Revealing inter-band electron pairing in a superconductor with spin-orbit coupling

Alfredo Levy Yeyati; Carmen Rubio-Verd\'u; Edwin Herrera; F. Sebastian Bergeret; Hermann Suderow; Javier Zald\'ivar; Jon Ortuzar; Jose Ignacio Pascual; Julie Baumard; Miguel Alvarado

REVIEW 3 major objections 6 minor 59 references

Revealing inter-band electron pairing in a superconductor with spin-orbit coupling

T0 review · 3 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Two wavevectors in the Yu-Shiba-Rusinov ripples around vanadium atoms reveal inter-band electron pairing in β-Bi2Pd.

desk verdict Solid YSR-BQPI data and a convincing hybridization model, but the 'inter-band pairing' claim outruns what the model actually shows. read the letter →

arxiv 2502.03326 v1 pith:PHOSKRPC submitted 2025-02-05 cond-mat.mes-hall cond-mat.supr-con

Javier Zaldívar , Jon Ortuzar , Miguel Alvarado , Stefano Trivini , Julie Baumard , Carmen Rubio-Verdú , Edwin Herrera , Hermann Suderow

show 3 more authors

Alfredo Levy Yeyati F. Sebastian Bergeret Jose Ignacio Pascual

This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.supr-con

keywords Yu-Shiba-RusinovstatesBogoliubovquasiparticleinterferenceinter-bandpairingspin-orbitcouplingmulti-bandsuperconductivityβ-Bi2Pdscanningtunnelingmicroscopyhelicalbands

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

The paper sets out to show that the superconductor β-Bi$_2$Pd pairs electrons across different electronic bands, not only within a single band. Its evidence comes from scanning tunneling microscopy images of the Yu-Shiba-Rusinov (YSR) states that vanadium adatoms create inside the superconducting gap: the amplitude of these states ripples away from the impurity with two distinct wavelengths, $0.7$ nm and $3$ nm. In momentum space these ripples appear at $q_1 = 2.2$ nm$^{-1}$ and $q_2 = 8.9$ nm$^{-1}$, matching two of the inter-band scattering vectors seen in the normal state. The paper argues that the only way a single magnetic impurity can generate such oscillations is if the helical surface bands hybridize, and that the observed band selectivity fingerprints Cooper pairs formed from electrons in different bands. If correct, this is direct evidence for a pairing mechanism that mixes singlet and triplet components and gives hybrid pairs a finite momentum.

What carries the argument

The central object is the Bogoliubov quasiparticle interference (BQPI) pattern of Yu-Shiba-Rusinov (YSR) states: the spatial modulation of the sub-gap density of states around a magnetic impurity, read out by Fourier-transforming dI/dV maps. The load-bearing mechanism is spin-conserving inter-band scattering of Bogoliubov quasiparticles between hybridized helical bands. The paper's model Hamiltonian couples two or three helical bands through an inter-band hopping $t$; the analysis shows that for decoupled helical bands the product of Green functions $G_0(x)$ and $G_0(-x)$ cancels the oscillatory part, so no BQPI exists, while finite $t$ generates oscillations with periods set by sums of the Fermi momenta of the original bands, plus corrections of order the ratio of hopping to chemical potential. This mechanism carries the argument because it explains both why only two wavevectors appear and why hybridization, not scattering, is required.

What would settle it

A decisive test would be to measure BQPI around a magnetic adatom whose d orbitals hybridize preferentially with a different band, such as S1: if the inter-band pairing picture is right, the two Fourier components should move to the wavevectors involving S1 (for instance q_E) rather than staying at q_F and q_B. Alternatively, a spin-polarized scanning tunneling measurement could check whether the two interfering quasiparticle branches have the spin helicities assigned to S2-S1 and S2-B2.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the sub-gap YSR states around V adatoms on the Bi-terminated surface of β-Bi$_2$Pd propagate as cross-shaped beams whose Fourier transform contains exactly two square contours, at $q_1$ and $q_2$. Those two vectors coincide with the spin-conserving inter-band scattering vectors $q_F$ (connecting outer surface band S2 to surface band S1) and $q_B$ (connecting S2 to projected bulk band B2), while the third inter-band vector $q_E$ (S1 to B2) is absent. The absence of any intra-band contour confirms the helical spin structure of the bands, since spin conservation forbids intra-band scattering. The authors show with a model Hamiltonian that a single impurity coupled to one helical band produces no real-space oscillations even when an inter-band scattering term is present; oscillations appear only when the bands are hybridized by an inter-band hopping $t$. From the selective participation of S2, they conclude that the vanadium d orbitals hybridize mainly with S2 and that only hybrid pairs with spectral weight in S2 contribute to sub-gap BQPI. Because the participating bands have different momenta, the Cooper pairs involved must be inter-band hybrid pairs with finite momentum, implying a condensate with both singlet and triplet pairing components.

