Pith. sign in

REVIEW 3 major objections 5 minor 40 references

Local control of parity and charge in nanoscale superconducting lead islands

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read On individual lead islands with effective radius below about 12 nm, the energy $E_C$ to add one electron exceeds the Cooper-pair binding energy $\Delta$, so the superconducting ground state can be flipped between even and odd…

desk verdict Clean static odd-parity signature in one small Pb island, but the advertised local parity control is an extrapolation from separate measurements. read the letter →

arxiv 2507.12150 v1 pith:6HYBPHFJ submitted 2025-07-16 cond-mat.mes-hall

Stefano Trivini , Jon Ortuzar , Katerina Vaxevani , Beatriz Viña-Bausá , F. Sebastian Bergeret , Jose Ignacio Pascual This is my paper · ORCID
classification cond-mat.mes-hall
keywords superconductingislandsCoulombblockadechargeparityeven-oddgroundstatesscanningtunnelingspectroscopyleadongraphenemagneticfieldgapreopeningelectrostaticgating
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 reports that on individual superconducting lead islands sitting on graphene, the charging energy $E_C$ and the pairing gap $\Delta$ can be measured separately, and the ground-state parity of the island can be switched locally. Using scanning tunneling spectroscopy fitted with a double-barrier tunneling junction model, the authors find that below an effective radius of about 12 nm, $E_C$ exceeds $\Delta$. In that regime the ground state can be either even (all electrons paired) or odd (one unpaired electron) depending on the island's residual charge $q_0$, and STM voltage pulses move that charge in a controlled way. The odd-parity state is identified by a magnetic-field-induced reopening of the spectral gap after the tip's superconductivity is quenched. If correct, this establishes a surface-supported, locally gate-tunable superconducting island whose parity and charge can be controlled with a single tip.

What carries the argument

The carrying object is the double-barrier tunneling junction (DBTJ) Hamiltonian for a small superconducting island, $H = H_S + H_C$, where the pairing term $H_S$ adds the pairing energy $\Delta$ when the island's electron number is odd, and the charging term is $H_C = E_C(n - q_0/e)^2$ with $n$ the island charge and $q_0$ the gate-controlled residual charge. Its eigenstates form parabolas in $q_0$, with odd-parity parabolas shifted upward by $\Delta$; when $E_C > \Delta$, the odd-parabola minimum drops below the even one at $q_0 = e$, making the odd ground state accessible. The experimental protocol separates the two energies through the magnetic-field evolution: the tip gap closes first near 0.8 T and the island gap near 1.5 T, so the residual gap at high field equals $E_C$. STM voltage pulses then act as the local gate that moves $q_0$ and drives the parity crossing.

What would settle it

Repeat the magnetic-field sweep on the 9.5 nm island with a normal-metal tip, so no tip superconducting gap is present: the zero-field spectral gap should be $2(E_C-\Delta)$ and the high-field gap $2E_C$ if the odd-parity assignment is right, whereas a gap that simply closes without reopening would point to an even-parity state or to a field-dependent $E_C$.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a size-controlled crossover in supported superconducting Pb islands: for effective radii above about 12 nm the pairing gap $\Delta$ dominates the charging energy $E_C$, while below it $E_C > \Delta$, and the even- and odd-parity ground states become nearly degenerate near residual charge $q_0 = e$. The authors demonstrate on a 9.5 nm island that the ground state can be odd: the spectral gap first closes as the tip's superconductivity is suppressed by magnetic field and then reopens as the bare Coulomb gap is restored, which is the predicted hallmark of an odd-parity state. They further show that repeated STM bias pulses shift the island's residual charge by more than one electron charge, reversibly moving the spectrum through the even/odd crossing and mapping the charge-parity landscape of an individual island.

Load-bearing premise

The 12 nm crossover and the odd-parity classification of the 9.5 nm island rest on assuming that $E_C$ is independent of magnetic field and that the tip gap is what closes near 0.8 T, leaving a high-field residual gap equal to $E_C$; if $E_C$ shifts with field or the closing order is misread, the critical size and the parity label could change.

