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REVIEW 3 major objections 5 minor 40 references

The charging energy of PbTe quantum dots is controlled by nanowire cross-sectional area, rising from unmeasurable to 210 µeV as the area shrinks sixtyfold.

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2026-08-02 23:43 UTC pith:6NWJJDFY

load-bearing objection Systematic area sweep resolves the PbTe E_C controversy, with a soft spot in causal attribution that the authors themselves flag. the 3 major comments →

arxiv 2602.12791 v2 pith:6NWJJDFY submitted 2026-02-13 cond-mat.mes-hall

Presence versus absence of charging energies in PbTe quantum dots

Yuhao Wang , Lining Yang , Wenyu Song , Li Chen , Zehao Yu , Xinchen He , Zeyu Yan , Jiaye Xu
show 13 more authors
Ruidong Li Weizhao Wang Zonglin Li Shuai Yang Shan Zhang Xiao Feng Tiantian Wang Yunyi Zang Lin Li Runan Shang Qi-Kun Xue Ke He Hao Zhang
This is my paper
classification cond-mat.mes-hall PACS 73.21.La73.23.Hk73.63.Nm
keywords charging energyPbTenanowirequantum dotCoulomb blockadecross-sectional areacontact capacitancegate-defined quantum dot
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper resolves a standing ambiguity: previous studies of PbTe nanowire quantum dots disagreed about whether a charging energy exists. The authors vary the nanowire cross-sectional area across four devices (plus three from earlier work), covering a factor of 60 in area. They find that for areas around 15,000 nm² or larger, the charging energy is below the 20 µeV thermal resolution, while quantized orbital levels remain visible; for areas of 5000, 1500, and 460 nm², the charging energy grows to 80, 160, and 210 µeV. This pattern indicates that the total dot capacitance is dominated by source/drain contacts, whose capacitance shrinks with wire area. If correct, the result turns a confusing scatter of reports into a single design curve and supports gate-defined PbTe quantum dots for topological qubit work.

Core claim

The central claim is that absence versus presence of charging energy in PbTe quantum dots is not a material mystery but a size effect. In the authors' data, the charging energy E_C is unmeasurable for cross-sectional areas at or above about 15,000 nm² (limit set by an electron temperature of 70 mK, i.e., 3.5 k_B T_e ≈ 20 µeV), and becomes finite—80 µeV, 160 µeV, 210 µeV—as the area drops to 5000, 1500, and 460 nm², respectively. The accompanying magnetic-field evolution (Coulomb peaks that do not split and odd valleys that widen) confirms that the finite values are charging energies rather than level spacings. The authors further argue from measured gate lever arms (C_PG/C ≤ 0.05) that gate

What carries the argument

The central object is the cross-sectional area of the PbTe nanowire, used as the independent variable that controls the contact capacitance and therefore the charging energy E_C = e²/C. The key identities are the even-odd pattern of Coulomb diamond sizes (alternating E_C and E_C + δ) and the magnetic-field behavior (odd valleys grow, even valleys shrink), which together distinguish finite E_C from pure level splitting. The measured plunger-gate lever arms (C_PG/C from 0.003 to 0.05) show the gate capacitances are small, so the total capacitance C is dominated by C_S + C_D, implying that shrinking the wire cross-section reduces the contact capacitance.

Load-bearing premise

The load-bearing assumption is that the observed rise in charging energy is caused by the smaller cross-sectional area, not by the other device differences that change alongside it (gate geometry, dot length, cross-section aspect ratio).

What would settle it

Fabricate two PbTe quantum dots with identical cross-sectional area but substantially different dot lengths (e.g., 200 nm vs 500 nm) and identical gate design; if their charging energies are the same, the area is the controlling parameter, but if they differ, the stated geometric control is incomplete. Alternatively, at a fixed area of ~1500 nm², enlarge the source/drain contact footprint; if E_C drops, the contact-capacitance mechanism is confirmed.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The E_C-versus-area curve from Fig. 3(c) functions as a design rule: PbTe wires with cross-sectional area below roughly 10,000 nm² are needed to resolve Coulomb blockade, while larger wires behave as level-only quantum dots.
  • The contradiction between earlier reports (no E_C vs. ~110–130 µeV) is resolved, since those devices fall on different ends of the same area dependence.
  • Quantized level spectroscopy (measuring δ) is possible even when E_C is below the thermal resolution, so quantum-dot physics in PbTe does not require visible Coulomb diamonds.
  • The gate-tunable QPC-to-QD transition, verified by electrostatic simulations, shows that the large dielectric constant does not prevent local gating—a necessary condition for gate-defined qubits in PbTe.
  • Ballistic transport and transparent contacts survive down to the smallest wires (460 nm²), so reducing area to raise E_C does not degrade the transport quality.

