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Probing crystal-field modulations with magnetic adatoms on the incipient charge-density-wave superconductor $2H$-NbS$_2$

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper uses individual Fe adatoms as movable atomic-scale sensors to show that Yu-Shiba-Rusinov excitation energies vary strongly across 225 crystallographically equivalent hollow sites on 2H-NbS2, and argues that the dominant cause is…

desk verdict A careful, genuinely new YSR sensor map on 2H-NbS2 whose interpretation is broader than its exclusion argument strictly supports, but the authors know it and the measurement is worth refereeing. read the letter →

arxiv 2608.09753 v1 pith:NFN7QZT6 submitted 2026-08-10 cond-mat.mes-hall cond-mat.supr-con

Werner M.J. van Weerdenburg , Margarete Huisinga , Constantin Flommersfeld , Lisa M. Rütten , Katharina J. Franke This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.supr-con
keywords Yu-Shiba-Rusinovstates2H-NbS2crystal-fieldmodulationscanningtunnelingmicroscopyatommanipulationincipientcharge-density-waveexchangecouplinglatticedistortion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that a single magnetic iron atom can act as an atomic-scale probe of hidden crystal-field variations in the superconductor 2H-NbS2, a material sitting on the verge of a charge-density-wave transition. By dragging one Fe atom across 225 equivalent hollow sites with an STM tip, the authors find that the energy of its strongest Yu-Shiba-Rusinov excitation moves between 0.10 meV and 0.49 meV even though the superconducting gap, the Josephson conductance, and the local density of states remain nearly uniform. They argue by elimination, ruling out gap variations, LDOS modulations, and potential scattering, that the shifts come from site-dependent exchange coupling, which reports local changes in the crystal field. The conclusion matters because it implies that intrinsic point defects reshape the lattice over nanometer scales in a material close to a CDW instability, and that mobile magnetic atoms are a general sensor for such distortions.

What carries the argument

The central object is the Yu-Shiba-Rusinov (YSR) bound state, the sub-gap excitation formed when a magnetic impurity exchange-couples to a superconductor. Its energy is described by the classical-spin formula $\epsilon_{YSR} = \Delta(1-A^2+B^2)/\sqrt{(1-A^2+B^2)^2+4A^2}$, where $A = \tfrac{1}{2}\pi S\rho_0 J$ is the exchange coupling and $B = \pi\rho_0 K$ is the potential scattering. This formula ties the excitation energy to the superconducting gap $\Delta$, the normal-state density of states $\rho_0$, the potential-scattering coefficient $K$, and the exchange coupling $J$. The measurement protocol, moving one Fe atom to 225 equivalent hollow sites, deconvolving the superconducting-tip spectra, and Gaussian-fitting the gamma resonance, turns the formula into a site-resolved sensor: after independently bounding $\Delta$, $\rho_0$, and $K$, the residual energy shifts are attributed to $J$, meaning the crystal-field environment.

What would settle it

The central claim would be falsified if an Fe atom shuttled across 225 equivalent sites in a region verified to be free of surface and subsurface defects still showed the same roughly 0.39 meV spread in gamma-state energy, since the proposed cause, defect-induced lattice relaxation, would be absent.

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Extended reading notes

Core claim

The central claim is that the spatial variation of Yu-Shiba-Rusinov excitation energy for Fe atoms on 2H-NbS2 is dominated by variations in the local crystal-field environment, not by any electronic inhomogeneity of the superconducting state. The evidence is a manipulation experiment: one Fe atom placed on 225 equivalent hollow sites shows gamma-state energies spanning about 70 percent of the inner superconducting gap, with the defect site giving the lowest energies but significant shifts appearing nanometers away. The experimental controls exclude the standard alternatives: the two-gap BCS spectrum is spatially homogeneous, the Josephson conductance is uniform, the Fermi-level dI/dV signal varies by only about five percent with no correlation to the YSR energy, and the YSR intensity asymmetry shows no potential-scattering trend. What remains is a spatially varying exchange coupling, and since that coupling is set by the overlap of the adatom d-orbitals with the surrounding crystal field, the paper concludes that the lattice is locally distorted around defects, most plausibly through small displacements of Nb atoms, consistent with the soft phonon physics that places 2H-NbS2 near a CDW instability.

Load-bearing premise

The load-bearing premise is that the classical single-spin YSR formula with one exchange parameter $J$ adequately describes a multiorbital Fe atom that actually shows four YSR pairs; if the spin state, magnetic anisotropy, or multiorbital structure changes from site to site in ways not captured by the LDOS and asymmetry checks, the residual variation need not be due to crystal-field-modulated exchange coupling.

