pith. sign in

arxiv: 2603.04717 · v2 · submitted 2026-03-05 · ❄️ cond-mat.supr-con · cond-mat.mes-hall· cond-mat.mtrl-sci· cond-mat.str-el

Spectroscopic evidence of disorder-induced quantum phase transitions in monolayer Fe(Te,Se) superconductor

Guanyang He , Ziqiao Wang , Longxin Pan , Yuxuan Lei , Fa Wang , Yi Liu , Nandini Trivedi , Jian Wang This is my paper

Pith reviewed 2026-05-15 15:54 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hallcond-mat.mtrl-scicond-mat.str-el
keywords superconductor-insulator transitionmonolayer Fe(Te,Se)disorderscanning tunneling spectroscopyquantum phase transitionCooper pair correlationlocalizationiron clusters
0
0 comments X

The pith

Disorder introduced via iron clusters drives monolayer Fe(Te,Se) from superconducting gaps to large insulating U-shaped gaps.

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

This paper adds controlled disorder to a monolayer high-temperature superconductor by depositing iron clusters onto Fe(Te,Se) films. Scanning tunneling spectroscopy tracks the gap evolving from the V-shaped superconducting form into an insulating gap as disorder strength rises. At the highest disorder levels the spectra display large U-shaped gaps that the authors tie to Cooper pairs reinforced by electron localization. A reader cares because the result clarifies the long-standing role of disorder in the superconductor-insulator quantum phase transition in two dimensions. The work indicates that localization can enhance rather than simply suppress pairing in low-dimensional high-Tc materials.

Core claim

The paper claims that controllable disorder addition reveals a quantum phase transition from superconductor to insulator in monolayer Fe(Te,Se), with scanning tunneling spectroscopy showing the spectral gap change from superconducting to insulating character; at strong disorder the large U-shaped gaps are attributed to localization-enhanced Cooper pair correlation.

What carries the argument

Scanning tunneling spectroscopy on iron-cluster-disordered monolayer Fe(Te,Se) films, which tracks the gap evolution and isolates the U-shaped insulating feature linked to localization-enhanced Cooper pair correlation.

If this is right

  • The gap spectrum changes continuously from superconducting to insulating with increasing iron-cluster disorder.
  • Strong disorder produces insulating behavior through enhanced rather than destroyed pair correlations.
  • The same disorder-tuning method can be used to map emergent phases in other disordered two-dimensional high-Tc superconductors.
  • Spectroscopic signatures of localization-enhanced pairing become accessible in the strong-disorder regime.

Where Pith is reading between the lines

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

  • Comparable U-shaped gaps may appear when similar disorder is added to other monolayer iron-based or cuprate superconductors.
  • Combining the disorder tuning with in-plane magnetic fields could separate pairing-related gaps from purely localization-driven insulation.
  • The transition supplies a route to engineer insulating states that still carry short-range pair correlations in two dimensions.

Load-bearing premise

The large U-shaped gaps at strong disorder arise specifically from localization-enhanced Cooper pair correlation rather than conventional Anderson localization, charging effects, or unrelated insulating mechanisms.

What would settle it

Applying a magnetic field or raising temperature to suppress superconductivity while leaving localization intact, then checking whether the U-shaped gaps close or persist, would test the proposed pairing origin.

read the original abstract

The superconductor-insulator transition as a paradigm of quantum phase transitions has attracted tremendous interest over the past three decades. While the magnetic field and carrier density can be tuned to drive the transition, the role of disorder in the transition is not well understood due to the complicated interplay between superconductivity and electron localization. In this work, we controllably introduce disorder in a two-dimensional high-temperature superconductor by depositing iron clusters onto the superconducting monolayer Fe(Te,Se) crystalline film. The spectral evolution from superconducting gaps to insulating gaps with increasing disorder is detected by scanning tunneling spectroscopy measurements. When the disorder is strong, large U-shaped gaps are observed and attributed to the localization-enhanced Cooper pair correlation. Our observations provide the insight into the emergent phases of low-dimensional and high-temperature superconductors with disorder.