Where Pith is reading between the lines

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

  • If contact capacitance dominates, then at a fixed cross-sectional area the charging energy should also depend on dot length and contact geometry; the paper's own data has dot lengths varying from 270 to 430 nm, so a dedicated length series should show E_C increasing as the dot is shortened.
  • The lever-arm data imply gate design has almost no effect on E_C, so side-gated devices with the same wire area should show the same charging energy as the top-gated devices here—something that could be checked by re-analyzing prior side-gated datasets.
  • A quantitative capacitance model, treating C_S and C_D as functions of wire dimensions, would presumably collapse the seven data points onto a single predicted curve; this paper establishes the experimental trend but leaves the model implicit.
  • The same geometric strategy might transfer to other high-dielectric-constant nanowires (e.g., PbSe), where charging energies are similarly suppressed, providing a path to tunable single-electron devices in materials with strong screening.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript reports a systematic investigation of charging energy (EC) in PbTe nanowire quantum dots as a function of nanowire cross-sectional area. For areas ≳15000 nm², Coulomb diamonds are absent and EC is below the stated ~20 µeV thermal resolution; for areas of 5000, 1500, and 460 nm², the authors extract EC = 80, 160, and 210 µeV from alternating diamond sizes, corroborated by magnetic-field evolution of odd/even valleys. The paper also demonstrates gate-defined QDs and QPC-to-QD tunability, supported by 2D electrostatic simulations with Thomas-Fermi screening. The central claim is that decreasing cross-sectional area reduces contact capacitance and thereby increases EC, resolving conflicting literature reports.

Significance. If the area dependence is real, it resolves the presence/absence ambiguity and offers a quantitative design rule for PbTe quantum devices. The paper's strengths include open data (Zenodo DOI), explicit statement of the 20 µeV detection floor, use of an independent magnetic-field signature (odd valleys grow, even valleys shrink) that was not used in the EC extraction, and inclusion of three prior devices as consistency checks. The electrostatic simulations for gate tunability are a useful complement. The main weakness is causal attribution: the area trend is inferred from one device per area with concurrent changes in gate geometry and dot length, so the paper does not yet isolate cross-sectional area as the controlling parameter.

major comments (3)
  1. [Sec. III, Fig. 3(c)] The central claim that EC is controlled by cross-sectional area is not isolated from concurrent device parameters. Device A is side-gated while devices B–D are top-gated, and dot lengths are 270, 390, and 430 nm for B–D, increasing as area decreases. With one device per area, the monotonic EC trend could be driven by these changes. The text concedes 'other factors such as the dot length and aspect ratio may also affect the contact capacitance' (Sec. III, Fig. 3(c) discussion). A quantitative capacitance model separating area from length/aspect-ratio dependence, or additional devices that vary area while keeping gate geometry and dot length fixed, is required to support the abstract's attribution of the trend to area.
  2. [Sec. III, Fig. 2(f) caption] The device B data point, which is the pivotal transition between undetectable and finite EC, uses a cross-sectional area measured on a sister nanowire rather than the measured device, because device B burned. This introduces an unquantified uncertainty in the area assignment for that point. The authors should state the estimated area variation across nominally identical wires and show how the EC-area trend in Fig. 3(c) changes under this uncertainty.
  3. [Sec. III, lever-arm argument] The lever-arm argument (C_PG/C ≤ 0.05) shows that gate capacitances are a small fraction of total capacitance, but it does not quantify how contact capacitance scales with area versus length. The direction claimed (area↓ increases EC) is consistent with a simple C ~ εA/L estimate, but since L also increases simultaneously, the data cannot distinguish area from length effects. A simple quantitative estimate using the reported dimensions would help support the proposed mechanism.
minor comments (5)
  1. [Introduction and abstract] The Introduction states device D area as 500 nm² while the abstract and Fig. 2(l) say 460 nm²; please correct the inconsistency.
  2. [Sec. III] Lever arms are quoted as 0.008, 0.04, and 0.05 for devices B–D; state explicitly whether these are dimensionless C_PG/C or in meV/V, and clarify the relation to the earlier '3 meV/V' for device A.
  3. [Sec. III] The 20 µeV floor is quoted as 3.5 kBTe; specify the lineshape/convention used (e.g., FWHM vs. half-width) and justify the electron temperature Te = 70 mK.
  4. [Fig. 2(p)] Odd/even valleys are labeled for device C but not for device D; adding labels to panel (p) would aid comparison.
  5. [Sec. V] The simulations treat PbEuTe as PbTe; a sentence on the expected effect of this approximation on barrier heights would be useful.