Editorial extensions

If this is right

  • YSR spectroscopy with manipulated magnetic adatoms becomes a general atomic-resolution probe of crystal-field and strain variations, not just of magnetic coupling.
  • Regions that appear flat and defect-free in topography can still host substantial lattice relaxation, so standard STM imaging underestimates structural heterogeneity in incipient CDW materials.
  • The defect response of 2H-NbS2 encodes its proximity to a CDW instability: local lattice relaxations around sulfur vacancies behave like nanoscale precursors of the charge-density-wave distortion.
  • Because the $d_{z^2}$-derived gamma state is the most sensitive channel, the method offers orbital selectivity: different YSR multiplets can report on different crystal-field components.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A quantitative step would be to convert measured YSR energy shifts into displacements: first-principles calculations of the exchange coupling $J$ as a function of Nb atomic positions could calibrate the sensor in picometers, something the paper does not do.
  • The same manipulation protocol could be applied near step edges, grain boundaries, or artificial defect arrays to separate long-range elastic relaxation from electronic scattering, testing whether the inferred distortions are purely defect-induced.
  • If the observed site-to-site spread scales with the density of surface and subsurface sulfur vacancies across different crystals, that would confirm the long-range lattice-relaxation scenario; if it persists in extremely clean regions, the origin would need revision.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript reports an STM atom-manipulation study in which an individual Fe adatom is placed on 225 nominally equivalent hollow sites of 2H-NbS2 and probed with Yu-Shiba-Rusinov (YSR) spectroscopy using a superconducting V tip. The authors find that the energy of the strongest YSR state (γ) varies between 0.10 meV and 0.49 meV across the map, while the superconducting gap, Josephson conductance, and local-density-of-states maps appear uniform or uncorrelated with the variation. After ruling out spatial variations of Δ, the bare-surface LDOS, and potential-scattering asymmetry, they conclude that the residual variation is dominated by spatial changes of the exchange coupling J, which they interpret as crystal-field modulations caused by defect-induced displacements of Nb atoms. They propose the method as a new atomic-scale probe of hidden lattice distortions in an incipient charge-density-wave material.

Significance. If the central attribution is correct, the paper introduces a genuinely new and highly sensitive probe of atomic-scale crystal-field modulations, with potential applicability to incipient-CDW and incipient-ferroelectric materials. The experimental work is substantial: 225 binding sites are measured; the tip-position control yields a standard deviation of 3 μeV; z-dependent spectroscopy shows that peak positions do not shift with tip height; the superconducting gap and Josephson conductance are checked for uniformity; and the deconvolution procedure is validated against the raw spectra. These controls make the raw observation—a large, position-dependent spread of εγ—very credible. However, the inference from that observation to exchange-coupling variations and Nb displacements rests on a model assumption that is not justified for the multiorbital Fe sensor. The significance is therefore conditional: the sensing method and the observation are likely to be valuable, but the specific physical interpretation needs either additional theoretical support or an explicit softening.

major comments (3)
  1. [§II C, Eq. (1)] The exclusion argument is built on Eq. (1), the classical single-spin YSR formula. However, the Fe sensor is introduced in §II B as a multiorbital impurity with four YSR pairs (α–δ) arising from crystal-field-split d orbitals, with the γ state assigned to dz2. For such an impurity, the energy of the γ resonance is set by the full impurity spin Hamiltonian (S, magnetic anisotropy, spin–orbit coupling) and by orbital-dependent hybridizations, not by the single product Sρ0J that appears in Eq. (1). Consequently, site-to-site changes in the Fe spin state, magnetic anisotropy, or orbital occupation—all crystal-field effects in a broad sense—could produce the observed 0.10–0.49 meV spread in εγ even if the scalar exchange coupling J were constant. The paper neither measures S or the anisotropy at each binding site nor fits a multiorbital model. The conclusion that the residual variation is dominated by exchange-coupling changes and, further, by Nb displacements is therefore not established by the presented exclusion analysis. I recommend either adding a model or calculation that justifies the single-spin reduction for the γ state, or softening the claim to 'variations in the local crystal-field environment' and explicitly labeling the Nb-displacement interpretation as speculative.
  2. [§II C, Fig. 3d and Fig. S8] The LDOS-uncorrelation test uses dI/dV maps of the bare surface at Fe-free hollow sites. The quantity that enters Eq. (1) is ρ0 at the impurity site in the presence of the adatom, including orbital-specific hybridization between the Fe d states and the substrate. A constant-current topographic/Friedel map at V_bias = 5 mV is not demonstrated to be a faithful proxy for this quantity. While the absence of correlation at eight energies is suggestive, the paper never validates the proxy directly, for example by measuring the LDOS at the Fe position before and after deposition or by checking orbital-resolved YSR maps. This weakens the otherwise careful exclusion of the ρ0 term.
  3. [§II C, Fig. 4c,d] The potential-scattering exclusion is also model-dependent. In the classical formula, the asymmetry of the two YSR peaks is governed by B = πρ0K; for a multiorbital impurity with several YSR pairs, the intensity asymmetry of one orbital-derived state need not map cleanly onto a scalar K, and the observed linewidth has an additional lifetime contribution (Ref. [59]) that is energy dependent. The near-symmetric A_YSR and the small variation of Γ_YSR are reasonable qualitative evidence, but they do not close the exclusion in the same quantitative way that the text implies.
minor comments (5)
  1. [Fig. S2 caption] The caption says the dI/dV maps were recorded at V_bias = −200 mV and −200 mV; the second value should presumably be +200 mV.
  2. [Eq. (1) and Fig. 4c] The symbol B is used for the potential-scattering parameter in Eq. (1), while A_YSR denotes the measured YSR intensity asymmetry in Fig. 4c; this notation is confusing and should be changed to avoid implying that A_YSR is the same A as in Eq. (1).
  3. [Fig. S4 and §S3 B] The deconvolution parameters (Δ_tip, Γ) are given for one representative spectrum; please state explicitly whether the same values were used for all 225 spectra and how any drift or tip changes over the long measurement sequence were handled.
  4. [Fig. 4a] Some binding sites show only three scatter points because a state is degenerate or too weak to fit; please state how unresolved states were treated in the Gaussian fitting and whether the sorting of binding sites by εγ is affected by this.
  5. [§S2, first paragraph] The sentence 'we still found a varying sample quality, depending on the cleave and positioning of the tip on the crystal' should be rephrased, since sample quality cannot depend on tip positioning; the intended meaning is presumably the choice of measurement area on the cleaved surface.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction: the YSR energy map is a direct measurement, and the crystal-field attribution is a residual after independent exclusion of superconducting-gap, LDOS, and potential-scattering contributions.