Load-bearing premise

The load-bearing premise is that all three vanadium d orbitals hybridize with the same surface band S2 and that the previously reported band structure of β-Bi2Pd correctly maps the two BQPI vectors to the S2-S1 and S2-B2 transitions; if the d orbitals coupled to different bands, the band selectivity and the inter-band pairing conclusion would not follow.

Editorial extensions

If this is right

The helical nature of the β-Bi$_2$Pd surface bands is confirmed: the absence of intra-band BQPI shows that intra-band scattering is forbidden by spin conservation.
The superconducting condensate in β-Bi$_2$Pd contains a mixture of spin-singlet and spin-triplet pairing components, because electrons within a single helical band cannot form a pure singlet.
Hybrid Cooper pairs connecting S2 with S1 and B2 carry finite momentum, a situation analogous to FFLO states but generated by helical bands instead of a Zeeman-split Fermi surface.
A sufficiently strong in-plane magnetic field should induce a net momentum of these hybrid pairs and give rise to non-reciprocal currents, providing an experimental handle to search for this pairing.

Reading between the lines

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

Editorial inference: If inter-band pairing holds, β-Bi$_2$Pd becomes a natural testbed for topological superconductivity, since a singlet-triplet mixed condensate in a strong-spin-orbit-coupling material is one known ingredient for topological phases; a search for Majorana-type signatures at impurities or edges would be a logical next experiment.
Editorial inference: The BQPI method demonstrated here is portable: any multi-band superconductor with helical-like bands and a magnetic adatom species whose d orbitals couple to a single band should show a similarly reduced set of scattering vectors, giving a general spectroscopic fingerprint of inter-band pairing.
Editorial inference: The paper's discussion of multi-impurity scattering as an effective inter-band coupling suggests a testable knob: increasing the density of V adatoms or other scatterers should strengthen the effective hybridization, which would show up as a change in the relative intensity or period of the two BQPI components.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things worth knowing. First, the experiment is well done: YSR maps around V adatoms on β-Bi2Pd show two sub-gap modulations with wavevectors 2.2 and 8.9 nm^-1, and the paper makes a decent case that these correspond to inter-band scattering vectors qF and qB between S2 and S1/B2. Second, the theoretical model in SM-V reproduces those two frequencies only when interband hopping t is turned on. That is a real result: band hybridization is necessary for the BQPI pattern. But the title and abstract claim this 'reveals inter-band electron pairing.' The model does not support that. The pairing term in Eqs. (3)-(4) is Δ τ1, diagonal in band index; the hopping t τ3 η1 is single-particle hybridization. Two-frequency oscillations appear with purely intraband pairing once hybridization is present. So the data evidence band hybridization and band-selective quasiparticle interference, not interband Cooper pairing. The discussion's line about hybrid Cooper pairs carrying finite momentum is also a step beyond the model: a pair formed by k in one band and -k in another has zero center-of-mass momentum here. That belongs in outlook, not in the abstract.

What is genuinely new: the first YSR-BQPI maps on this material, the band-selective absence of most normal-state scattering vectors, and the demonstration that a single immobile impurity cannot produce interband oscillations without hybridization. That last point is clean and the derivation in the SM is transparent. The normal-state QPI and band assignment rest on earlier ARPES/DFT work, which is cited properly; the self-citations to the focusing mechanism are appropriate.

The weakest link is the interpretive leap. The assumption that all three V d-orbitals couple to the same surface band S2 appears only in SM-III; if they couple to different bands, the band-selectivity argument gets less solid. And the paper itself concedes in the Discussion that no direct experimental signature of unconventional pairing is evident. That concession sits awkwardly with the title.