Circularity Check

0 steps flagged

No significant circularity: the E_C versus area trend is read from transport data and independently corroborated, not produced by a fit or by a self-citation chain.

full rationale

The central claim—that E_C is unmeasurable for large PbTe nanowire cross-sections and rises to 80, 160, and 210 µeV for smaller areas—is an empirical compilation of Coulomb-diamond measurements. For devices B–D, E_C values are read directly from the bias-axis diamond heights (alternating diamond sizes), and the magnetic-field odd/even valley evolution is an independent check of the finite-E_C interpretation that was not used to set those values. Device A gives new evidence for the large-area absence, while the three large-area points taken from the authors' Ref. [17] are raw transport data re-presented in the Supplemental Material, not a fitted parameter renamed as a prediction; Refs. [16] and [18] also frame the prior presence/absence ambiguity externally. The lever-arm argument (C_PG/C ≤ 0.05) is used only to rationalize the trend, not to derive E_C values. The admitted confounds—dot length, aspect ratio, and gate-geometry changes—weaken causal attribution but are a correctness concern, not circularity. No uniqueness theorem, ansatz smuggled via citation, definitional equivalence, or fitted-input-called-prediction step is present; the derivation chain is self-contained measurement plus standard Coulomb-blockade interpretation.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The paper's central claim rests on standard Coulomb-blockade electrostatics plus a small set of measurement-interpretation choices (Te, lever arms, o/e assignment). No new physical entities are postulated. The most load-bearing entry is the contact-capacitance dominance assumption, which converts the area variation into an EC variation without a quantitative capacitance model.

free parameters (2)
  • Electron temperature Te and 20 µeV detection floor = 70 mK; 3.5 kBT ≈ 20 µeV
    Chosen from the 30 mK base temperature; sets the resolution floor that defines 'absence' of EC and the error bars in Fig. 3(c). All reported finite EC values (80–210 µeV) sit above this floor, but the large-area 'undetectable' points depend on this choice.
  • PG lever arm per device = A: 0.003 (3 meV/V); B: 0.008; C: 0.04; D: 0.05
    Extracted from diamond gate/bias sizes and used for gate-axis ↔ energy conversions and for the δ~600 µeV / δ=320 µeV level-spacing estimates. EC values themselves are read from the bias axis, so this is a calibration rather than a fitted target of the central claim.
axioms (5)
  • domain assumption Constant-interaction model: single-particle level spacing δ, no orbital degeneracy (δ≠0), spin degeneracy lifted by EC when EC>0
    Used throughout Sec. II–III to interpret diamond patterns and to assign EC and δ from alternating diamond sizes (Fig. 1 and Fig. 2).
  • domain assumption EC = e²/C with C dominated by source/drain contact capacitances (C_PG/C ≤ 0.05)
    Sec. III: measured lever arms ≪ 1 imply gate capacitances are negligible; this links cross-sectional area to EC through contact capacitance, the paper's proposed mechanism.
  • domain assumption 'Absence of EC' in device A means EC below the 20 µeV resolution, not a different transport regime
    Explicitly scoped in Sec. III; the B-scan peak splitting is read as Zeeman splitting of singly-occupied quantized levels.
  • domain assumption Thomas-Fermi electrostatics at zero temperature with bulk PbTe parameters (ε=1350, Eg=0.15 eV, masses from Refs. 35–36) in a 2D infinite-length geometry; PbEuTe treated as PbTe
    Sec. V, Eqs. (1)–(2): a crude model for an 8-nm wire, used only as design corroboration for the gate-tunability claim, not for the EC extraction.
  • domain assumption Device-to-device comparison is valid: similar growth, measurement, and contact conditions across devices A–D and the three Ref. 17 devices
    Sec. III and Fig. 3(c): the entire size-sweep inference rests on the comparability of devices that also differ in gate design and dot length.

