605.16943 by Hao Du, Hong-Min Jiang, Shun-Li Yu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Structure of the kagome lattice with lattice vect [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Solid curves in panels (a) and (b) show the LDOS at [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Contributions of impurities to the LDOS at the mid [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Contributions of impurities to the LDOS on intersti [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Contributions of impurities to the LDOS for the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

The superconducting (SC) pairing symmetry and its link to time-reversal symmetry breaking (TRSB) in the vanadium-based kagome superconductors remain unresolved, with ambiguities stemming from sublattice interference and charge-density-wave (CDW) entanglement with superconductivity. Using two representative SC pairings, i.e., the conventional on-site $s$-wave and the TRSB $d_{x^2-y^2}+id_{xy}$-wave, as a model study, we theoretically show that while single magnetic impurity yield qualitatively identical spectral behavior of local density of states (LDOS) for these two symmetries, two magnetic impurities give rise to distinct LDOS patterns. For the conventional on-site $s$-wave pairing, time-reversal symmetry (TRS) enforces equivalent forward and backward scattering between two impurities across all impurity configurations, leading to near disappearance of a Yu-Shiba-Rusinov (YSR) state pair along the line connecting the two impurities. However, for the TRSB $d_{x^2-y^2}+id_{xy}$-wave pairing, this scattering equivalence holds only for inversion-symmetric impurity configurations, with a pair of YSR disappearance restricted to this case. These distinct spectral features are resolvable in scanning tunneling microscopy (STM) experiments, providing a direct avenue to discriminate TRSB and non-TRSB SC pairing symmetries in kagome superconductors and an alternative method to probe SC nonreciprocity that circumvents the ambiguities of conventional critical current-based techniques.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a model study of magnetic impurity scattering in kagome superconductors to distinguish pairing symmetries. Using tight-binding BdG Hamiltonians with on-site s-wave and TRSB d_{x^2-y^2}+id_{xy} pairings, single-impurity LDOS spectra are shown to be qualitatively similar, while two-impurity configurations produce distinct patterns: TRS enforces equivalent forward/backward scattering (and consequent near-disappearance of a YSR pair along the connecting line) for all geometries in the s-wave case, but only for inversion-symmetric geometries in the d+id case. These STM-resolvable features are proposed as a discriminator for TRSB versus non-TRSB pairing that circumvents sublattice and CDW ambiguities.

Significance. If the configuration-dependent LDOS distinctions prove robust, the work supplies a concrete, symmetry-based STM protocol for probing pairing symmetry and nonreciprocity in AV3Sb5-type materials, complementing critical-current measurements. The explicit comparison of two representative Hamiltonians without adjustable parameters is a strength.

major comments (2)
  1. [theoretical framework / model Hamiltonian] The model Hamiltonian (defined in the theoretical framework section) employs pure on-site s-wave and d_{x^2-y^2}+id_{xy} pairings without CDW order or sublattice interference. The abstract itself identifies these as sources of ambiguity in the real materials; it is therefore necessary to show that the reported TRS-enforced scattering equivalence and the restriction of YSR disappearance to inversion-symmetric configurations survive the additional scattering channels and band reconstruction introduced by CDW. This directly affects the central claim that the method circumvents those ambiguities.
  2. [two-impurity LDOS calculations] In the two-impurity LDOS results, the forward/backward scattering equivalence is attributed to TRS for s-wave across all configurations but only to inversion symmetry for d+id. An explicit symmetry analysis of the impurity matrix elements on the kagome lattice (including how the d+id phase structure breaks the equivalence for non-inversion geometries) would make the origin of the distinction more transparent and testable.
minor comments (2)
  1. [results / figure captions] The phrase 'near disappearance' of the YSR pair is used repeatedly; a quantitative measure of the residual spectral weight (e.g., integrated intensity or peak height ratio) in the relevant figures would strengthen the presentation.
  2. [methods / computational details] A brief statement on the range of impurity strengths and distances explored would help readers assess how generic the reported patterns are.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript, positive assessment of its significance, and constructive suggestions. We address each major comment below and indicate the revisions we plan to incorporate.

read point-by-point responses

  1. Referee: The model Hamiltonian (defined in the theoretical framework section) employs pure on-site s-wave and d_{x^2-y^2}+id_{xy} pairings without CDW order or sublattice interference. The abstract itself identifies these as sources of ambiguity in the real materials; it is therefore necessary to show that the reported TRS-enforced scattering equivalence and the restriction of YSR disappearance to inversion-symmetric configurations survive the additional scattering channels and band reconstruction introduced by CDW. This directly affects the central claim that the method circumvents those ambiguities.

