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arxiv: 2510.13641 · v2 · submitted 2025-10-15 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Momentum-resolved spectroscopy of superconductivity with the quantum twisting microscope

Yuval Waschitz , Ady Stern , Yuval Oreg This is my paper

Pith reviewed 2026-05-18 07:14 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords quantum twisting microscopemomentum-resolved spectroscopysuperconductivityBogoliubov coherence factorspairing symmetryrotational symmetry breakingtwo-dimensional materials
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The pith

The quantum twisting microscope uses in-plane momentum conservation to measure the momentum-dependent superconducting pairing in two-dimensional materials.

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

This paper presents a theoretical framework for using the quantum twisting microscope to achieve momentum-resolved spectroscopy of superconductivity. In-plane momentum conservation during tunneling from a rotated graphene tip to the sample allows direct measurement of the spectral function along specific trajectories in momentum space. The intensities of electron versus hole excitations directly encode the Bogoliubov coherence factors that determine the size of the superconducting gap at each momentum. Multiple tunneling channels related by threefold rotational symmetry provide a way to detect if the pairing breaks rotational symmetry or has nodes where the gap vanishes. The approach is illustrated with calculations for both noninteracting and interacting models of two-dimensional superconductivity.

Core claim

Because of in-plane momentum conservation, the QTM directly measures the superconducting spectral function along well-defined trajectories in momentum space. The relative intensities of electron and hole excitations encode the Bogoliubov coherence factors, revealing the momentum dependence of the pairing magnitude. Three C3z-related tunneling channels enable direct detection of rotational symmetry breaking as well as nodal points.

What carries the argument

In-plane momentum conservation during planar tunneling between the rotated graphene tip and the sample, which selects well-defined momentum trajectories for the spectral function measurement.

If this is right

  • The momentum dependence of the pairing magnitude is revealed through the relative intensities of electron and hole excitations.
  • Rotational symmetry breaking in the order parameter can be detected using the three C3z-related tunneling channels.
  • Nodal points in the superconducting gap are directly identifiable from the tunneling signals.
  • The framework applies to both noninteracting electron models and interacting heavy-fermion models in two dimensions.

Where Pith is reading between the lines

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

  • This could help distinguish pairing symmetries arising from different interaction mechanisms in moiré superlattices.
  • Similar momentum resolution might be achievable in other planar tunneling setups beyond graphene tips.
  • Testing in actual devices could confirm if coherence factors match predictions for unconventional superconductors.

Load-bearing premise

In-plane momentum is strictly conserved in the tunneling process, with no significant scattering or broadening that mixes different momentum trajectories.

What would settle it

If experiments show that the tunneling current does not vary with tip rotation angle in a way that traces distinct momentum paths, or if the electron-hole intensity ratios do not match the expected coherence factors, the assumption of strict momentum conservation would be falsified.

Figures

Figures reproduced from arXiv: 2510.13641 by Ady Stern, Yuval Oreg, Yuval Waschitz.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic diagram of the QTM junction (adapted [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a–c) Superconducting pairing magnitude in the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: illustrates this procedure. For an s-wave state, the I ′′ spectra ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Band structure of MATBG at [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of QTM spectra for an isotropic superconducting gap in MATBG between two measurement modes. (a) [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Normalized line cuts from [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison between the band structure of BM model and HF model along a trajectory in the mBZ. The bands [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Comparison between the band structure and tunneling matrix element of BM model and HF model along the QTM [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Schematic diagram of parabolic band structure with finite (blue) and zero (cyan) superconducting pairing. The color [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Calculated [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
read the original abstract

We develop a theoretical framework for probing superconductivity with momentum resolution using the quantum twisting microscope (QTM), a planar tunneling device where a graphene tip is rotated relative to a two-dimensional sample. Because of in-plane momentum conservation, the QTM directly measures the superconducting spectral function along well-defined trajectories in momentum space. The relative intensities of electron and hole excitations encode the Bogoliubov coherence factors, revealing the momentum dependence of the pairing magnitude. Three $C_{3z}$-related tunneling channels enable direct detection of rotational symmetry breaking, as well as nodal points in the superconducting order parameter. We apply our framework to superconductivity within the Bistritzer-MacDonald model of noninteracting electrons and the topological heavy-fermion model, which accounts for electron-electron interactions. Together, these capabilities establish the QTM as a direct probe of the pairing symmetry and microscopic origin of superconductivity in two-dimensional materials.