full rationale

The derivation chain is not circular. The central observable, epsilon_gamma, is extracted directly from measured dI/dV spectra after a deconvolution whose validity is checked against the data and against a tip-position control (sigma = 3 micro-eV). The spatial variation is not a fitted parameter; it is the raw input. The attribution of the variation to the exchange coupling J is an exclusion argument: the superconducting gap is shown to be uniform by gap spectroscopy and Josephson maps; the local density of states is measured at multiple energies and shows no correlation with epsilon_gamma; and potential scattering is assessed via YSR asymmetry and linewidth and found to be too small. None of these exclusions is equivalent to assuming the conclusion, and each uses an independent measurement. The final step from 'J varies' to 'crystal-field/lattice modulations' is an interpretive causal claim, not a definitional identity: the paper does not define crystal-field modulations as YSR-energy shifts, but connects them through wavefunction-overlap physics. The multiorbital nature of the Fe atom is a genuine model limitation because the classical Eq. (1) may miss spin-state or magnetic-anisotropy effects, but that is a correctness risk, not a circular reduction. Self-citations, including Refs. [45] and [57], support the Fe binding-site and orbital assignments, but the exclusion argument does not depend on them; even if the dz2 assignment were incorrect, the residual-variation conclusion would still follow from the measured uniformities of the gap, LDOS, and potential-scattering proxies. Therefore, no load-bearing circular step is present; the score reflects only minor, non-load-bearing self-citations.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles, mediators, forces, or conserved quantities. The hypothesized Nb displacements are a physical scenario inferred from the data rather than a new entity; no independent falsifiable handle beyond the YSR shifts themselves is provided. The central claim depends on the four free parameters and assumptions listed above, most notably the adequacy of the classical-spin YSR model and the fidelity of the LDOS proxy.