Editorial extensions

If this is right

  • Below the critical size, an island at $q_0 = e$ can sit in an odd-parity ground state, identified by the high-field reopening of its spectral gap.
  • Voltage-pulse gating provides local electrostatic control without a three-terminal gate, so the same island can be switched repeatedly between even and odd parity.
  • The magnetic-field protocol separates $E_C$ from $\Delta$ in a single island, so the measured spectral gap no longer conflates the two energies.
  • Smaller islands enter a Coulomb-dominated regime where pairing alone no longer fixes the ground state, linking the data to the breakdown of Cooper pairing at the nanoscale.
  • The tunable even/odd platform is proposed by the authors as a basis for $\pi$-junction superconducting devices and for parity-based or topological qubit designs.

Reading between the lines

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

  • The field-reopening signature could serve as a general spectroscopic fingerprint of odd-parity ground states in other superconducting islands, even where a full DBTJ fit is not available.
  • Because the island's residual charge responds to static charge puddles in the graphene, the same islands could act as scanning point-charge sensors, with the local potential landscape read out through the imbalance of the $\alpha$ and $\beta$ spectral peaks.
  • If the crossover radius is set by the ratio $E_C/\Delta$ rather than lead-specific parameters, similar parity-tunable islands should appear in other strong-coupling superconductors on low-capacitance supports; growing islands of other materials at different sizes would test this.
  • Combined with spin-orbit coupling or a magnetic field tuned to the parity degeneracy point, the odd-parity island would form a two-level system whose charge and parity both respond to the tip; whether this becomes a usable qubit is not demonstrated in the paper.
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.

Referee Report

3 major / 5 minor

Summary. The manuscript reports STS measurements on Pb nano-islands grown on graphene, aimed at separating charging energy (EC) and superconducting pairing energy (Δ) in the double-barrier tunneling junction (DBTJ) regime. From the magnetic-field evolution of the spectral gap, the authors extract EC and Δ for 18 islands and assert a crossover at effective radius r_eff ≈ 12 nm below which EC > Δ. They further show that voltage pulses from the STM tip can alter the residual charge q0 of larger islands (r_eff ≥ 15 nm), producing gate-dependent spectral maps interpreted with the DBTJ model. For one small island (r_eff = 9.5 nm), they observe a gap that first closes and then reopens with magnetic field, which they identify as the signature of an odd-parity ground state. The paper concludes that even- and odd-parity ground states coexist below 12 nm and can be tuned with electrostatic gating.

Significance. If fully supported, the result would establish a surface-supported platform for parity control in superconducting islands, relevant for Majorana-box and parity-based qubit proposals. The work has clear strengths: the DBTJ model is standard and not invented for this paper; the magnetic-field-induced gap reopening in Fig. 5(d) is a distinctive, falsifiable signature of an odd-parity ground state; and the demonstration of local q0 control via STM voltage pulses (Fig. 3) is a useful technical advance. The spatial mapping in Fig. 4 also provides a creative way to visualize electrostatic puddle effects. However, the central claim of tunable parity is weakened by the fact that the gate-tuned maps and the odd-parity island are disjoint observations, and by the absence of error bars or robustness analysis in the extraction of EC and Δ. The significance of the paper depends on whether the authors can either supply the missing direct demonstration or appropriately soften the headline claim.

major comments (3)
  1. [§Locally gating the Pb islands with voltage pulses; Figs. 3 and 5]
  2. [Fig. 2(b,c) and the extraction of EC and Δ from magnetic-field data]
  3. [Fig. 5(d) and the identification of odd parity]
minor comments (5)
  1. [Abstract and Introduction]
  2. [Fig. 3 caption and text]
  3. [Fig. 5(c) and related text]
  4. [Introduction, first paragraph]
  5. [Fig. 2(c) caption]

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the EC/Delta crossover and odd-parity identification rest on a standard external DBTJ model and an independent magnetic-field reopening signature, not on a fitted parameter renamed as a prediction.

full rationale

The derivation chain is not circular. The DBTJ Hamiltonian (Eqs. 1-3) is a standard, externally cited model, and the paper does not fit the parity outcome and then present it as a prediction. EC and Delta are extracted from the magnetic-field evolution of the spectral gap, with the high-field residual gap attributed to EC; this is a measurement calibration consistent with the model, not a self-justifying definition. The odd-parity classification of the 9.5 nm island rests on a distinct experimental signature: the gap initially closes with magnetic field (tip gap suppression) and then reopens at higher fields (quenching of pairing, leaving the Coulomb gap). This reopening signature is not used to set the EC and Delta values, providing independent grounding. Gate-induced changes of q0 are separately demonstrated on even-parity islands, so the conclusion that parity would be tunable in the EC>Delta regime is a model-based extrapolation rather than a directly observed single-island gate sweep. That is an evidentiary limitation or overstatement, not a circular reduction. The self-citations [22,23] supply background on Pb island growth and manipulation and are not load-bearing for the core physical claim. The main weakness of the paper, namely the absence of a gate sweep across the even/odd degeneracy on the sub-12 nm island, concerns completeness of demonstration rather than circularity of the derivation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a standard DBTJ model and a few domain assumptions about the STM geometry and field independence of EC. The main free parameters are the size-dependent Delta and EC, plus the pulse-tunable residual charge q0. No new entities are introduced.