pith-pipeline@v1.3.0-alltime-deepseek · 13778 in / 17700 out tokens · 173948 ms · 2026-08-02T23:43:10.779706+00:00 · methodology

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read the original abstract

Charging energy ($E_C$) is essential in quantum dot (QD) devices. Previous studies on PbTe QDs have reported both the presence and absence of $E_C$. To resolve this ambiguity, we vary the QD size, i.e. the cross-sectional area of PbTe nanowires, and track the evolution of $E_C$. For large crosssectional areas ($\sim$ 16000 nm$^2$), the PbTe QDs exhibit no measurable $E_C$, while quantized levels are well resolved. Decreasing this area successively to 5000, 1500, and 460 nm$^2$, $E_C$ becomes finite and increases to 80, 160, and 210 $\mu$eV, respectively. We further demonstrate the strong tunability of local gates, which can tune the PbTe device from the QD regime to the regime of ballistic transport. These results address concerns regarding the large dielectric constant of PbTe and provide key insights in engineering advanced PbTe quantum devices.

Figures

Figures reproduced from arXiv: 2602.12791 by Hao Zhang, Jiaye Xu, Ke He, Li Chen, Lining Yang, Lin Li, Qi-Kun Xue, Ruidong Li, RuNan Shang, Shan Zhang, Shuai Yang, Tiantian Wang, Weizhao Wang, Wenyu Song, Xiao Feng, Xinchen He, Yuhao Wang, Yunyi Zang, Zehao Yu, Zeyu Yan, Zonglin Li.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematics of QDs with and without [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. PbTe QD characteristics. (a-d) SEMs of four PbTe QDs. Scale bars are 300 nm. (e-h) The corresponding cross [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Effects of local gates. (a) Pinch off curves of a QD [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Numerical simulations of the potential landscape. (a) Longitudinal schematic of the a PbTe QD. The scale bar [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

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Reference graph

Works this paper leans on

40 extracted references

  1. [1]

    Z. Cao, D. E. Liu, W.-X. He, X. Liu, K. He, and H. Zhang, Numerical study of PbTe-Pb hybrid nanowires for engineering Majorana zero modes, Phys. Rev. B105, 085424 (2022)

    2022

  2. [2]

    R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Ma- jorana fermions and a topological phase transition in semiconductor-superconductor heterostructures, Phys. Rev. Lett.105, 077001 (2010). 7

    2010

  3. [3]

    Y. Oreg, G. Refael, and F. von Oppen, Helical liquids and Majorana bound states in quantum wires, Phys. Rev. Lett.105, 177002 (2010)

    2010

  4. [4]

    W. Song, Y. Wang, W. Miao, Z. Yu, Y. Gao, R. Li, S. Yang, F. Chen, Z. Geng, Z. Zhang, S. Zhang, Y. Zang, Z. Cao, D. E. Liu, R. Shang, X. Feng, L. Li, Q.-K. Xue, K. He, and H. Zhang, Conductance quantization in PbTe nanowires, Phys. Rev. B108, 045426 (2023)

    2023

  5. [5]

    Y. Wang, F. Chen, W. Song, Z. Geng, Z. Yu, L. Yang, Y. Gao, R. Li, S. Yang, W. Miao, W. Xu, Z. Wang, Z. Xia, H.-D. Song, X. Feng, T. Wang, Y. Zang, L. Li, R. Shang, Q. Xue, K. He, and H. Zhang, Ballistic PbTe nanowire devices, Nano Letters23, 11137 (2023)