free parameters (4)
  • Delta_tip (superconducting tip gap) = approx. 0.74 meV
    Used in numerical deconvolution of YSR spectra (Fig. S4); fitted to minimize difference between experimental and calculated spectra. Uncertainties in this value propagate into absolute epsilon_gamma, though the paper argues the relative map is robust.
  • Dynes broadening Gamma of the tip = 0.008 meV
    Second deconvolution parameter (Fig. S4), fitted together with Delta_tip. Affects peak widths and positions in the extracted sample DOS.
  • Superconducting gaps Delta1, Delta2 of 2H-NbS2 = 0.60 +/- 0.04 and 0.84 +/- 0.03 meV
    Dynes-broadened two-gap fit in Fig. 1c. Used only to characterize the uniform superconducting state, not to derive the central YSR-variation claim.
  • Gaussian peak fit parameters for YSR states = per spectrum
    Each deconvolved spectrum is fitted with multiple Gaussian profiles to extract epsilon_gamma (Fig. 2d). The extracted epsilon_gamma is the measured observable, but systematic uncertainties from fitting are not propagated to the 225-site map.
assumptions (4)
  • domain assumption Classical single-spin YSR formula (Eq. 1) applies to the multiorbital Fe adatom with four YSR pairs.
    The paper uses Eq. (1) (epsilon = Delta (1-A^2+B^2)/sqrt((1-A^2+B^2)^2+4A^2)) to enumerate the parameters that can shift the YSR energy. Real Fe on NbS2 exhibits four YSR pairs from crystal-field-split d-levels, and the single-spin model is assumed to be adequate for the residual analysis in Section II.C.
  • domain assumption dI/dV at V_bias = 5 mV is a faithful proxy for the Fermi-level LDOS at the adatom position.
    Used in Section II.C and Fig. 3d/S7 to rule out LDOS variations as the cause of the epsilon_gamma map. A wider energy window is checked, but the 5 mV proxy is the primary comparison, and the relevant LDOS at the adatom (including hybridization) is not directly measured.
  • domain assumption The two hollow adsorption sites (FeA and FeB) are reliably distinguishable, and all 225 probed sites belong to the FeA type.
    Section S3A distinguishes the sites by YSR fingerprint. If a moved atom were misassigned or switched between FeA and FeB during the campaign, the apparent epsilon_gamma variation would partly reflect site-type differences rather than continuous crystal-field modulations.
  • domain assumption Tip-induced effects (position, height, deconvolution) do not shift the extracted YSR energy by more than about 3 micro-eV.
    Control in Fig. S6 gives sigma = 3 micro-eV for tip position and no shift with tip-sample distance over 1 Angstrom. The assumption is that this bound holds across all 225 sites and repeated manipulations, which underlies the claim that the 0.10 to 0.49 meV variation is intrinsic to the sample.

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Pith. "Pith review of Probing crystal-field modulations with magnetic adatoms on the incipient charge-density-wave superconductor $2H$-NbS$_2$." pith.science (2026). https://pith.science/paper/NFN7QZT6

@misc{pith2026260809753,
  author       = {Pith},
  title        = {Pith review of: Probing crystal-field modulations with magnetic adatoms on the incipient charge-density-wave superconductor $2H$-NbS$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NFN7QZT6}},
  note         = {Machine review of arXiv:2608.09753}
}
abstract

The interplay between multiple quantum phases in layered materials may lead to incipient quantum behavior, where the material's ground state is close to a phase transition and sensitive to local disorder. The transition metal dichalcogenide material $2H$-NbS$_2$ exhibits incipient charge-density-wave behavior along with a well-developed superconducting state, creating a scenario where the local lattice instabilities play a crucial role. Here we present how an individual magnetic atom on $2H$-NbS$_2$ can be applied as a local sensor to reveal hidden crystal-field modulations. By manipulating the adatom across the surface with the tip of a scanning tunneling microscope, we measure variations in the Yu-Shiba-Rusinov (YSR) excitation spectra and map the local environment around an intrinsic point defect. We find that while the superconducting state is spatially uniform, the YSR excitation energy strongly depends on the position of the atom. We determine that the main contribution to this effect originates from variations in the local crystal-field environment. These results establish a new approach to investigate crystal-field modulations at the atomic scale and reveal how defects and lattice instabilities shape the atomic landscape of an incipient charge-density-wave material.

Figures

Figures reproduced from arXiv: 2608.09753 by the authors.

Figure 1
Figure 1. FIG. 1. Superconductivity and intrinsic defects of 2 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Yu-Shiba-Rusinov states of an individual Fe atom [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Spatial variation of Yu-Shiba-Rusinov energies on 2 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Yu-Shiba-Rusinov state variation. a) Scatter plot [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Works this paper leans on

64 extracted references · 57 canonical work pages

  1. [59]

    M. Ruby, F. Pientka, Y. Peng, F. von Oppen, B. W. Hein- rich, and K. J. Franke, Tunneling Processes into Local- ized Subgap States in Superconductors, Phys. Rev. Lett. 115, 087001 (2015)

    work page 2015

  2. [1]

    Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3Oy

    J. Chang, E. Blackburn, A. T. Holmes, N. B. Chris- tensen, J. Larsen, J. Mesot, R. Liang, D. A. Bonn, W. N. Hardy, A. Watenphul, M. V. Zimmermann, E. M. Forgan, and S. M. Hayden, Direct observation of competition be- tween superconductivity and charge density wave order in YBa2Cu3O6.67, Nat. Phys.8, 871 (2012), 1206.4333

    work page Pith review arXiv 2012

  3. [2]

    Y. Wang, H. Wu, G. T. McCandless, J. Y. Chan, and M. N. Ali, Quantum states and intertwining phases in kagome materials, Nature Reviews Physics5, 635 (2023)

    2023

  4. [3]