free parameters (3)
  • Superconducting gap Delta of island = ranges from ~1.3 meV for large islands to smaller values for small islands
    Extracted from DBTJ fits to the magnetic-field dependence of the spectral gap for each island (Fig. 2b).
  • Charging energy EC = negligible for large islands, increasing for small islands; e.g., implied by ~3.8 mV gap for 9.5 nm island
    Determined from the residual spectral gap at high magnetic fields after the tip and island gaps close.
  • Residual charge q0 = tuned by voltage pulses in range roughly -1e to +1e
    Set by voltage pulses and determined from the asymmetry of coherence peaks via DBTJ fits.
assumptions (4)
  • domain assumption The island is described by the DBTJ Hamiltonian H = HS + HC with HS = (1 - (-1)^n) Delta/2 and HC = EC (n - q0/e)^2 (Eqs. 1-3).
    Standard model for Coulomb blockade in superconducting islands, but assumes a single charging energy and a mean-field BCS pairing term.
  • domain assumption C1 << C2, so the charging energy is dominated by the island-substrate capacitance.
    Typical for STM geometry; if C1 were comparable, the extracted EC would mix both junctions.
  • ad hoc to paper EC is independent of magnetic field, allowing its separation from Delta in the field-dependent gap.
    This assumption is central to the disentangling procedure in Fig. 2(b); it is plausible but not directly verified.
  • domain assumption The tip gap closes first at ~0.8 T, followed by the island gap at ~1.5 T.
    Based on measurements on bulk-like islands and the model fit; misidentification would bias the extracted EC.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Local control of parity and charge in nanoscale superconducting lead islands." pith.science (2026). https://pith.science/paper/6HYBPHFJ

@misc{pith2026250712150,
  author       = {Pith},
  title        = {Pith review of: Local control of parity and charge in nanoscale superconducting lead islands},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6HYBPHFJ}},
  note         = {Machine review of arXiv:2507.12150}
}
abstract

Small superconducting islands can exhibit charge quantization, where Coulomb interactions compete with Cooper pairing. Using scanning tunneling spectroscopy, we probe this interplay by measuring the charging energy ($E_C$) and the pairing energy ($\Delta$) of individual nano-islands. Below a critical island size, where $E_C > \Delta$, we observe a crossover between even and odd parity ground states. By applying controlled voltage pulses, we continuously tune the island's electrostatic potential and map the full charge-parity landscape. These results demonstrate tunable superconducting ground states, offering a potential platform for qubit design and control.

Figures

Figures reproduced from arXiv: 2507.12150 by the authors.

Figure 1
Figure 1. FIG. 1. a) STM image of Pb islands on graphene. (b) STS on [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. a) Evolution of the spectral gap with an out-of-plane [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. a) (bottom) Differential conductance on a Pb island with [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. a) Topographic image of an island with [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. a) Calculated LDOS map varying the excess charge. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references · 39 canonical work pages

  1. [1]

    Theory of dirty superconductors,

    P. W. Anderson, “Theory of dirty superconductors,” J. Phys. Chem. Solids 11, 26–30 (1959)

    work page 1959

  2. [2]

    Coulomb gap and low temperature conductivity of disordered systems,

    A. L. Efros and B. I. Shklovskii, “Coulomb gap and low temperature conductivity of disordered systems,” J. Phys. C: Solid State Phys. 8, L49 (1975)

    work page 1975

  3. [3]

    Correlated discrete transfer of single electrons in ultrasmall tunnel junctions,

    K. K. Likharev, “Correlated discrete transfer of single electrons in ultrasmall tunnel junctions,” IBM J. Res. & Dev. 32, 144–158 (1988)

    work page 1988

  4. [4]