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 / 1 minor

Summary. The paper develops a theoretical framework for momentum-resolved tunneling spectroscopy of superconductivity using the quantum twisting microscope (QTM), in which a graphene tip is rotated relative to a 2D sample. Due to in-plane momentum conservation, the QTM is claimed to measure the superconducting spectral function along well-defined k-space trajectories; relative electron/hole intensities encode Bogoliubov coherence factors that reveal the momentum dependence of the gap, while three C3z-related channels allow detection of rotational symmetry breaking and nodal points. The framework is applied to the non-interacting Bistritzer-MacDonald model and the interacting topological heavy-fermion model.

Significance. If the central assumptions hold, the work would provide a direct, momentum-resolved probe of pairing symmetry and microscopic origin of superconductivity in 2D materials, extending standard tunneling and Bogoliubov theory to a rotatable planar geometry. The dual application to the BM and THFM models is a strength, as is the emphasis on falsifiable signatures such as coherence-factor intensity contrasts and C3z channel differences.

major comments (2)
  1. [§§2–3] §§2–3 (tunneling Hamiltonian and spectral function derivation): the central claim that the QTM measures well-defined trajectories and cleanly extracts coherence factors and nodal signatures rests on strict in-plane momentum conservation (delta-function tunneling matrix elements). No quantitative estimate or convolution kernel is supplied for momentum broadening arising from finite tip radius, interface disorder, or inelastic scattering; without this, the predicted intensity contrasts for nodes in the BM and THFM applications cannot be assessed for robustness.
  2. [Application sections (BM and THFM)] Application sections (BM and THFM): the predicted rotational-symmetry-breaking and nodal signatures via the three C3z channels assume that the three tunneling trajectories remain spectrally distinct after any realistic broadening; the manuscript provides no numerical folding of a finite-Δk kernel into the spectral functions to demonstrate that the contrasts survive.
minor comments (1)
  1. Notation for the three C3z channels and the coherence-factor expressions could be introduced with a single summary equation or table for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. The points raised concern the robustness of our predictions under realistic momentum broadening, which we address below by committing to specific additions in the revised manuscript.

read point-by-point responses

  1. Referee: [§§2–3] the central claim that the QTM measures well-defined trajectories and cleanly extracts coherence factors and nodal signatures rests on strict in-plane momentum conservation (delta-function tunneling matrix elements). No quantitative estimate or convolution kernel is supplied for momentum broadening arising from finite tip radius, interface disorder, or inelastic scattering; without this, the predicted intensity contrasts for nodes in the BM and THFM applications cannot be assessed for robustness.

    Authors: We agree that a quantitative estimate of momentum broadening is needed to assess robustness. In the revised manuscript we will add a dedicated paragraph in §2 estimating the momentum resolution set by finite tip radius (via the Fourier transform of the tip-sample overlap for a typical 10–50 nm tip diameter), together with order-of-magnitude bounds on disorder and inelastic contributions drawn from existing QTM and STM literature on graphene–2D interfaces. These estimates will be used to show that the dominant broadening remains smaller than the nodal separation and coherence-factor contrast scales in both models. revision: yes

  2. Referee: [Application sections (BM and THFM)] the predicted rotational-symmetry-breaking and nodal signatures via the three C3z channels assume that the three tunneling trajectories remain spectrally distinct after any realistic broadening; the manuscript provides no numerical folding of a finite-Δk kernel into the spectral functions to demonstrate that the contrasts survive.

    Authors: We accept that explicit demonstration is required. In the revised version we will numerically convolve the computed spectral functions for both the BM and THFM models with a Gaussian kernel whose width matches the estimated Δk from the new §2 estimate, and we will display the resulting intensity contrasts and C3z-channel differences to confirm that the qualitative signatures remain visible. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation rests on standard momentum-conserving tunneling and Bogoliubov theory

full rationale

The paper constructs its framework from the tunneling Hamiltonian incorporating in-plane momentum conservation (a standard assumption for planar devices) and applies established Bogoliubov quasiparticle coherence factors to extract pairing symmetry. These inputs are independent physical principles, not quantities fitted or defined inside the manuscript. Applications to the Bistritzer-MacDonald and topological heavy-fermion models use known Hamiltonians without self-referential fitting or renaming of results as predictions. No load-bearing step reduces by construction to a self-citation chain or internal ansatz; any prior QTM references support device context but do not justify the superconductivity claims. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard assumptions from tunneling spectroscopy and superconductivity theory with no new free parameters or invented entities.

axioms (2)
  • domain assumption In-plane momentum is conserved during tunneling from the rotated graphene tip into the sample.
    This conservation is invoked to map rotation angle directly to specific momentum trajectories.
  • standard math Superconducting excitations are described by Bogoliubov quasiparticles whose electron and hole components determine tunneling intensities.
    Standard result from BCS/BdG theory used to link intensities to coherence factors.