    Suderow, V

    H. Suderow, V. G. Tissen, J. P. Brison, J. L. Mart ´ ınez, and S. Vieira, Pressure Induced Effects on the Fermi Sur- face of Superconducting 2H-NbSe 2, Phys. Rev. Lett.95, 117006 (2005)

    work page 2005

  5. [4]

    T. Kiss, T. Yokoya, A. Chainani, S. Shin, T. Hanaguri, M. Nohara, and H. Takagi, Charge-order-maximized momentum-dependent superconductivity, Nature Phys. 3, 720 (2007)

    work page 2007

  6. [5]

    S. V. Borisenko, A. A. Kordyuk, V. B. Zabolotnyy, D. S. Inosov, D. Evtushinsky, B. B¨ uchner, A. N. Yaresko, vii A. Varykhalov, R. Follath, W. Eberhardt, L. Patthey, and H. Berger, Two Energy Gaps and Fermi-Surface “Arcs” in NbSe 2, Phys. Rev. Lett.102, 166402 (2009)

    work page 2009

  7. [6]

    K. Cho, M. Ko´ nczykowski, S. Teknowijoyo, M. A. Tanatar, J. Guss, P. B. Gartin, J. M. Wilde, A. Kreyssig, R. J. McQueeney, A. I. Goldman, V. Mishra, P. J. Hirschfeld, and R. Prozorov, Using controlled disorder to probe the interplay between charge order and super- conductivity in NbSe2, Nature Commun.9, 2796 (2018)

    work page 2018

  8. [7]

    X. Liu, Y. X. Chong, R. Sharma, and J. C. S. Davis, Dis- covery of a Cooper-pair density wave state in a transition- metal dichalcogenide, Science372, 1447 (2021)

    work page 2021

Show all 64 references
  1. [8]

    Aishwarya, J

    A. Aishwarya, J. May-Mann, A. Raghavan, L. Nie, M. Romanelli, S. Ran, S. R. Saha, J. Paglione, N. P. Butch, E. Fradkin, and V. Madhavan, Magnetic-field- sensitive charge density waves in the superconductor UTe2, Nature618, 928 (2023)

    2023

  2. [9]

    Q. Gu, J. P. Carroll, S. Wang, S. Ran, C. Broyles, H. Sid- diquee, N. P. Butch, S. R. Saha, J. Paglione, J. C. S. Davis, and X. Liu, Detection of a pair density wave state in UTe2, Nature618, 921 (2023)

    2023

  3. [10]

    Y. Liu, T. Wei, G. He, Y. Zhang, Z. Wang, and J. Wang, Pair density wave state in a monolayer high-T c iron- based superconductor, Nature618, 934 (2023)

    2023

  4. [11]

    Sokolovi´ c, M

    I. Sokolovi´ c, M. Schmid, U. Diebold, and M. Setvin, In- cipient ferroelectricity: A route towards bulk-terminated SrTiO3, Phys. Rev. Mater.3, 034407 (2019)

    2019

  5. [12]

    C. Guo, G. Wagner, C. Putzke, D. Chen, K. Wang, L. Zhang, M. Gutierrez-Amigo, I. Errea, M. G. Vergniory, C. Felser, M. H. Fischer, T. Neupert, and P. J. W. Moll, Correlated order at the tipping point in the kagome metal CsV3Sb5, Nature Physics20, 579 (2024)

    2024

  6. [13]

    Xiang, H

    Z. Xiang, H. Li, J. Xiao, M. H. Naik, Z. Ge, Z. He, S. Chen, J. Nie, S. Li, Y. Jiang, R. Sailus, R. Baner- jee, T. Taniguchi, K. Watanabe, S. Tongay, S. G. Louie, M. F. Crommie, and F. Wang, Imaging quantum melting in a disordered 2D Wigner solid, Science388, 736 (2025)

    2025

  7. [14]

    Z. Ge, C. Smith, Z. He, Y. Yang, Q. Li, H.-L. Kim, Z. Xiang, J. Xiao, W. Zhou, S. Kahn, A. Hu, M. Erdi, R. Banerjee, T. Taniguchi, K. Watanabe, S. A. Tongay, M. A. Morales, S. Zhang, F. Wang, and M. F. Crom- mie, Visualizing the impact of quenched disorder on 2D electron Wigne...