    2023

  6. [6]

    W. Song, Z. Yu, Y. Wang, Y. Gao, Z. Li, S. Yang, S. Zhang, Z. Geng, R. Li, Z. Wang, F. Chen, L. Yang, W. Miao, J. Xu, X. Feng, T. Wang, Y. Zang, L. Li, R. Shang, Q. Xue, K. He, and H. Zhang, Reducing dis- order in PbTe nanowires for Majorana research, Nano Letters25, 2350 (2025)

    2025

  7. [7]

    Y. Wang, W. Song, Z. Cao, Z. Yu, S. Yang, Z. Li, Y. Gao, R. Li, F. Chen, Z. Geng, L. Yang, J. Xu, Z. Wang, S. Zhang, X. Feng, T. Wang, Y. Zang, L. Li, R. Shang, Q.-K. Xue, D. E. Liu, K. He, and H. Zhang, Gate- tunable subband degeneracy in semiconductor nanowires, Proceedings of the National Academy of Sciences121, e2406884121 (2024)

    2024

  8. [8]

    Y. Gao, W. Song, Y. Wang, Z. Geng, Z. Cao, Z. Yu, S. Yang, J. Xu, F. Chen, Z. Li,et al., Quantized An- dreev conductance in semiconductor nanowires, Phys. Rev. Appl.23, L061004 (2025)

    2025

  9. [9]

    J. Liu, A. C. Potter, K. T. Law, and P. A. Lee, Zero-bias peaks in the tunneling conductance of spin-orbit-coupled superconducting wires with and without Majorana end- states, Phys. Rev. Lett.109, 267002 (2012)

    2012

  10. [10]

    Prada, P

    E. Prada, P. San-Jose, and R. Aguado, Transport spectroscopy of NS nanowire junctions with Majorana fermions, Physical Review B86, 180503 (2012)

    2012

  11. [11]

    Pan and S

    H. Pan and S. Das Sarma, Physical mechanisms for zero- bias conductance peaks in Majorana nanowires, Phys. Rev. Research2, 013377 (2020)

    2020

  12. [12]

    S. Ahn, H. Pan, B. Woods, T. D. Stanescu, and S. Das Sarma, Estimating disorder and its adverse ef- fects in semiconductor majorana nanowires, Phys. Rev. Materials5, 124602 (2021)

    2021

  13. [13]

    Das Sarma and H

    S. Das Sarma and H. Pan, Disorder-induced zero-bias peaks in Majorana nanowires, Phys. Rev. B103, 195158 (2021)

    2021

  14. [14]

    C. Zeng, G. Sharma, S. Tewari, and T. Stanescu, Par- tially separated Majorana modes in a disordered medium, Phys. Rev. B105, 205122 (2022)

    2022

  15. [15]

    R. Hess, H. F. Legg, D. Loss, and J. Klinovaja, Trivial Andreev band mimicking topological bulk gap reopening in the nonlocal conductance of long Rashba nanowires, Phys. Rev. Lett.130, 207001 (2023)

    2023

  16. [16]

    Gomanko, E

    M. Gomanko, E. J. de Jong, Y. Jiang, S. G. Schellinger- hout, E. P. A. M. Bakkers, and S. M. Frolov, Spin and Orbital Spectroscopy in the Absence of Coulomb Block- ade in Lead Telluride Nanowire Quantum Dots, SciPost Phys.13, 089 (2022)

    2022

  17. [17]

    Z. Li, W. Song, S. Zhang, Y. Wang, Z. Wang, Z. Yu, R. Li, Z. Yan, J. Xu, Y. Gao, S. Yang, L. Yang, X. Feng, T. Wang, Y. Zang, L. Li, R. Shang, Q.-K. Xue, K. He, and H. Zhang, Anisotropy of PbTe nanowires with and without a superconductor, Phys. Rev. B111, 195416 (2025)

    2025

  18. [18]

    S. C. ten Kate, M. F. Ritter, A. Fuhrer, J. Jung, S. G. Schellingerhout, E. P. A. M. Bakkers, H. Riel, and F. Nichele, Small charging energies and g-factor anisotropy in PbTe quantum dots, Nano Letters22, 7049 (2022)