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Reference graph

Works this paper leans on

87 extracted references · 87 canonical work pages · 2 internal anchors

  1. [1]

    Bardeen, L

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957)

    work page 1957

  2. [2]

    C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys.72, 969 (2000)

    work page 2000

  3. [3]

    Sigrist and K

    M. Sigrist and K. Ueda, Rev. Mod. Phys.63, 239 (1991)

    work page 1991

  4. [4]

    Sigrist, inAIP Conference Proceedings, Vol

    M. Sigrist, inAIP Conference Proceedings, Vol. 789 (American Institute of Physics, 2005) pp. 165–243

    work page 2005

  5. [5]

    Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Nature556, 43 (2018)

    work page 2018

  6. [6]

    Yankowitz, S

    M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watan- abe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Science363, 1059 (2019)

    work page 2019

  7. [7]

    X. Lu, P. Stepanov, W. Yang, M. Xie, M. A. Aamir, I. Das, C. Urgell, K. Watanabe, T. Taniguchi, G. Zhang, et al., Nature574, 653 (2019)

    work page 2019

  8. [8]

    J. M. Park, Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Nature590, 249 (2021)

    work page 2021

  9. [9]

    Z. Hao, A. Zimmerman, P. Ledwith, E. Khalaf, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Science371, 1133 (2021)

    work page 2021

  10. [10]

    H. Zhou, T. Xie, T. Taniguchi, K. Watanabe, and A. F. Young, Nature598, 434 (2021)

    work page 2021

  11. [11]

    H. Zhou, L. Holleis, Y. Saito, L. Cohen, W. Huynh, C. L. Patterson, F. Yang, T. Taniguchi, K. Watanabe, and A. F. Young, Science375, 774 (2022)

    work page 2022

  12. [12]

    Y. Cao, D. Rodan-Legrain, J. M. Park, N. F. Yuan, K. Watanabe, T. Taniguchi, R. M. Fernandes, L. Fu, and P. Jarillo-Herrero, science372, 264 (2021)

    work page 2021

  13. [13]

    N. J. Zhang, P. A. Nosov, O. E. Sommer, Y. Wang, K. Watanabe, T. Taniguchi, E. Khalaf, and J. Li, arXiv preprint arXiv:2503.15767 (2025)

    work page arXiv 2025

  14. [14]

    Banerjee, Z

    A. Banerjee, Z. Hao, M. Kreidel, P. Ledwith, I. Phinney, J. M. Park, A. Zimmerman, M. E. Wesson, K. Watanabe, T. Taniguchi,et al., Nature638, 93 (2025)

    work page 2025

  15. [15]

    Tanaka, J

    M. Tanaka, J. ˆI.-j. Wang, T. H. Dinh, D. Rodan-Legrain, S. Zaman, M. Hays, A. Almanakly, B. Kannan, D. K. Kim, B. M. Niedzielski,et al., Nature638, 99 (2025)

    work page 2025

  16. [16]

    M. Oh, K. P. Nuckolls, D. Wong, R. L. Lee, X. Liu, K. Watanabe, T. Taniguchi, and A. Yazdani, Nature600, 240 (2021)

    work page 2021

  17. [17]

    H. Kim, Y. Choi, C. Lewandowski, A. Thomson, Y. Zhang, R. Polski, K. Watanabe, T. Taniguchi, J. Al- icea, and S. Nadj-Perge, Nature606, 494 (2022)

    work page 2022

  18. [18]

    J. M. Park, S. Sun, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, arXiv preprint arXiv:2503.16410 (2025)

    work page arXiv 2025

  19. [19]

    E. Lake, A. S. Patri, and T. Senthil, Phys. Rev. B106, 104506 (2022). 7

    work page 2022

  20. [20]