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

1 major / 2 minor

Summary. The manuscript reports an experimental study in which controlled disorder is introduced into monolayer Fe(Te,Se) films by deposition of iron clusters. Scanning tunneling spectroscopy is used to track the evolution of the local density of states, showing a transition from superconducting gaps at low disorder to large U-shaped gaps at high disorder; the latter are attributed to localization-enhanced Cooper-pair correlations. The work aims to illuminate the role of disorder in the superconductor-insulator transition in a two-dimensional high-Tc material.

Significance. If the mechanistic attribution is substantiated, the results would provide direct spectroscopic evidence for how increasing disorder drives a quantum phase transition in a high-temperature superconductor, highlighting the interplay between localization and pairing in two dimensions. The controllable, in-situ disorder introduction via cluster deposition represents a useful experimental platform for such studies.

major comments (1)
  1. [Abstract and strong-disorder discussion] Abstract and the section discussing the strong-disorder regime: the claim that the observed large U-shaped gaps arise specifically from localization-enhanced Cooper-pair correlation is not supported by distinguishing signatures. The spectra are consistent with conventional Anderson localization or charging effects, yet no temperature-dependent gap evolution, coherence-peak remnants, or quantitative comparison to a pairing-enhanced density of states is presented to exclude these alternatives.
minor comments (2)
  1. [Methods] Methods section: provide quantitative metrics for disorder strength (e.g., cluster density, coverage fraction, or mean inter-cluster distance) rather than qualitative descriptions of deposition time.
  2. [Figures] Figure captions and main text: ensure consistent labeling of disorder levels across all STS spectra panels to facilitate direct comparison of gap evolution.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help clarify the interpretation of our results. We address the major comment below and will incorporate revisions to strengthen the discussion of the strong-disorder regime while preserving the core claims supported by the data.

read point-by-point responses

  1. Referee: [Abstract and strong-disorder discussion] Abstract and the section discussing the strong-disorder regime: the claim that the observed large U-shaped gaps arise specifically from localization-enhanced Cooper-pair correlation is not supported by distinguishing signatures. The spectra are consistent with conventional Anderson localization or charging effects, yet no temperature-dependent gap evolution, coherence-peak remnants, or quantitative comparison to a pairing-enhanced density of states is presented to exclude these alternatives.

    Authors: We thank the referee for highlighting this point. The attribution in the abstract and main text is grounded in the systematic, in-situ evolution of the local density of states: at low cluster coverage the spectra show clear superconducting gaps with coherence peaks that close with increasing temperature, while at high coverage the gaps become large, U-shaped, and lack coherence peaks, consistent with theoretical expectations for localization-enhanced pairing near the 2D SIT. Conventional Anderson localization in 2D typically produces soft gaps or power-law tails rather than the hard U-shaped gaps we observe, and charging effects are suppressed by the metallic substrate and the continuous film geometry. Nevertheless, we agree that the manuscript would benefit from a more explicit exclusion of alternatives. We will revise the strong-disorder discussion section to add a direct comparison of the observed line shapes with expected Anderson-localized and charging-effect spectra, include a quantitative estimate of the expected charging energy, and note the absence of temperature-dependent data in the present study. The abstract claim will be softened to “consistent with localization-enhanced Cooper-pair correlations” to reflect the level of support provided by the existing data. revision: partial

Circularity Check

0 steps flagged

No circularity: purely experimental report with no derivation chain

full rationale

The manuscript presents scanning tunneling spectroscopy data on disorder-tuned monolayer Fe(Te,Se), documenting the evolution of spectral gaps from superconducting to large U-shaped insulating features with increasing iron-cluster disorder. All load-bearing statements are direct observational claims or interpretive attributions of the measured spectra; no equations, fitted parameters, self-citations, or ansatzes are invoked that would reduce any result to its own inputs by construction. The work is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the domain assumption that iron-cluster deposition adds only disorder without introducing new chemical phases or charge-transfer effects that would dominate the spectra.

axioms (1)
  • domain assumption Iron clusters deposited on the surface introduce tunable disorder without significantly altering the underlying electronic band structure or doping level.
    Invoked to interpret the gap evolution as purely disorder-driven.

pith-pipeline@v0.9.0 · 5472 in / 1238 out tokens · 53758 ms · 2026-05-15T15:54:35.925596+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

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

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    A. M. Goldman and N. Marković. Superconductor‐insulator transitions in the two‐dimensional limit. Physics Today 51(11):39 - 44 (1998)

    work page 1998

  2. [2]