Who is this for? People working on Shiba physics, multiband superconductors, and STM QPI. They will find the data and the hybridization argument useful; they should be wary of the pairing claim. A serious referee should get this before publication, not for desk reject, because the experimental core deserves an audience and the overclaim is fixable by reframing. I'd suggest the authors replace 'inter-band pairing' with 'band hybridization' in the abstract and move the FFLO speculation to the outlook.

Referee Report

3 major / 6 minor

Summary. The manuscript reports scanning tunneling microscopy/spectroscopy experiments on vanadium adatoms on the superconductor β-Bi2Pd, resolving Yu-Shiba-Rusinov (YSR) states and their spatial extension. The authors observe anisotropic Bogoliubov quasiparticle interference (BQPI) with two wavevectors, q1 = 2.2 nm^-1 and q2 = 8.9 nm^-1, which they identify with the normal-state interband scattering vectors qF (S2-S1) and qB (S2-B2). A one-dimensional two- and three-band model of helical bands with a magnetic impurity is presented in Supplementary Note V; the model shows that interband hybridization is required to produce the two-frequency oscillations, whereas isolated helical bands give no oscillations. The manuscript concludes that the data reveal inter-band pairing, with a mixture of singlet and triplet components and finite-momentum, FFLO-like hybrid Cooper pairs.

Significance. The experimental data are of high quality: the intra-gap dI/dV maps and the FFT analysis are carefully presented, and the observation that only two of the six normal-state QPI vectors survive in the sub-gap YSR maps is striking and potentially informative. The theoretical demonstration that a single magnetic impurity coupled to a helical band produces no BQPI, and that interband hybridization generates oscillatory patterns, is a clean and useful result. If the central claim were supported, the paper would constitute an important step toward detecting band-mixed pairing in spin-orbit-coupled multiband superconductors. However, as analyzed below, the paper's own model supports interband single-particle hybridization, not interband pairing; the strongest defensible conclusion is that the YSR-BQPI maps reveal band hybridization and band-selective Bogoliubov scattering. The novelty lies in the experimental observation and the hybridzation-based interpretation, but the title and abstract overstate what the evidence establishes.

major comments (3)

[SM-V, Eqs. (3)-(4); main text 'Band hybridization'] The Hamiltonian in Eqs. (3)-(4) contains only a band-diagonal order parameter Δ τ1 η0 together with interband hopping t τ3 η1; there is no interband pairing amplitude of the form that couples the particle branch of one band to the hole branch of another. The two-frequency BQPI patterns in Fig. 5(b,d) and SM Fig. S6 are generated by this hybridization-only model, so the calculation demonstrates that interband single-particle hybridization plus intraband pairing is sufficient to produce the observed oscillations. It does not demonstrate that the superconductor has inter-band pairing. The abstract and title claim that 'Analysis of the BQPI patterns at the YSR energy exposes inter-band pairing' is therefore not supported by the paper's own theory. To make the central claim, the authors should either include an explicit interband pairing term and identify a discriminating signature, or reframe the conclusion as evidence for interband hybridization and band-selective Bogoliubov scattering, with inter-band pairing treated as a speculative interpretation.
[Discussion, final paragraph] The statement 'Since the mixed bands also have different wave vectors, the hybrid Cooper pairs should have a finite momentum' is not a consequence of the model. In the translationally invariant Hamiltonian of Eqs. (3)-(4), all pairing terms conserve momentum, so Cooper pairs have zero center-of-mass momentum; a pair formed from k and -k states of a hybridized band has no net momentum even if the Bloch state contains multiple orbital or band characters. The FFLO analogy introduced in Fig. 1 and the subsequent discussion of non-reciprocal currents are therefore speculative extrapolations, not results of the presented calculation. These statements should be removed or explicitly labeled as conjectures that require a model with finite-momentum pairing.
[SM-III, 'Orbital character of YSR states'] The identification of q1 and q2 with the interband transitions S2-S1 and S2-B2 relies on the assumption, stated explicitly in SM-III, that 'the three orbitals of Vanadium are coupled to the same surface band.' The orbital-resolved maps in SM Fig. S4 establish different d-orbital symmetries, but they do not identify which substrate band each orbital couples to. If different V d-orbitals couple to different bands, the band-selectivity argument—and hence the identification of S2 as the YSR channel—would not follow. The authors should justify this assumption quantitatively, for example by comparing the BQPI wavevectors and decay lengths of the α, β, and γ YSR states; the qualitative statement that they show 'the same extension' is not sufficient, especially because the quantitative FFT analysis is performed only on the α state.