    2026

  8. [15]

    Rossnagel, O

    K. Rossnagel, O. Seifarth, L. Kipp, M. Skibowski, D. Voß, P. Kr¨ uger, A. Mazur, and J. Pollmann, Fermi surface of 2H-NbSe 2 and its implications on the charge- density-wave mechanism, Phys. Rev. B64, 235119 (2001)

    2001

  9. [16]

    M. D. Johannes, I. I. Mazin, and C. A. Howells, Fermi- surface nesting and the origin of the charge-density wave in NbSe2, Phys. Rev. B73, 205102 (2006)

    2006

  10. [17]

    C. J. Arguello, E. P. Rosenthal, E. F. Andrade, W. Jin, P. C. Yeh, N. Zaki, S. Jia, R. J. Cava, R. M. Fernan- des, A. J. Millis, T. Valla, R. M. Osgood, and A. N. Pasupathy, Quasiparticle Interference, Quasiparticle In- teractions, and the Origin of the Charge Density Wave in ...

    2015

  11. [18]

    Yokoya, T

    T. Yokoya, T. Kiss, A. Chainani, S. Shin, M. Nohara, and H. Takagi, Fermi Surface Sheet-Dependent Super- conductivity in 2H-NbSe 2, Science294, 2518 (2001)

    2001

  12. [19]

    Rodrigo and S

    J. Rodrigo and S. Vieira, STM study of multiband su- perconductivity in NbSe 2 using a superconducting tip, Physica C: Superconductivity404, 306 (2004)

    2004

  13. [20]

    Y. Noat, T. Cren, F. Debontridder, D. Roditchev, W. Sacks, P. Toulemonde, and A. San Miguel, Signatures of multigap superconductivity in tunneling spectroscopy, Phys. Rev. B82, 014531 (2010)

    2010

  14. [21]

    Y. Noat, J. A. Silva-Guill´ en, T. Cren, V. Cherkez, C. Brun, S. Pons, F. Debontridder, D. Roditchev, W. Sacks, L. Cario, P. Ordej´ on, A. Garc ´ ıa, and E. Canadell, Quasiparticle spectra of 2H-NbSe 2: Two- band superconductivity and the role of tunneling selec- tivity, Phys....

    2015

  15. [22]

    Sanna, C

    A. Sanna, C. Pellegrini, E. Liebhaber, K. Rossnagel, K. J. Franke, and E. K. U. Gross, Real-space anisotropy of the superconducting gap in the charge-density wave material 2H-NbSe 2, npj Quantum Materials7, 6 (2022)

    2022

  16. [23]

    E. Oh, G. Gye, and H. W. Yeom, Defect-Selective Charge-Density-Wave Condensation in 2H-NbSe2, Phys. Rev. Lett.125, 036804 (2020)

    2020

  17. [24]

    Sheng, M

    S. Sheng, M. Abdo, S. Rolf-Pissarczyk, K. Lichtenberg, S. Baumann, J. A. J. Burgess, L. Malavolti, and S. Loth, Terahertz spectroscopy of collective charge density wave dynamics at the atomic scale, Nature Physics20, 1603 (2024)

    2024

  18. [25]

    L. M. R¨ utten, E. Liebhaber, K. Rossnagel, and K. J. Franke, Charge-Density-Wave Control by Adatom Ma- nipulation and Its Effect on Magnetic Nanostructures, Nano Lett.25, 115 (2025)

    2025

  19. [26]

    L. Cao, Y. Xue, Y. Wang, F.-C. Zhang, J. Kang, H.- J. Gao, J. Mao, and Y. Jiang, Directly visualizing ne- matic superconductivity driven by the pair density wave in NbSe2, Nature Commun.15, 7234 (2024)

    2024

  20. [27]

    Machida, T

    K. Machida, T. K¯ oyama, and T. Matsubara, Theory of charge-density-wave superconductors, Phys. Rev. B23, 99 (1981)

    1981

  21. [28]

    W. G. Fisher and M. J. Sienko, Stoichiometry, struc- ture, and physical properties of niobium disulfide, Inorg. Chem.19, 39 (1980)

    1980

  22. [29]

    Leroux, M

    M. Leroux, M. Le Tacon, M. Calandra, L. Cario, M.- A. M´ easson, P. Diener, E. Borrissenko, A. Bosak, and P. Rodi` ere, Anharmonic suppression of charge density waves in 2H-NbS 2, Phys. Rev. B86, 155125 (2012)

    2012

  23. [30]

    Guillam´ on, H

    I. Guillam´ on, H. Suderow, S. Vieira, L. Cario, P. Diener, and P. Rodi` ere, Superconducting Density of States and Vortex Cores of 2H-NbS 2, Phys. Rev. Lett.101, 166407 (2008)

    2008

  24. [31]

    Suzuki and H

    M.-T. Suzuki and H. Harima, Electronic band structures and charge density wave of 2H-MX2(M=Nb,Ta,X=S,Se), Physica B: Cond. Matt.359-361, 1180 (2005)

    2005

  25. [32]

    Majumdar, D

    A. Majumdar, D. VanGennep, J. Brisbois, D. Chareev, A. V. Sadakov, A. S. Usoltsev, M. Mito, A. V. Silhanek, T. Sarkar, A. Hassan, O. Karis, R. Ahuja, and M. Abdel- Hafiez, Interplay of charge density wave and multiband superconductivity in layered quasi-two-dimensional ma- ter...