    D. M. Kennes, J. Lischner, and C. Karrasch, Phys. Rev. B98, 241407 (2018)

    work page 2018

  21. [21]

    T. J. Peltonen, R. Ojaj¨ arvi, and T. T. Heikkil¨ a, Phys. Rev. B98, 220504 (2018)

    work page 2018

  22. [22]

    Isobe, N

    H. Isobe, N. F. Q. Yuan, and L. Fu, Phys. Rev. X8, 041041 (2018)

    work page 2018

  23. [23]

    Liu, L.-D

    C.-C. Liu, L.-D. Zhang, W.-Q. Chen, and F. Yang, Phys. Rev. Lett.121, 217001 (2018)

    work page 2018

  24. [24]

    F. Wu, A. H. MacDonald, and I. Martin, Phys. Rev. Lett. 121, 257001 (2018)

    work page 2018

  25. [25]

    Wu, Phys

    F. Wu, Phys. Rev. B99, 195114 (2019)

    work page 2019

  26. [26]

    B. Lian, Z. Wang, and B. A. Bernevig, Phys. Rev. Lett. 122, 257002 (2019)

    work page 2019

  27. [27]

    Huang, L

    T. Huang, L. Zhang, and T. Ma, Science Bulletin64, 310 (2019)

    work page 2019

  28. [28]

    Kozii, H

    V. Kozii, H. Isobe, J. W. F. Venderbos, and L. Fu, Phys. Rev. B99, 144507 (2019)

    work page 2019

  29. [29]

    Cea and F

    T. Cea and F. Guinea, Proceedings of the National Academy of Sciences118, e2107874118 (2021)

    work page 2021

  30. [30]

    Y. Wang, J. Kang, and R. M. Fernandes, Phys. Rev. B 103, 024506 (2021)

    work page 2021

  31. [31]

    Shavit, E

    G. Shavit, E. Berg, A. Stern, and Y. Oreg, Phys. Rev. Lett.127, 247703 (2021)

    work page 2021

  32. [32]

    Khalaf, S

    E. Khalaf, S. Chatterjee, N. Bultinck, M. P. Zaletel, and A. Vishwanath, Science advances7, eabf5299 (2021)

    work page 2021

  33. [33]

    J. Yu, M. Xie, F. Wu, and S. Das Sarma, Phys. Rev. B 107, L201106 (2023)

    work page 2023

  34. [34]

    Wang, G.-D

    Y.-J. Wang, G.-D. Zhou, S.-Y. Peng, B. Lian, and Z.-D. Song, Phys. Rev. Lett.133, 146001 (2024)

    work page 2024

  35. [35]

    Liu and B

    C.-X. Liu and B. A. Bernevig, Phys. Rev. B111, L020502 (2025)

    work page 2025

  36. [36]

    J. Xiao, E. Berg, L. I. Glazman, F. Guinea, S. Ilani, and F. von Oppen, Phys. Rev. B110, 205407 (2024)

    work page 2024

  37. [37]

    Inbar, J

    A. Inbar, J. Birkbeck, J. Xiao, T. Taniguchi, K. Watan- abe, B. Yan, Y. Oreg, A. Stern, E. Berg, and S. Ilani, Nature614, 682 (2023)

    work page 2023

  38. [38]

    V. Peri, S. Ilani, P. A. Lee, and G. Refael, Phys. Rev. B 109, 035127 (2024)

    work page 2024

  39. [39]

    Pichler, W

    F. Pichler, W. Kadow, C. Kuhlenkamp, and M. Knap, Phys. Rev. B110, 045116 (2024)

    work page 2024

  40. [40]

    N. Wei, F. Guinea, F. von Oppen, and L. I. Glazman, arXiv preprint arXiv:2506.05485 (2025)

    work page arXiv 2025

  41. [41]

    N. Wei, F. von Oppen, and L. I. Glazman, Phys. Rev. B 111, 085128 (2025)

    work page 2025

  42. [42]

    J. Xiao, Y. Vituri, and E. Berg, Phys. Rev. B108, 094520 (2023)

    work page 2023

  43. [43]

    M. Lee, I. Das, J. Herzog-Arbeitman, J. Papp, J. Li, M. Daschner, Z. Zhou, M. Bhatt, M. Currle, J. Yu,et al., arXiv preprint arXiv:2507.03189 (2025)

    work page arXiv 2025

  44. [44]