    M. P. Fisher. Quantum phase transitions in disordered two - dimensional superconductors. Physical Review Letters 65(7):923 (1990)

    work page 1990

  3. [3]

    Dobrosavljevic, N

    V . Dobrosavljevic, N. Trivedi, and J. M. Valles Jr. Conductor insulator quantum phase transitions. Oxford University Press (2012)

    work page 2012

  4. [4]

    Z. Wang, Y . Liu, C. Ji, and J. Wang. Quantum phase transitions in two - dimensional superconductors: a review on recent experimental progress. Reports on Progress in Physics 87, 014502 (2024)

    work page 2024

  5. [5]

    Ghosal, M

    A. Ghosal, M. Randeria, and N. Trivedi. Role of spatial amplitude fluctuations in highly disordered s - wave superconductors. Physical Review Letters 81(18):3940 (1998)

    work page 1998

  6. [6]

    Ghosal, M

    A. Ghosal, M. Randeria, and N. Trivedi. Inhomogeneous pairing in highly disordered s - wave superconductors. Physical Review B 65(1):014501 (2001)

    work page 2001

  7. [7]

    Bouadim, Y

    K. Bouadim, Y . L. Loh, M. Randeria, and N. Trivedi. Single - and two - particle energy gaps across the disorder - driven superconductor – insulator transition. Nature Physics 7(11):884 - 889 (2011)

    work page 2011

  8. [8]

    Y . Dubi, Y . Meir, and Y . Avishai. Nature of the superconductor – insulator transition in disordered superconductors. Nature 449(7164):876 - 880 (2007)

    work page 2007

  9. [9]

    Sacépé, T

    B. Sacépé, T. Dubouchet, C. Chapelier, M. Sanquer, M. Ovadia, D. Shahar, M. Feigel’Man, and L. Ioffe. Localization of preformed Cooper pairs in disordered superconductors. Nature Physics 7(3):239 - 244 (2011)

    work page 2011

  10. [10]

    Mondal, A

    M. Mondal, A. Kamlapure, M. Chand, G. Saraswat, S. Kumar, J. Jesudasan, L. Benfatto, V . Tripathi, and P. Raychaudhuri. Phase fluctuations in a strongly disordered s - wave NbN superconductor close to the metal - insulator transition. Physical Review Letters 106(4):047001 (2011)

    work page 2011

  11. [11]

    Lemarié, A

    G. Lemarié, A. Kamlapure, D. Bucheli, L. Benfatto, J. Lorenzana, G. Seibold, S. Ganguli, P. Raychaudhuri, and C. Castellani. Universal scaling of the order - parameter distribution in strongly disordered superconductors. Physical Review B — Condensed Matter Materials Physics 87(18):184509 (2013)

    work page 2013

  12. [12]

    Seibold, L

    G. Seibold, L. Benfatto, C. Castellani, and J. Lorenzana. Superfluid density and phase relaxation in superconductors with strong disorder. Physical Review Letters 108(20):207004 (2012)

    work page 2012

  13. [13]

    Chand, G

    M. Chand, G. Saraswat, A. Kamlapure, M. Mondal, S. Kumar, J. Jesudasan, V . Bagwe, L. Benfatto, V . Tripathi, and P. Raychaudhuri. Phase diagram of the strongly disordered s - wave superconductor NbN close to the metal - insulator transition. Physical Review B 85(1):014508 (2012)

    work page 2012

  14. [14]

    Swanson, Y

    M. Swanson, Y . L. Loh, M. Randeria, and N. Trivedi. Dynamical conductivity across the disorder - tuned superconductor - insulator transition. Physical Review X 4(2):021007 (2014)

    work page 2014

  15. [15]

    Charpentier, D

    T. Charpentier, D. Perconte, S. Léger, K. R. Amin, F. Blondelle, F. Gay, O. Buisson, L. Ioffe, A. Khvalyuk, I. Poboiko, M. Feigel’man, N. Roch, and B. Sacépé. First - order quantum breakdown of superconductivity in an amorphous superconductor. Nature Physics 21:104 – 109 (2025)

    work page 2025

  16. [16]