minor comments (6)

[Table of contents] The contents list contains the typo 'Bogoliuvov'; it should read 'Bogoliubov'.
[SM Fig. S2 caption] The caption contains the typo 'follwong' and the table of scattering vectors should be cross-checked against the text, since the labels in the caption and the main text are not fully consistent.
[SM-V, Eq. (12)] The expression 'p = −V (µ±iΩ±)' appears to have an unbalanced bracket or a missing term; please check the derivation and correct the formula.
[Main text, Fig. 4] The comparison of the BQPI FFT cut with the normal-state QPI cut is described in the text but the qF and qB features are not labeled in Fig. 4(d); adding labels would make the assignment much easier to follow.
[Main text, reference [17]] Reference [17] is cited in support of the four bands crossing E_F, but the cited work appears unrelated to the band structure of β-Bi2Pd; please verify this citation and replace it if it is incorrect.
[SM-V, 1D model justification] The model is one-dimensional, while the wavevectors q1 and q2 are extracted from two-dimensional FFT contours; the mapping from the 1D model's oscillatory wavevectors to the 2D nesting vectors along (100)/(010) should be stated explicitly rather than only referenced through the focusing effect.

Circularity Check

1 steps flagged · score 6.0 of 10

The central 'inter-band pairing' conclusion is a definitional relabeling of the single-particle band hybridization that the paper's own model uses to reproduce the BQPI data.

self definitional [Discussion, main text (final paragraph); cf. Fig. 1 caption and SM-V Eqs. (3)-(4)]
"Since the mixed bands also have different wave vectors, the hybrid Cooper pairs should have a finite momentum. This case resembles the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states [41, 42] but produced with helical states instead of the Zeeman-split Fermi surface [5]."

The model that reproduces the two-frequency BQPI pattern (SM-V, Eqs. 3-4) contains only an intraband order parameter Δτ1η0 plus single-particle interband hopping tτ3η1; no interband pairing amplitude appears. The text first concludes from this model that the participating bands are hybridized, then defines inter-band pairing (Fig. 1) as 'hybrid pairs formed by electrons from different bands'. In the Discussion, the same hybridization is restated as 'mixed bands' and immediately converted into 'hybrid Cooper pairs' with finite momentum. Thus the headline result—inter-band pairing—is obtained by renaming the single-particle hybridization that is the actual model input, rather than by detecting or fitting any pairing amplitude connecting bands.

full rationale

The derivation chain is partially circular. The measured BQPI vectors q1 and q2 are identified with independently reported normal-state QPI vectors qF and qB, and the band-structure input comes from external ARPES/DFT work, so the wavevector assignment itself is not circular. The model in SM-V is not fitted to the data to extract an interband pairing parameter; it shows that interband hopping t is sufficient to produce the two-frequency YSR oscillations. The circular step occurs when the paper converts this single-particle hybridization into the central claim of 'inter-band pairing': the Discussion takes 'mixed bands' (the model's hybridized single-particle bands) and, using the Fig. 1 definition of inter-band pairing as 'hybrid pairs formed by electrons from different bands', asserts 'hybrid Cooper pairs should have a finite momentum'. Since the model's observable consequences arise from t≠0 and not from any band-off-diagonal pairing term, the inter-band pairing conclusion is a definitional relabeling of the hybridization input rather than an independent result. Self-citations (refs. 24 and 36) support the superconducting-tip method and the focusing/1D approximation but are not load-bearing for the inter-band pairing claim. The paper's own theory therefore best supports a conclusion about band hybridization and band-selective BQPI; the finite-momentum/FFLO language is an extrapolation not derived from the presented equations.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim (inter-band pairing) is not quantitatively fitted to the data; the model is qualitative. However, the model relies on several assumptions: spin-helical bands with spin-conservation-scattering selection, equal single gap Δ, and the ad hoc assumption that all V d-orbitals couple to the same band S2. The 1D approximation is justified by Fermi-surface focusing. No new entities are introduced.

free parameters (3)

Interband hopping t = t/Δ = 0.5 in the two-band and three-band models
Introduced to generate BQPI oscillations; not fitted to experimental data.
Fermi velocities v1, v2, v3 = v1=0.1, v2=0.25, v3=0.6 (relative units)
Chosen for illustration in Fig. S6; qualitative result does not depend on exact values.
Chemical potential μ = Δ/μ = 0.01
Sets the scale for the calculation; not fitted to the BQPI data.