    Birkbeck, J

    J. Birkbeck, J. Xiao, A. Inbar, T. Taniguchi, K. Watan- abe, E. Berg, L. Glazman, F. Guinea, F. von Oppen, and S. Ilani, Nature , 1 (2025)

    work page 2025

  45. [45]

    J. Xiao, A. Inbar, J. Birkbeck, N. Gershon, Y. Zamir, T. Taniguchi, K. Watanabe, E. Berg, and S. Ilani, arXiv preprint arXiv:2506.20738 (2025)

    work page arXiv 2025

  46. [46]

    The Mott-semiconducting state in the magic angle bilayer graphene

    M. Haule, E. Andrei, and K. Haule, arXiv preprint arXiv:1901.09852 (2019)

    work page internal anchor Pith review Pith/arXiv arXiv 1901

  47. [47]

    M. J. Calder´ on and E. Bascones, Phys. Rev. B102, 155149 (2020)

    work page 2020

  48. [48]

    Song and B

    Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett.129, 047601 (2022)

    work page 2022

  49. [49]

    G. D. Mahan,Many-Particle Physics, 2nd ed., Physics of Solids and Liquids (Plenum Press, New York, 1990) pp. XIV+1032, hardcover ISBN 978-0-306-43423-5 (1990- 03-31), Softcover ISBN 978-1-4612-8778-0 (2011-10-18), eBook ISBN 978-1-4613-1469-1 (2012-12-06)

    work page 1990

  50. [50]

    Bistritzer and A

    R. Bistritzer and A. H. MacDonald, Phys. Rev. B81, 245412 (2010)

    work page 2010

  51. [51]

    V. P. Mineev, K. Samokhin, and L. Landau,Introduction to unconventional superconductivity(CRC Press, 1999)

    work page 1999

  52. [52]

    Bistritzer and A

    R. Bistritzer and A. H. MacDonald, Proceedings of the National Academy of Sciences108, 12233 (2011)

    work page 2011

  53. [53]

    Pangburn, L

    E. Pangburn, L. Haurie, A. Cr´ epieux, O. A. Awoga, A. M. Black-Schaffer, C. P´ epin, and C. Bena, Phys. Rev. B108, 134514 (2023)

    work page 2023

  54. [54]

    Fujita, I

    K. Fujita, I. Grigorenko, J. Lee, W. Wang, J. X. Zhu, J. C. Davis, H. Eisaki, S. Uchida, and A. V. Balatsky, Phys. Rev. B78, 054510 (2008)

    work page 2008

  55. [55]

    A. V. Balatsky, W. S. Lee, and Z. X. Shen, Phys. Rev. B 79, 020505 (2009)

    work page 2009

  56. [56]

    L. Liu, S. Zhang, Y. Chu, C. Shen, Y. Huang, Y. Yuan, J. Tian, J. Tang, Y. Ji, R. Yang,et al., Nature Commu- nications13, 3292 (2022)

    work page 2022

  57. [57]

    M. Kim, A. Timmel, L. Ju, and X.-G. Wen, Phys. Rev. B111, 014508 (2025)

    work page 2025

  58. [58]

    Y.-Z. Chou, J. Zhu, and S. Das Sarma, Phys. Rev. B111, 174523 (2025)

    work page 2025

  59. [59]

    Parra-Mart´ ınez, A

    G. Parra-Mart´ ınez, A. Jimeno-Pozo, V. o. T. Phong, H. Sainz-Cruz, D. Kaplan, P. Emanuel, Y. Oreg, P. A. Pantale´ on, J. A. Silva-Guill´ en, and F. Guinea, Phys. Rev. Lett.135, 136503 (2025)

    work page 2025

  60. [60]

    T. Han, Z. Lu, Z. Hadjri, L. Shi, Z. Wu, W. Xu, Y. Yao, A. A. Cotten, O. S. Sedeh, H. Weldeyesus,et al., Nature , 1 (2025)

    work page 2025

  61. [61]

    May-Mann, T

    J. May-Mann, T. Helbig, and T. Devakul, arXiv preprint arXiv:2503.05697 (2025)

    work page arXiv 2025

  62. [62]

    Friedlan, H

    A. Friedlan, H. Li, and H.-Y. Kee, Phys. Rev. B111, 024504 (2025)

    work page 2025

  63. [63]