    2022

  19. [19]

    Aasen, M

    D. Aasen, M. Hell, R. V. Mishmash, A. Higginbotham, J. Danon, M. Leijnse, T. S. Jespersen, J. A. Folk, C. M. Marcus, K. Flensberg, and J. Alicea, Milestones toward Majorana-based quantum computing, Phys. Rev. X6, 031016 (2016)

    2016

  20. [20]

    Plugge, A

    S. Plugge, A. Rasmussen, R. Egger, and K. Flensberg, Majorana box qubits, New Journal of Physics19, 012001 (2017)

    2017

  21. [21]

    Karzig, C

    T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonder- son, M. B. Hastings, C. Nayak, J. Alicea, K. Flens- berg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, Scalable designs for quasiparticle-poisoning- protected topological quantum computation with Majo- rana zero modes, Phys. Rev. B95, 235305 (2017)

    2017

  22. [22]

    Jiang, S

    Y. Jiang, S. Yang, L. Li, W. Song, W. Miao, B. Tong, Z. Geng, Y. Gao, R. Li, F. Chen, Q. Zhang, F. Meng, L. Gu, K. Zhu, Y. Zang, R. Shang, Z. Cao, X. Feng, Q.-K. Xue, D. E. Liu, H. Zhang, and K. He, Selective area epi- taxy of PbTe-Pb hybrid nanowires on a lattice-matched substrate, Phys. Rev. Materials6, 034205 (2022)

    2022

  23. [23]

    J. Jung, S. G. Schellingerhout, M. F. Ritter, S. C. ten Kate, O. A. van der Molen, S. de Loijer, M. A. Verheijen, H. Riel, F. Nichele, and E. P. Bakkers, Selective area growth of PbTe nanowire networks on InP, Advanced Functional Materials32, 2208974 (2022)

    2022

  24. [24]

    Z. Geng, Z. Zhang, F. Chen, S. Yang, Y. Jiang, Y. Gao, B. Tong, W. Song, W. Miao, R. Li, Y. Wang, Q. Zhang, F. Meng, L. Gu, K. Zhu, Y. Zang, L. Li, R. Shang, X. Feng, Q.-K. Xue, K. He, and H. Zhang, Observation of Aharonov-Bohm effect in PbTe nanowire networks, Phys. Rev. B105, L241112 (2022)

    2022

  25. [25]

    Zhang, W

    Z. Zhang, W. Song, Y. Gao, Y. Wang, Z. Yu, S. Yang, Y. Jiang, W. Miao, R. Li, F. Chen, Z. Geng, Q. Zhang, F. Meng, T. Lin, L. Gu, K. Zhu, Y. Zang, L. Li, R. Shang, X. Feng, Q.-K. Xue, K. He, and H. Zhang, Proximity effect in PbTe-Pb hybrid nanowire Josephson junctions, Phys. Rev. Mater.7, 086201 (2023)

    2023

  26. [26]

    Y. Gao, W. Song, S. Yang, Z. Yu, R. Li, W. Miao, Y. Wang, F. Chen, Z. Geng, L. Yang, Z. Xia, X. Feng, Y. Zang, L. Li, R. Shang, Q.-K. Xue, K. He, and H. Zhang, Hard superconducting gap in PbTe nanowires, Chinese Physics Letters41, 038502 (2024)

    2024

  27. [27]

    R. Li, W. Song, W. Miao, Z. Yu, Z. Wang, S. Yang, Y. Gao, Y. Wang, F. Chen, Z. Geng, L. Yang, J. Xu, X. Feng, T. Wang, Y. Zang, L. Li, R. Shang, Q. Xue, K. He, and H. Zhang, Selective-area-grown PbTe-Pb pla- nar Josephson junctions for quantum devices, Nano Let- ters24, 4658 (2024)

    2024

  28. [28]

    Gupta, V

    M. Gupta, V. Khade, C. Riggert, L. Shani, G. Menning, P. J. H. Lueb, J. Jung, R. M´ elin, E. P. A. M. Bakkers, and V. S. Pribiag, Evidence forπ-shifted cooper quartets and few-mode transport in pbte nanowire three-terminal josephson junctions, Nano Letters24, 13903 (2024)