    Authors: We appreciate the referee's point that a more complete treatment including CDW order would strengthen applicability to real kagome materials. Our manuscript is explicitly framed as a minimal model study that isolates the role of TRS versus TRSB in the pairing symmetry itself. The central claim is that the resulting configuration-dependent LDOS distinctions provide a symmetry-based discriminator independent of the specific microscopic details that generate ambiguities in other probes. We agree that explicit verification with CDW would be desirable; however, incorporating a specific CDW reconstruction would require additional assumptions about its structure and strength, which themselves remain under debate. We will add a clarifying paragraph in the discussion section emphasizing the scope of the model and arguing that the TRS-enforced equivalence is a general consequence of the pairing symmetry that should remain qualitatively robust against CDW-induced band reconstruction, provided the CDW does not itself break time-reversal symmetry. revision: partial

  2. Referee: In the two-impurity LDOS results, the forward/backward scattering equivalence is attributed to TRS for s-wave across all configurations but only to inversion symmetry for d+id. An explicit symmetry analysis of the impurity matrix elements on the kagome lattice (including how the d+id phase structure breaks the equivalence for non-inversion geometries) would make the origin of the distinction more transparent and testable.

    Authors: We agree that an explicit symmetry analysis would enhance the clarity and testability of the reported distinction. In the revised manuscript we will insert a new subsection (or expanded paragraph within the theoretical framework) that analyzes the impurity scattering matrix elements under the point-group symmetries of the kagome lattice. This will explicitly demonstrate how time-reversal symmetry enforces forward/backward equivalence for arbitrary impurity separations in the s-wave case, while the momentum-dependent phase winding of the d+id pairing lifts this equivalence except when the impurity pair is related by inversion. We expect this addition to make the microscopic origin of the LDOS patterns more transparent without altering the numerical results. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit model comparison of independent BdG Hamiltonians

full rationale

The paper computes LDOS spectra from two distinct tight-binding BdG Hamiltonians, one for on-site s-wave pairing and one for TRSB d_{x^2-y^2}+id_{xy} pairing. The reported distinction—that TRS enforces forward/backward scattering equivalence (and YSR-pair disappearance) for all two-impurity geometries in the s-wave case but only inversion-symmetric geometries in the d+id case—follows directly from solving the impurity scattering problem in each Hamiltonian separately. No parameters are fitted to data and then presented as predictions, no self-citations supply load-bearing uniqueness theorems, and no ansatz is smuggled in. The derivation remains self-contained within the stated model assumptions and explicit symmetry analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the two chosen model pairings capture the essential physics and that magnetic impurities interact primarily via exchange with the superconducting condensate.

axioms (1)
  • domain assumption The superconducting state can be modeled by either on-site s-wave or d+id pairing on the kagome lattice.
    Stated in the abstract as the two representative pairings used for the model study.

pith-pipeline@v0.9.0 · 5801 in / 1117 out tokens · 26499 ms · 2026-05-19T18:57:02.466691+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Using two representative SC pairings, i.e., the conventional on-site s-wave and the TRSB d_{x^2-y^2}+id_{xy}-wave, as a model study, we theoretically show that while single magnetic impurity yield qualitatively identical spectral behavior of local density of states (LDOS) for these two symmetries, two magnetic impurities give rise to distinct LDOS patterns.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    For the conventional on-site s-wave pairing, time-reversal symmetry (TRS) enforces equivalent forward and backward scattering between two impurities across all impurity configurations

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Reference graph

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