    Probing superconductivity with tunneling spectroscopy in rhombohedral graphene

    D. Sedov and M. S. Scheurer, arXiv preprint arXiv:2503.12650 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  64. [64]

    Christos, S

    M. Christos, S. Sachdev, and M. S. Scheurer, Nature Communications14, 7134 (2023)

    work page 2023

  65. [65]

    Bultinck, E

    N. Bultinck, E. Khalaf, S. Liu, S. Chatterjee, A. Vish- wanath, and M. P. Zaletel, Phys. Rev. X10, 031034 (2020)

    work page 2020

  66. [66]

    J. Kang, B. A. Bernevig, and O. Vafek, Phys. Rev. Lett. 127, 266402 (2021)

    work page 2021

  67. [67]

    Datta, M

    A. Datta, M. J. Calderon, A. Camjayi, and E. Bascones, Nature Communications14, 5036 (2023)

    work page 2023

  68. [68]

    G. Rai, L. Crippa, D. C˘ alug˘ aru, H. Hu, F. Paoletti, L. de’ Medici, A. Georges, B. A. Bernevig, R. Valent´ ı, G. Sangiovanni, and T. Wehling, Phys. Rev. X14, 031045 (2024)

    work page 2024

  69. [69]

    Zhou, Y.-J

    G.-D. Zhou, Y.-J. Wang, N. Tong, and Z.-D. Song, Phys. Rev. B109, 045419 (2024)

    work page 2024

  70. [70]

    M. J. Calder´ on, A. Camjayi, A. Datta, and E. Bascones, Phys. Rev. B112, L041126 (2025)

    work page 2025

  71. [71]

    R. L. Merino, D. C˘ alug˘ aru, H. Hu, J. D´ ıez-M´ erida, A. D´ ıez-Carl´ on, T. Taniguchi, K. Watanabe, P. Seifert, B. A. Bernevig, and D. K. Efetov, Nature Physics , 1 (2025)

    work page 2025

  72. [72]

    C˘ alug˘ aru, H

    D. C˘ alug˘ aru, H. Hu, L. Crippa, G. Rai, N. Regnault, T. O. Wehling, R. Valent´ ı, G. Sangiovanni, and B. A. Bernevig, arXiv preprint arXiv:2509.18256 (2025)

    work page arXiv 2025

  73. [73]

    N. Wei, F. von Oppen, and L. I. Glazman, arXiv preprint arXiv:2509.22902 (2025)

    work page arXiv 2025

  74. [74]

    Z. Song, Z. Wang, W. Shi, G. Li, C. Fang, and B. A. Bernevig, Phys. Rev. Lett.123, 036401 (2019). 8

    work page 2019

  75. [75]

    C˘ alug˘ aru, M

    D. C˘ alug˘ aru, M. Borovkov, L. L. Lau, P. Coleman, Z.-D. Song, and B. A. Bernevig, Low Temperature Physics49, 640 (2023)

    work page 2023

  76. [76]

    R. C. Dynes, V. Narayanamurti, and J. P. Garno, Phys. Rev. Lett.41, 1509 (1978)

    work page 1978

  77. [77]

    F. c. v. Herman and R. Hlubina, Phys. Rev. B94, 144508 (2016)

    work page 2016

  78. [78]

    Kondo, W

    T. Kondo, W. Malaeb, Y. Ishida, T. Sasagawa, H. Sakamoto, T. Takeuchi, T. Tohyama, and S. Shin, Nature communications6, 7699 (2015)

    work page 2015

  79. [79]

    M. R. Norman, M. Randeria, H. Ding, and J. C. Cam- puzano, Phys. Rev. B57, R11093 (1998). Appendix A: Electrostatics of the QTM junction We follow Ref. [36] to derive the electrostatic relations governing the QTM junction, with minor modifications. For the tip (T) and sample (S), we define the electrochemical potentialµ ec X =µ X −ϕ X withX∈ {T, S}, where...

    work page 1998

  80. [80]

    Singularity from the tip Dirac point crossing normal bands We review the derivation of the singularities ind 2I/dV 2 b that arise when the tip Dirac point crosses the sample bands, following Ref. [41]. We begin from the current equation, Eq. (1) I= 2πe ℏ X kT ,kS X α,β Tαβ(kT ,k S) 2 Z dω AT,α(kT , ω+eV b)A S,β(kS, ω) [f(ω)−f(ω+eV b)].(C1) We assume infin...

    work page

Showing first 80 references.