    Grabert and M

    H. Grabert and M. H. Devoret, eds., Single Charge Tun- neling, NATO ASI Series, Vol. 294 (Springer US, Boston, MA, 1992)

    work page 1992

  5. [5]

    Variation of the Coulomb staircase in a two-junction system by fractional electron charge,

    A. E. Hanna and M. Tinkham, “Variation of the Coulomb staircase in a two-junction system by fractional electron charge,” Phys. Rev. B 44, 5919–5922 (1991)

    work page 1991

  6. [6]

    Superconducting parity effect across the An- derson limit,

    S. Vlaic, S. Pons, T. Zhang, A. Assouline, A. Zimmers, C. David, G. Rodary, J.-C. Girard, D. Roditchev, and H. Aubin, “Superconducting parity effect across the An- derson limit,” Nat Commun 8, 14549 (2017)

    work page 2017

  7. [7]

    B. L. Al’tshuler, P. A. Lee, and R. A. Webb, Mesoscopic Phenomena in Solids , Modern Problems in Condensed Matter Sciences No. v. 30 (North Holland Sole distribu- tors for the USA and Canada, Elsevier Science, Amster- dam New York New York, NY, USA, 1991)

    work page 1991

  8. [8]

    Charge Tunneling Rates in Ultrasmall Junctions,

    G.-L. Ingold and Yu. V. Nazarov, “Charge Tunneling Rates in Ultrasmall Junctions,” in Single Charge Tunnel- ing, Vol. 294, edited by H. Grabert and M. H. Devoret (Springer US, Boston, MA, 1992) pp. 21–107

    work page 1992

Show all 40 references
  1. [9]

    Coulomb blockade of single-electron tunneling, and coherent oscillations in small tunnel junctions,

    D. V. Averin and K. K. Likharev, “Coulomb blockade of single-electron tunneling, and coherent oscillations in small tunnel junctions,” J Low Temp Phys 62, 345–373 (1986)

    1986

  2. [10]

    Con- ductance of a proximitized nanowire in the Coulomb blockade regime,

    B. van Heck, R. M. Lutchyn, and L. I. Glazman, “Con- ductance of a proximitized nanowire in the Coulomb blockade regime,” Phys. Rev. B 93, 235431 (2016)

    2016

  3. [11]

    Dittrich, ed., Quantum Transport and Dissipation (Wiley-VCH, Weinheim ; New York, 1998)

    T. Dittrich, ed., Quantum Transport and Dissipation (Wiley-VCH, Weinheim ; New York, 1998)

    1998

  4. [12]

    Parity-induced suppression of the Coulomb blockade of Josephson tunneling,

    K. A. Matveev, M. Gisself¨ alt, L. I. Glazman, M. Jonson, and R. I. Shekhter, “Parity-induced suppression of the Coulomb blockade of Josephson tunneling,” Phys. Rev. Lett. 70, 2940–2943 (1993)

    1993

  5. [13]

    Ef- fects of Charge Parity in Tunneling Through A Supercon- ducting Grain,

    K. A. Matveev, L. I. Glazman, and R. I. Shekhter, “Ef- fects of Charge Parity in Tunneling Through A Supercon- ducting Grain,” Modern Physics Letters B08, 1007–1026 (1994)

    1994

  6. [14]

    Parity-Affected Superconductivity in Ultrasmall Metal- lic Grains,

    J. Von Delft, A. D. Zaikin, D. S. Golubev, and W. Tichy, “Parity-Affected Superconductivity in Ultrasmall Metal- lic Grains,” Phys. Rev. Lett. 77, 3189–3192 (1996)

    1996

  7. [15]

    Quan- tum breakdown of superconductivity in low-dimensional materials,

    B. Sac´ ep´ e, M. Feigel’man, and T. M. Klapwijk, “Quan- tum breakdown of superconductivity in low-dimensional materials,” Nature Physics 16, 734–746 (2020). 6

    2020

  8. [16]

    Confinement-Engineered Superconductor to Correlated-Insulator Transition in a van der Waals Monolayer,

    S. C. Ganguli, V. Vaˇ no, S. Kezilebieke, J. L. Lado, and P. Liljeroth, “Confinement-Engineered Superconductor to Correlated-Insulator Transition in a van der Waals Monolayer,” Nano Lett. 22, 1845–1850 (2022)

    2022

  9. [17]

    Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler- Aronov density of states suppression in ultrathin NbN films,

    C. Carbillet, V. Cherkez, M. A. Skvortsov, M. V. Feigel’man, F. Debontridder, L. B. Ioffe, V. S. Stol- yarov, K. Ilin, M. Siegel, D. Roditchev, T. Cren, and C. Brun, “Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler- Aronov d...