assumptions (5)

standard math BCS mean-field and Green's function formalism underlie the model calculations (SM-V).
Unproved background result used to compute the YSR state spectral density.
domain assumption The surface bands are helical with spin-momentum locking, so intra-band scattering is forbidden by spin conservation (main text, Fig. 2; SM-V).
This drives the interpretation that the observed BQPI vectors are inter-band; if intraband scattering were allowed, the pattern could be read differently.
ad hoc to paper The three V d-orbitals all couple to the same surface band S2, restricting sub-gap quasiparticles to that band (SM-III).
Explicitly stated as an assumption in SM-III; it is required for the band-selectivity conclusion.
domain assumption A 1D Hamiltonian captures the spatial dependence of YSR states along the high-symmetry directions due to Fermi-surface nesting/focusing (SM-V).
The justification is qualitative; the 2D band structure is reduced to 1D along (100) and (010).
domain assumption The superconducting order parameter Δ is equal in all participating bands, consistent with the measured single gap (SM-V).
The model assumes equal gaps; if the gap were band-dependent, the BQPI pattern could differ.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Revealing inter-band electron pairing in a superconductor with spin-orbit coupling." pith.science (2026). https://pith.science/paper/PHOSKRPC

@misc{pith2026250203326,
  author       = {Pith},
  title        = {Pith review of: Revealing inter-band electron pairing in a superconductor with spin-orbit coupling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PHOSKRPC}},
  note         = {Machine review of arXiv:2502.03326}
}

read the original abstract

Most superconducting mechanisms pair electrons within the same band, forming spin singlets. However, the discovery of multi-band superconductivity has opened new scenarios for pairing, particularly in systems with strong spin-orbit coupling. Here, we reveal inter-band pairing in the superconductor \bipd\ by mapping the amplitude of sub-gap Yu-Shiba-Rusinov (YSR) states around Vanadium adatoms deposited on its surface. The surface of \bipd\ is characterized by spin-helical-like bands near the Fermi level. Scanning tunneling spectroscopy reveals anisotropic YSR amplitude oscillations around the impurity, driven by spin-conserving Bogoliubov quasiparticle interference (BQPI). Analysis of the BQPI patterns at the YSR energy exposes inter-band pairing in this material. Interestingly, only a small subset of all possible inter-band scattering processes observed in the normal state contribute to the BQPI patterns. Combining experimental data and theory, we demonstrate that the observed band selectivity results from the hybridization of the band coupled with the impurity with other bands. Our findings reveal unconventional pairing mechanisms in \bipd\ and highlight the crucial role of spin-orbit interactions in their formation.

Figures

Figures reproduced from arXiv: 2502.03326 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: a], the DoS decays smoothly with distance [blue line in Fig. 5b]. The absence of oscillations indicates that both intra-band and inter-band BQPI are forbidden, as they involve either different spin states or orthogonal bands. Thus, the lack of oscillations associated…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 57 canonical work pages

[1]

A. M. Black-Schaffer and A. V. Balatsky, Phys. Rev. B - Condens. Matter Mater. Phys. 88, 1 (2013)

work page 2013
[2]

L. P. Gor’kov and E. I. Rashba, Phys. Rev. Lett. 87, 37004 (2001), arXiv:0103449 [cond-mat]

work page 2001
[3]

Y. Kim, J. Zhang, E. Rossi, and R. M. Lutchyn, Phys. Rev. Lett. 114, 236804 (2015), arXiv:arXiv:1410.4558v3

work page Pith review arXiv 2015
[4]

Sato and Y

M. Sato and Y. Ando, Reports on Progress in Physics 80, 076501 (2017)

2017
[5]

Asaba, M

T. Asaba, M. Naritsuka, H. Asaeda, Y. Kosuge, S. Ikemori, S. Suetsugu, Y. Kasahara, Y. Kohsaka, T. Terashima, A. Daido, Y. Yanase, and Y. Matsuda, Nature Communications 15, 3861 (2024)

work page 2024
[6]

P. O. Sprau, A. Kostin, A. Kreisel, A. E. B¨ ohmer, V. Tau- four, P. C. Canfield, S. Mukherjee, P. J. Hirschfeld, B. M. Andersen, and J. C. Davis, Science 357, 75 (2017), arXiv:1611.02134

work page Pith review arXiv 2017
[10]