    2020

  26. [33]

    C. Heil, S. Ponc´ e, H. Lambert, M. Schlipf, E. R. Margine, and F. Giustino, Origin of Superconductivity and Latent Charge Density Wave in NbS 2, Phys. Rev. Lett.119, 087003 (2017)

    2017

  27. [34]

    Bianco, I

    R. Bianco, I. Errea, L. Monacelli, M. Calandra, and F. Mauri, Quantum Enhancement of Charge Density Wave in NbS2 in the Two-Dimensional Limit, Nano Lett. 19, 3098 (2019)

    2019

  28. [35]

    C. Wen, Y. Xie, Y. Wu, S. Shen, P. Kong, H. Lian, J. Li, H. Xing, and S. Yan, Impurity-pinned incommensurate viii charge density wave and local phonon excitations in 2H- NbS2, Phys. Rev. B101, 241404 (2020)

    2020

  29. [36]

    Yu, Bound state in superconductors with paramag- netic impurities, Acta Phys

    L. Yu, Bound state in superconductors with paramag- netic impurities, Acta Phys. Sin.21, 75 (1965)

    1965

  30. [37]

    Shiba, Classical spins in superconductors, Prog

    H. Shiba, Classical spins in superconductors, Prog. of Theo. Phys.40, 435 (1968)

    1968

  31. [38]

    A. I. Rusinov, Superconductivity near a Paramagnetic Impurity, ZhETF Pisma Redaktsiiu9, 146 (1968)

    1968

  32. [39]

    K. J. Franke, G. Schulze, and J. I. Pascual, Competition of superconducting phenomena and Kondo screening at the nanoscale, Science332, 940 (2011)

    2011

  33. [40]

    Hatter, B

    N. Hatter, B. W. Heinrich, M. Ruby, J. I. Pascual, and K. J. Franke, Magnetic anisotropy in Shiba bound states across a quantum phase transition, Nat. Commun.6, 8988 (2015)

    2015

  34. [41]

    Cornils, A

    L. Cornils, A. Kamlapure, L. Zhou, S. Pradhan, A. A. Khajetoorians, J. Fransson, J. Wiebe, and R. Wiesendan- ger, Spin-Resolved Spectroscopy of the Yu-Shiba-Rusinov States of Individual Atoms, Phys. Rev. Lett.119, 197002 (2017)

    2017

  35. [42]

    Farinacci, G

    L. Farinacci, G. Ahmadi, G. Reecht, M. Ruby, N. Bog- danoff, O. Peters, B. W. Heinrich, F. von Oppen, and K. J. Franke, Tuning the coupling of an individual mag- netic impurity to a superconductor: Quantum phase transition and transport, Phys. Rev. Lett.121, 196803 (2018)

    2018

  36. [43]

    Malavolti, M

    L. Malavolti, M. Briganti, M. H¨ anze, G. Serrano, I. Cimatti, G. McMurtrie, E. Otero, P. Ohresser, F. Totti, M. Mannini, R. Sessoli, and S. Loth, Tunable Spin- Superconductor Coupling of Spin 1/2 Vanadyl Phthalo- cyanine Molecules, Nano Lett.18, 7955 (2018)

    2018

  37. [44]

    Huang, R

    H. Huang, R. Drost, J. Senkpiel, C. Padurariu, B. Kubala, A. L. Yeyati, J. C. Cuevas, J. Ankerhold, K. Kern, and C. R. Ast, Quantum phase transitions and the role of impurity-substrate hybridization in Yu-Shiba- Rusinov states, Commun. Phys.3, 199 (2020)

    2020

  38. [45]

    Liebhaber, S

    E. Liebhaber, S. Acero Gonz´ alez, R. Baba, G. Reecht, B. W. Heinrich, S. Rohlf, K. Rossnagel, F. von Op- pen, and K. J. Franke, Yu–Shiba–Rusinov States in the Charge-Density Modulated Superconductor NbSe2, Nano Lett.20, 339 (2020)

    2020

  39. [46]

    Kiendl, F

    T. Kiendl, F. von Oppen, and P. W. Brouwer, Effects of nonmagnetic disorder on the energy of Yu-Shiba-Rusinov states, Phys. Rev. B96, 134501 (2017)

    2017

  40. [47]

    S. S. Babkin, A. A. Lyublinskaya, and I. S. Burmistrov, Broadened Yu-Shiba-Rusinov states in dirty supercon- ducting films and heterostructures, Phys. Rev. Res.4, 023202 (2022)

    2022

  41. [48]