    Sherman, G

    D. Sherman, G. Kopnov, D. Shahar, and A. Frydman. Measurement of a superconducting energy gap in a homogeneously amorphous insulator. Physical review letters 108(17):177006 (2012)

    work page 2012

  17. [17]

    Feigel'Man, L

    M. Feigel'Man, L. Ioffe, V . Kravtsov, and E. Cuevas. Fractal superconductivity near localization threshold. Annals of Physics 325(7):1390 - 1478 (2010)

    work page 2010

  18. [18]

    Sacépé, M

    B. Sacépé, M. Feigel’man, and T. M. Klapwijk. Quantum breakdown of superconductivity in low - dimensional materials. Nature Physics 16(7):734 - 746 (2020)

    work page 2020

  19. [19]

    Feigel’man, L

    M. Feigel’man, L. Ioffe, V . Kravtsov, and E. Yuzbashyan. Eigenfunction fractality and pseudogap state 6 near the superconductor - insulator transition. Physical Review Letters 98(2):027001 (2007)

    work page 2007

  20. [20]

    Sacépé, C

    B. Sacépé, C. Chapelier, T. I. Baturina, V . M. Vinokur, M. R. Baklanov, and M. Sanquer. Pseudogap in a thin film of a conventional superconductor. Nature Communications 1(1):140 (2010)

    work page 2010

  21. [21]

    K. Zhao, H. Lin, X. Xiao, W. Huang, W. Yao, M. Yan, Y . Xing, Q. Zhang, Z. - X. Li, S. Hoshino, J. Wang, S. Zhou, L. Gu, M. S. Bahramy, H. Yao, N. Nagaosa, Q. - K. Xue, K. T. Law, X. Chen, and S. - H. Ji. Disorder - induced multifractal superconductivity in monola yer niobium dichalcogenides. Nature Physics 15(9):904 - 910 (2019)

    work page 2019

  22. [22]

    J. He, X. Liu, W. Zhang, L. Zhao, D. Liu, S. He, D. Mou, F. Li, C. Tang, Z. Li, L. Wang, Y . Peng, Y . Liu, C. Chen, L. Yu, G. Liu, X. Dong, J. Zhang, C. Chen, Z. Xu, X. Chen, X. - C. Ma, Q. - K. Xue, and X. J. Zhou. Electronic evidence of an insulator – supercon ductor crossover in single - layer FeSe/SrTiO 3 films. Proceedings of the National Academy of...

    work page 2014

  23. [23]

    Schneider, A

    R. Schneider, A. Zaitsev, D. v. Fuchs, and H. v. Löhneysen. Superconductor - insulator quantum phase transition in disordered FeSe thin films. Physical Review Letters 108(25):257003 (2012)

    work page 2012

  24. [24]

    W. Li, H. Ding, P. Deng, K. Chang, C. Song, K. He, L. Wang, X. Ma, J. - P. Hu, X. Chen, and Q. - K. Xue. Phase separation and magnetic order in K - doped iron selenide superconductor. Nature Physics 8(2):126 - 130 (2012)

    work page 2012

  25. [25]

    Q. Wang, W. Zhang, Z. Zhang, Y . Sun, Y . Xing, Y . Wang, L. Wang, X. Ma, Q. - K. Xue, and J. Wang. Thickness dependence of superconductivity and superconductor – insulator transition in ultrathin FeSe films on SrTiO 3 (001) substrate. 2D Materials 2(4):044012 (2015)

    work page 2015

  26. [26]

    G. He, Y . Li, Y . Lei, A. Kreisel, B. M. Andersen, and J. Wang. Lateral quantum confinement effect on monolayer high - T c superconductors. Nano letters 24(25):7654 - 7661 (2024)

    work page 2024

  27. [27]

    X. Shi, Z. - Q. Han, P. Richard, X. - X. Wu, X. - L. Peng, T. Qian, S. - C. Wang, J. - P. Hu, Y . - J. Sun, and H. Ding. FeTe 1− x Se x monolayer films: towards the realization of high - temperature connate topological superconductivity. Science Bulletin 62(7):503 - 507 (2017)

    work page 2017

  28. [28]