Petersen and P

L. Petersen and P. Hedeg˚ ard, Surface Science 459, 49 (2000)

work page 2000
[11]

J. I. Pascual, G. Bihlmayer, Yu. M. Koroteev, H.-P. Rust, G. Ceballos, M. Hansmann, K. Horn, E. V. Chulkov, S. Bl¨ ugel, P. M. Echenique, and Ph. Hofmann, Physical Review Letters 93, 196802 (2004)

work page 2004

Show all 59 references

[12]

Str´ o˙ zecka, A

A. Str´ o˙ zecka, A. Eiguren, and J. I. Pascual, Phys. Rev. Lett. 107, 186805 (2011)

2011
[13]

Steinbrecher, H

M. Steinbrecher, H. Harutyunyan, C. R. Ast, and D. Wegner, Phys. Rev. B 87, 245436 (2013)

2013
[14]

Herrera, I

E. Herrera, I. Guillam´ on, V. Barrena, W. J. Herrera, J. A. Galvis, A. L. Yeyati, J. Rusz, P. M. Oppeneer, G. Knebel, J. P. Brison, J. Flouquet, D. Aoki, and H. Suderow, Nature 616, 465 (2023). 6

2023
[15]

Y. Imai, F. Nabeshima, T. Yoshinaka, K. Miyatani, R. Kondo, S. Komiya, I. Tsukada, and A. Maeda, J. Phys. Soc. Japan 81, 113708 (2012)

2012
[16]

Herrera, I

E. Herrera, I. Guillam´ on, J. A. Galvis, A. Correa, A. Fente, R. F. Luccas, F. J. Mompean, M. Garc´ ıa- Hern´ andez, S. Vieira, J. P. Brison, and H. Suderow, Phys. Rev. B 92, 1 (2015)

2015
[17]

J. I. Pascual, A. Dick, M. Hansmann, H.-P. Rust, J. Neugebauer, and K. Horn, Phys. Rev. Lett. 96, 046801 (2006)

2006
[18]

Yu, Acta Physica Sinica 21, 75 (1965)

L. Yu, Acta Physica Sinica 21, 75 (1965)

1965
[19]

Shiba, Prog

H. Shiba, Prog. Theor. Phys. 40, 435 (1968)

1968
[20]

A. I. Rusinov, Sov. J. Exp. Theor. Phys. 29, 1101 (1969)

1969
[21]

S.-H. Ji, T. Zhang, Y.-S. Fu, X. Chen, X.-C. Ma, J. Li, W.-H. Duan, J.-F. Jia, and Q.-K. Xue, Phys. Rev. Lett. 100, 226801 (2008)

2008
[23]

D. J. Choi, C. G. Fern´ andez, E. Herrera, C. Rubio-Verd´ u, M. M. Ugeda, I. Guillam´ on, H. Suderow, J. I. Pascual, and N. Lorente, Phys. Rev. Lett. 120, 1 (2018)

2018
[24]

Trivini, J

S. Trivini, J. Ortuzar, J. Zaldivar, E. Herrera, I. Guil- lam´ on, H. Suderow, F. S. Bergeret, and J. I. Pascual, Physical Review B 110, 235405 (2024)

2024
[25]

S. H. Pan, E. W. Hudson, and J. C. Davis, Appl. Phys. Lett. 73, 2992 (1998)

1998
[26]

Suderow, M

H. Suderow, M. Crespo, P. Martinez-Samper, J. G. Ro- drigo, G. Rubio-Bollinger, S. Vieira, N. Luchier, J. P. Brison, and P. C. Canfield, in Phys. C Supercond. its Appl., Vol. 369 (North-Holland, 2002) pp. 106–112

2002
[27]

J. G. Rodrigo, H. Suderow, and S. Vieira, Eur. Phys. J. B 40, 483 (2004)

2004
[28]

K. J. Franke, G. Schulze, and J. I. Pascual, Science 332, 940 (2011)

2011
[31]

Kaˇ cmarˇ c´ ık, Z

J. Kaˇ cmarˇ c´ ık, Z. Pribulov´ a, T. Samuely, P. Szab´ o, V. Cambel, J. ˇSolt´ ys, E. Herrera, H. Suderow, A. Correa- Orellana, D. Prabhakaran, and P. Samuely, Physical Re- view B 93, 144502 (2016)