    Soumyanarayanan, M

    A. Soumyanarayanan, M. M. Yee, Y. He, J. van Wezel, D. J. Rahn, K. Rossnagel, E. W. Hudson, M. R. Nor- man, and J. E. Hoffman, Quantum phase transition from triangular to stripe charge order in NbSe 2, Proc. Natl. Acad. Sci.110, 1623 (2013)

    2013

  42. [49]

    S. Gao, F. Flicker, R. Sankar, H. Zhao, Z. Ren, B. Rachmilowitz, S. Balachandar, F. Chou, K. S. Burch, Z. Wang, J. van Wezel, and I. Zeljkovic, Atomic-scale strain manipulation of a charge density wave, Proc. Nat. Acad. Sci.115, 6986–6990 (2018)

    2018

  43. [50]

    Zhang, C.-W

    M.-M. Zhang, C.-W. Liao, C. Zhang, Y.-X. Zhao, R.-H. Zhang, L. He, and Q. Zheng, Tunable one-dimensional charge density waves induced by atomic-scale strain, Phys. Rev. B112, L121402 (2025)

    2025

  44. [51]

    R. C. Dynes, V. Narayanamurti, and J. P. Garno, Di- rect measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor, Phys. Rev. Lett.41, 1509 (1978)

    1978

  45. [52]

    M. Ruby, B. W. Heinrich, J. I. Pascual, and K. J. Franke, Experimental Demonstration of a Two-Band Supercon- ducting State for Lead Using Scanning Tunneling Spec- troscopy, Phys. Rev. Lett.114, 157001 (2015)

    2015

  46. [53]

    Hanaguri, Modulation of superconducting properties by the charge density wave at the surface of 2H−NbSe 2, Phys

    T. Hanaguri, Modulation of superconducting properties by the charge density wave at the surface of 2H−NbSe 2, Phys. Rev. Res.8, 013164 (2026)

    2026

  47. [54]

    M. T. Randeria, B. E. Feldman, I. K. Drozdov, and A. Yazdani, Scanning Josephson spectroscopy on the atomic scale, Phys. Rev. B93, 161115 (2016)

    2016

  48. [55]

    Trahms, L

    M. Trahms, L. Melischek, J. F. Steiner, B. Mahendru, I. Tamir, N. Bogdanoff, O. Peters, G. Reecht, C. B. Winkelmann, F. von Oppen, and K. J. Franke, Diode ef- fect in Josephson junctions with a single magnetic atom, Nature615, 628–633 (2023)

    2023

  49. [56]

    M. H. Hamidian, S. D. Edkins, S. H. Joo, A. Kostin, H. Eisaki, S. Uchida, M. J. Lawler, E.-A. Kim, A. P. Mackenzie, K. Fujita, J. Lee, and J. C. S. Davis, Detec- tion of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x, Nature532, 343 (2016)

    2016

  50. [57]

    M. Ruby, Y. Peng, F. von Oppen, B. W. Heinrich, and K. J. Franke, Orbital Picture of Yu-Shiba-Rusinov Mul- tiplets, Phys. Rev. Lett.117, 186801 (2016)

    2016

  51. [58]

    A. V. Balatsky, I. Vekhter, and J. X. Zhu, Impurity- induced states in conventional and unconventional su- perconductors, Rev. Mod. Phys.78, 373 (2006)

    2006

  52. [60]

    C. D. Malliakas and M. G. Kanatzidis, Nb-Nb Interac- tions Define the Charge Density Wave Structure of 2H- NbSe2, J. Am. Chem. Soc.135, 1719 (2013)

    2013

  53. [61]

    C. S. Lian, C. Si, and W. Duan, Unveiling Charge- Density Wave, Superconductivity, and Their Competi- tive Nature in Two-Dimensional NbSe 2, Nano Lett.18, 2924 (2018)

    2018

  54. [62]

    Leroux, L

    M. Leroux, L. Cario, A. Bosak, and P. Rodi` ere, Traces of charge density waves in NbS 2, Phys. Rev. B97, 195140 (2018)

    2018

  55. [63]

    Witteveen, K

    C. Witteveen, K. G´ ornicka, J. Chang, M. M ˚ ansson, T. Klimczuk, and F. O. von Rohr, Polytypism and su- perconductivity in the NbS2 system, Dalton Transactions 50, 3216 (2021)

    2021

  56. [64]

    Amini, L

    M. Amini, L. Yan, O. J. Silveira, A. O. Fumega, V. Vaˇ no, J. L. Lado, S. Kezilebieke, P. Liljeroth, and R. Drost, Atomic-scale probe of molecular magneto-electric cou- pling, arXiv:2512.07489 (2025). ix SUPPLEMENT AL MA TERIAL S1. METHODS All measurements were recorded using ...

    2025

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