    C. Chen, K. Jiang, Y . Zhang, C. Liu, Y . Liu, Z. Wang, and J. Wang. Atomic line defects and zero - energy end states in monolayer Fe (Te, Se) high - temperature superconductors. Nature Physics 16(5):536 - 540 (2020)

    work page 2020

  29. [29]

    G. He, Y . Li, Y . Lei, F. Wang, and J. Wang. Enhanced proximity effect near the submonolayer terrace of the high - T c superconductor Fe (Te, Se). Physical Review B 109(17):174527 (2024)

    work page 2024

  30. [30]

    F. Li, H. Ding, C. Tang, J. Peng, Q. Zhang, W. Zhang, G. Zhou, D. Zhang, C. - L. Song, K. He, S. - H. Ji, X. Chen, L. Gu, L. Wang, X. - C. Ma, and Q. - K. Xue. Interface - enhanced high - temperature superconductivity in single - unit - cell FeTe 1− x Se x films on SrTiO 3 . Physical Review B 91(22):220503 (2015)

    work page 2015

  31. [31]

    C. Liu, C. Chen, X. Liu, Z. Wang, Y . Liu, S. Ye, Z. Wang, J. Hu, and J. Wang. Zero - energy bound states in the high - temperature superconductors at the two - dimensional limit. Science Advances 6(13):eaax7547 (2020)

    work page 2020

  32. [32]

    Dubouchet, B

    T. Dubouchet, B. Sacépé, J. Seidemann, D. Shahar, M. Sanquer, and C. Chapelier. Collective energy gap of preformed Cooper pairs in disordered superconductors. Nature Physics 15(3):233 - 236 (2019)

    work page 2019

  33. [33]

    B. D. Faeth, S. - L. Yang, J. K. Kawasaki, J. N. Nelson, P. Mishra, C. Parzyck, C. Li, D. Schlom, and K. Shen. Incoherent Cooper Pairing and Pseudogap Behavior in Single - Layer FeSe/SrTiO 3 . Physical Review X 11(2):021054 (2021)

    work page 2021

  34. [34]

    Z. Wang, C. Liu, Y . Liu, and J. Wang. High - temperature superconductivity in one - unit - cell FeSe films. Journal of Physics: Condensed Matter 29(15):153001 (2017)

    work page 2017

  35. [35]

    B. Jäck, F. Zinser, E. J. König, S. N. Wissing, A. B. Schmidt, M. Donath, K. Kern, and C. R. Ast. Visualizing the multifractal wave functions of a disordered two - dimensional electron gas. Physical Review 7 Research 3(1):013022 (2021)

    work page 2021

  36. [36]

    Richardella, P

    A. Richardella, P. Roushan, S. Mack, B. Zhou, D. A. Huse, D. D. Awschalom, and A. Yazdani. Visualizing critical correlations near the metal - insulator transition in Ga1 - x Mn x As. Science 327(5966):665 - 669 (2010)

    work page 2010

  37. [37]

    B. G. Shin, J. - H. Park, J. - Y . Juo, J. Kong, and S. J. Jung. Structural - disorder - driven critical quantum fluctuation and localization in two - dimensional semiconductors. Nature Communications 14(1):2283 (2023)

    work page 2023

  38. [38]

    Rubio - Verdú, A

    C. Rubio - Verdú, A. M. Garcı́a - Garcı́a, H. Ryu, D. - J. Choi, J. Zaldı́var, S. Tang, B. Fan, Z. - X. Shen, S. - K. Mo, and J. I. Pascual. Visualization of multifractal superconductivity in a two - dimensional transition metal dichalcogenide in the weak - disorder re gime. Nano Letters 20(7):5111 - 5118 (2020)

    work page 2020

  39. [39]

    Nakayama and K

    T. Nakayama and K. Yakubo. Fractal concepts in condensed matter physics. Springer Berlin, Heidelberg 140 (2003)

    work page 2003

  40. [40]

    Evers and A

    F. Evers and A. D. Mirlin. Anderson transitions. Reviews of Modern Physics 80(4):1355 - 1417 (2008). 8 FIG. 1 (a) STM topography of the pristine monolayer FTS grown on STO terraces (higher terrace in brighter color), with the atomically resolved image in the inset. (b) Normalized spectra G N of the pristine monolayer FTS in (a) at varying temperatures. (c...

    work page 2008