2016
[32]

Prist´ aˇ s, M

G. Prist´ aˇ s, M. Orend´ aˇ c, S. Gab´ ani, J. Kaˇ cmarˇ c´ ık, E. Gaˇ zo, Z. Pribulov´ a, A. Correa-Orellana, E. Herrera, H. Suderow, and P. Samuely, Phys. Rev. B 97, 134505 (2018)

2018
[33]

L. Che, T. Le, C. Q. Xu, X. Z. Xing, Z. Shi, X. Xu, and X. Lu, Phys. Rev. B 94, 024519 (2016)

2016
[35]

H. Kim, L. R´ ozsa, D. Schreyer, E. Simon, and R. Wiesen- danger, Nat. Commun. 11, 1 (2020)

2020
[36]

Ortuzar, S

J. Ortuzar, S. Trivini, M. Alvarado, M. Rouco, J. Zal- divar, A. L. Yeyati, J. I. Pascual, and F. S. Bergeret, Phys. Rev. B 105, 245403 (2022)

2022
[37]

Uldemolins, A

M. Uldemolins, A. Mesaros, and P. Simon, Phys. Rev. B 105, 144503 (2022)

2022
[38]

F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Rev. Mod. Phys. 77, 1321 (2005)

2005
[39]

F. S. Bergeret and A. F. Volkov, Annals of Physics 456, 169232 (2023)

2023
[40]

Kanasugi and Y

S. Kanasugi and Y. Yanase, Commun Phys 5, 39 (2022)

2022
[41]

Fulde and R

P. Fulde and R. A. Ferrell, Physical Review 135, A550–A563 (1964)

1964
[42]

A. I. Larkin, Sov. Phys. JETP 20, 762 (1965)

1965
[43]

N. F. Q. Yuan and L. Fu, Proceedings of the National Academy of Sciences 119, e2119548119 (2022)

2022
[44]

Ili´ c and F

S. Ili´ c and F. S. Bergeret, Physical Review Letters 128, 177001 (2022)

2022
[45]

Powell, W

L. Powell, W. Kuang, G. Hawkins-Pottier, R. Jalil, J. Birkbeck, Z. Jiang, M. Kim, Y. Zou, S. Komrakova, S. Haigh, I. Timokhin, G. Balakrishnan, A. K. Geim, N. Walet, A. Principi, and I. V. Grigorieva, Nature Com- munications 16, 291 (2025). Revealing inter-band electron pairin...

2025 arXiv
[46]

A single impurity interacting with a helical band does not generate any BQPI pattern
[47]

A single impurity coupled to a helical band does not generate any BQPI pattern, even if an interband scattering term is present
[48]

Interband hybridization is required to account for the complex BQPI patterns observed in our system, not a scattering term. We describe the system superconductor plus impurity by the following effective Hamil- tonian: ˆH = ˆH0 + ˆHimp (2) where, ˆH0 describes the superconducti...
[49]

Herrera, I

E. Herrera, I. Guillam´ on, J. A. Galvis, A. Correa, A. Fente, R. F. Luccas, F. J. Mompean, M. Garc´ ıa-Hern´ andez, S. Vieira, J. P. Brison, and H. Suderow, Phys. Rev. B92, 1 (2015)

2015
[50]

Trivini, J

S. Trivini, J. Ortuzar, J. Zaldivar, E. Herrera, I. Guillam´ on, H. Suderow, F. S. Bergeret, and J. I. Pascual, Physical Review B 110, 235405 (2024)

2024
[51]

Iwaya, Y

K. Iwaya, Y. Kohsaka, K. Okawa, T. Machida, M. S. Bahramy, T. Hanaguri, and T. Sasagawa, Nat. Commun. 8, 976 (2017)

2017
[52]

Sakano, K

M. Sakano, K. Okawa, M. Kanou, H. Sanjo, T. Okuda, T. Sasagawa, and K. Ishizaka, Nat. Commun. 6, 8595 (2015), arXiv:1505.07231

2015 arXiv
[53]

M. Ruby, Y. Peng, F. von Oppen, B. W. Heinrich, and K. J. Franke, Phys. Rev. Lett. 117, 186801 (2016)

2016
[54]