    2020

  10. [18]

    See Supplemental Material for additional data and details on the theoretical model

  11. [19]

    X-Ray studies of graphite formed by decom- posing silicon carbide,

    D. Badami, “X-Ray studies of graphite formed by decom- posing silicon carbide,” Carbon 3, 53–57 (1965)

    1965

  12. [20]

    Electric field effect in atomically thin carbon films,

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004)

    2004

  13. [21]

    Observa- tion of Yu–Shiba–Rusinov States in Superconducting Graphene,

    E. Cort´ es-del R ´ ıo, J. L. Lado, V. Cherkez, P. Mallet, J.-Y. Veuillen, J. C. Cuevas, J. M. G´ omez-Rodr ´ ıguez, J. Fern´ andez-Rossier, and I. Brihuega, “Observa- tion of Yu–Shiba–Rusinov States in Superconducting Graphene,” Adv. Mater. 33, 2008113 (2021)

    2021

  14. [22]

    Shaping Graphene Superconductivity with Nanometer Precision,

    E. Cort´ es-del R ´ ıo, Stefano. Trivini, J. I. Pascual, V. Cherkez, P. Mallet, J.-Y. Veuillen, Juan. C. Cuevas, and I. Brihuega, “Shaping Graphene Superconductivity with Nanometer Precision,” Small 20, 2308439 (2024)

    2024

  15. [23]

    From local to collective superconductivity in proximitized graphene,

    S. Trivini, T. Kokkeler, J. Ortuzar, E. C.-d. R ´ ıo, B. V. Baus´ a, P. Mallet, J.-Y. Veuillen, J. C. Cuevas, I. Bri- huega, F. S. Bergeret, and J. I. Pascual, “From local to collective superconductivity in proximitized graphene,” (2025), 10.48550/arXiv.2504.19620

    2025 doi arXiv

  16. [24]

    SPECS gmbh Joule-Thomson 1.2K STM, 3T uniaxial magnetic field

  17. [25]

    Dynamical Coulomb Blockade Observed in Nanosized Electrical Contacts,

    C. Brun, K. H. M¨ uller, I.-P. Hong, F. Patthey, C. Flindt, and W.-D. Schneider, “Dynamical Coulomb Blockade Observed in Nanosized Electrical Contacts,” Phys. Rev. Lett. 108, 126802 (2012)

    2012

  18. [26]

    Observation of Coulomb blockade and Coulomb staircases in superconducting Pr 0.8 Sr 0.2 NiO 2 films,

    R.-F. Wang, Y.-L. Xiong, H. Yan, X. Hu, M. Osada, D. Li, H. Y. Hwang, C.-L. Song, X.-C. Ma, and Q.-K. Xue, “Observation of Coulomb blockade and Coulomb staircases in superconducting Pr 0.8 Sr 0.2 NiO 2 films,” Phys. Rev. B 107, 115411 (2023)

    2023

  19. [27]

    Effect of the electromagnetic environment on the Coulomb blockade in ultrasmall tun- nel junctions,

    M. H. Devoret, D. Esteve, H. Grabert, G.-L. Ingold, H. Pothier, and C. Urbina, “Effect of the electromagnetic environment on the Coulomb blockade in ultrasmall tun- nel junctions,” Phys. Rev. Lett. 64, 1824–1827 (1990)

    1990

  20. [28]

    Single-electron charg- ing of a superconducting island,

    D. V. Averin and Yu. V. Nazarov, “Single-electron charg- ing of a superconducting island,” Phys. Rev. Lett. 69, 1993–1996 (1992)

    1992

  21. [29]

    Even- odd asymmetry of a superconductor revealed by the Coulomb blockade of Andreev reflection,

    T. M. Eiles, J. M. Martinis, and M. H. Devoret, “Even- odd asymmetry of a superconductor revealed by the Coulomb blockade of Andreev reflection,” Phys. Rev. Lett. 70, 1862–1865 (1993)

    1993

  22. [30]

    Charge transport by Andreev reflection through a mesoscopic superconducting island,