G. C. M´ enard, S. Guissart, C. Brun, S. Pons, V. S. Stolyarov, F. Debontridder, M. V. Leclerc, E. Janod, L. Cario, D. Roditchev, P. Simon, and T. Cren, Nature Physics 11, 1013 (2015)

2015
[55]

H. Kim, L. R´ ozsa, D. Schreyer, E. Simon, and R. Wiesendanger, Nat. Commun. 11, 1 (2020)

2020
[56]

D.-J. Choi, C. Rubio-Verd´ u, J. de Bruijckere, M. M. Ugeda, N. Lorente, and J. I. Pascual, Nat. Commun. 8, 15175 (2017)

2017
[57]

B. W. Heinrich, J. I. Pascual, and K. J. Franke, Prog. Surf. Sci.93, 1 (2018), arXiv:1705.03672

2018 arXiv
[58]

Ortuzar, S

J. Ortuzar, S. Trivini, M. Alvarado, M. Rouco, J. Zaldivar, A. L. Yeyati, J. I. Pascual, and F. S. Bergeret, Phys. Rev. B 105, 245403 (2022)

2022
[59]

Wang and D.-H

Q.-H. Wang and D.-H. Lee, Phys. Rev. B 67, 020511 (2003). 12

2003
[60]

Bena and S

C. Bena and S. A. Kivelson, Phys. Rev. B 72, 125432 (2005)

2005
[61]

A. V. Balatsky, I. Vekhter, and J.-X. Zhu, Rev. Mod. Phys. 78, 373 (2006)

2006
[62]

(9), proportional to the DoS, the magnitude that we measure

We are only considering the trace of Eq. (9), proportional to the DoS, the magnitude that we measure. Non-diagonal terms can oscillate
[63]

Kohsaka, T

Y. Kohsaka, T. Machida, K. Iwaya, M. Kanou, T. Hanaguri, and T. Sasagawa, Phys. Rev. B 95, 115307 (2017)

2017
[64]

Sharma, S

R. Sharma, S. D. Edkins, Z. Wang, A. Kostin, C. Sow, Y. Maeno, A. P. Mackenzie, J. C. S´ eamus Davis, and V. Madhavan, Proc. Natl. Acad. Sci. U. S. A. 117, 5222 (2020)

2020
[65]

A. Dutt, A. A. Golubov, O. V. Dolgov, and D. V. Efremov, Phys. Rev. B 96, 054513 (2017)

2017
[66]

M. M. Korshunov, Y. N. Togushova, and O. V. Dolgov, Phys.-Usp. 59, 1211 (2016). 13

2016

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

A. M. Black-Schaffer and A. V. Balatsky, Phys. Rev. B - Condens. Matter Mater. Phys. 88, 1 (2013)

work page 2013

[2] [2]

L. P. Gor’kov and E. I. Rashba, Phys. Rev. Lett. 87, 37004 (2001), arXiv:0103449 [cond-mat]

work page 2001

[3] [3]

Y. Kim, J. Zhang, E. Rossi, and R. M. Lutchyn, Phys. Rev. Lett. 114, 236804 (2015), arXiv:arXiv:1410.4558v3

work page Pith review arXiv 2015

[4] [4]

Sato and Y

M. Sato and Y. Ando, Reports on Progress in Physics 80, 076501 (2017)

2017

[5] [5]

Asaba, M

T. Asaba, M. Naritsuka, H. Asaeda, Y. Kosuge, S. Ikemori, S. Suetsugu, Y. Kasahara, Y. Kohsaka, T. Terashima, A. Daido, Y. Yanase, and Y. Matsuda, Nature Communications 15, 3861 (2024)

work page 2024

[6] [6]

P. O. Sprau, A. Kostin, A. Kreisel, A. E. B¨ ohmer, V. Tau- four, P. C. Canfield, S. Mukherjee, P. J. Hirschfeld, B. M. Andersen, and J. C. Davis, Science 357, 75 (2017), arXiv:1611.02134

work page Pith review arXiv 2017

[7] [10]

Petersen and P

L. Petersen and P. Hedeg˚ ard, Surface Science 459, 49 (2000)

work page 2000

[8] [11]

J. I. Pascual, G. Bihlmayer, Yu. M. Koroteev, H.-P. Rust, G. Ceballos, M. Hansmann, K. Horn, E. V. Chulkov, S. Bl¨ ugel, P. M. Echenique, and Ph. Hofmann, Physical Review Letters 93, 196802 (2004)

work page 2004