    J. M. Hergenrother, M. T. Tuominen, and M. Tin- kham, “Charge transport by Andreev reflection through a mesoscopic superconducting island,” Phys. Rev. Lett. 72, 1742–1745 (1994)

    1994

  23. [31]

    Sensing the quantum limit in scanning tunnelling spectroscopy,

    C. R. Ast, B. J¨ ack, J. Senkpiel, M. Eltschka, M. Etzkorn, J. Ankerhold, and K. Kern, “Sensing the quantum limit in scanning tunnelling spectroscopy,” Nat. Commun. 7, 13009 (2016)

    2016

  24. [32]

    Dy- namical Coulomb Blockade as a Local Probe for Quan- tum Transport,

    J. Senkpiel, J. C. Kl¨ ockner, M. Etzkorn, S. Dambach, B. Kubala, W. Belzig, A. L. Yeyati, J. C. Cuevas, F. Pauly, J. Ankerhold, C. R. Ast, and K. Kern, “Dy- namical Coulomb Blockade as a Local Probe for Quan- tum Transport,” Phys. Rev. Lett. 124, 156803 (2020)

    2020

  25. [33]

    Scanning Tunneling Spec- troscopy Study of the Proximity Effect in a Disordered Two-Dimensional Metal,

    L. Serrier-Garcia, J. C. Cuevas, T. Cren, C. Brun, V. Cherkez, F. Debontridder, D. Fokin, F. S. Berg- eret, and D. Roditchev, “Scanning Tunneling Spec- troscopy Study of the Proximity Effect in a Disordered Two-Dimensional Metal,” Phys. Rev. Lett. 110, 157003 (2013)

    2013

  26. [34]

    Observation of Coulomb Gap and Enhanced Superconducting Gap in Nano-Sized Pb Islands Grown on SrTiO 3,

    Y. Yuan, X. Wang, C. Song, L. Wang, K. He, X. Ma, H. Yao, W. Li, and Q.-K. Xue, “Observation of Coulomb Gap and Enhanced Superconducting Gap in Nano-Sized Pb Islands Grown on SrTiO 3,” Chinese Phys. Lett. 37, 017402 (2020)

    2020

  27. [35]

    Gate- controlled ionization and screening of cobalt adatoms on a graphene surface,

    V. W. Brar, R. Decker, H.-M. Solowan, Y. Wang, L. Maserati, K. T. Chan, H. Lee, C ¸ . O. Girit, A. Zettl, S. G. Louie, M. L. Cohen, and M. F. Crommie, “Gate- controlled ionization and screening of cobalt adatoms on a graphene surface,” Nature Phys 7, 43–47 (2011)

    2011

  28. [36]

    Coulomb blockade phenomena observed in supported metallic nanoislands,

    I.-P. Hong, C. Brun, M. Pivetta, F. Patthey, and W.- D. Schneider, “Coulomb blockade phenomena observed in supported metallic nanoislands,” Front. Physics1 (2013), 10.3389/fphy.2013.00013

    2013

  29. [37]

    Parity transitions in the super- conducting ground state of hybrid InSb–Al Coulomb is- lands,

    J. Shen, S. Heedt, F. Borsoi, B. van Heck, S. Gazibegovic, R. L. M. Op het Veld, D. Car, J. A. Logan, M. Pend- harkar, S. J. J. Ramakers, G. Wang, D. Xu, D. Bouman, A. Geresdi, C. J. Palmstrøm, E. P. A. M. Bakkers, and L. P. Kouwenhoven, “Parity transitions in the super- condu...

    2018

  30. [38]

    Exponential protection of zero modes in Majorana islands,

    S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nyg ˚ ard, P. Krogstrup, and C. M. Marcus, “Exponential protection of zero modes in Majorana islands,” Nature 531, 206–209 (2016)

    2016

  31. [39]

    Majorana box qubits,

    S. Plugge, A. Rasmussen, R. Egger, and K. Flensberg, “Majorana box qubits,” New J. Phys. 19, 012001 (2017)

    2017

  32. [40]

    Majorana zero modes in superconductor–semiconductor heterostructures,

    R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwen- hoven, P. Krogstrup, C. M. Marcus, and Y. Oreg, “Majorana zero modes in superconductor–semiconductor heterostructures,” Nature Reviews Materials 3, 52–68 (2018)

    2018

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.