    2024

  29. [29]

    Z. Geng, F. Chen, Y. Gao, L. Yang, Y. Wang, S. Yang, S. Zhang, Z. Li, W. Song, J. Xu, Z. Yu, R. Li, Z. Wang, X. Feng, T. Wang, Y. Zang, L. Li, R. Shang, Q.-K. Xue, K. He, and H. Zhang, Enhanced superconductivity in PbTe-In hybrids, Phys. Rev. Mater.9, 084802 (2025). 8

    2025

  30. [30]

    Y. Gao, W. Song, Z. Yu, S. Yang, Y. Wang, R. Li, F. Chen, Z. Geng, L. Yang, J. Xu,et al., SQUID os- cillations in PbTe nanowire networks, Phys. Rev. B110, 045405 (2024)

    2024

  31. [31]

    Grabecki, J

    G. Grabecki, J. Wr´ obel, T. Dietl, E. Polakowska, E. Kaminska, A. Piotrowska, A. Ratuszna, G. Springholz, and G. Bauer, Ballistic transport in PbTe-based nanostructures, Physica E: Low-dimensional Systems and Nanostructures20, 236 (2004)

    2004

  32. [32]

    A. E. Antipov, A. Bargerbos, G. W. Winkler, B. Bauer, E. Rossi, and R. M. Lutchyn, Effects of gate-induced elec- tric fields on semiconductor Majorana nanowires, Phys. Rev. X8, 031041 (2018)

    2018

  33. [33]

    A. E. G. Mikkelsen, P. Kotetes, P. Krogstrup, and K. Flensberg, Hybridization at superconductor- semiconductor interfaces, Phys. Rev. X8, 031040 (2018)

    2018

  34. [34]

    L. Chen, Z. Cao, K. He, X. Liu, and D. E. Liu, Electro- static effects of MnBi 2Te4-superconductor heterostruc- tures in the chiral majorana search, Phys. Rev. B107, 165405 (2023)

    2023

  35. [35]

    E. A. de Andrada e Silva, Optical transition energies for lead-salt semiconductor quantum wells, Phys. Rev. B60, 8859 (1999)

    1999

  36. [36]

    Ridolfi, E

    E. Ridolfi, E. A. d. A. e. Silva, and G. C. La Rocca, Effec- tiveg-factor tensor for carriers in IV-VI semiconductor quantum wells, Phys. Rev. B91, 085313 (2015)

    2015

  37. [37]

    Zhang, D

    H. Zhang, D. E. Liu, M. Wimmer, and L. P. Kouwen- hoven, Next steps of quantum transport in Majorana nanowire devices, Nature Communications10, 5128 (2019)

    2019

  38. [38]

    Prada, P

    E. Prada, P. San-Jose, M. W. de Moor, A. Geresdi, E. J. Lee, J. Klinovaja, D. Loss, J. Nyg ˚ ard, R. Aguado, and L. P. Kouwenhoven, From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires, Nature Reviews Physics2, 575 (2020)

    2020

  39. [39]

    Presence versus absence of charging energies in PbTe quantum dots

    L. Kouwenhoven, Perspective on Majorana bound-states in hybrid superconductor-semiconductor nanowires, Modern Physics Letters B0, 2540002 (0). Supplemental Materials for “Presence versus absence of charging energies in PbTe quantum dots” Yuhao Wang,1, 2,∗ Lining Yang,1,∗ Wenyu Song,1,∗ Li Chen, 3,∗ Zehao Yu,1 Xinchen He, 1 Zeyu Yan,1 Jiaye Xu, 1 Ruidong L...

  40. [40]

    Z. Li, W. Song, S. Zhang, Y. Wang, Z. Wang, Z. Yu, R. Li, Z. Yan, J. Xu, Y. Gao, S. Yang, L. Yang, X. Feng, T. Wang, Y. Zang, L. Li, R. Shang, Q.-K. Xue, K. He, and H. Zhang, Anisotropy of PbTe nanowires with and without a superconductor, Phys. Rev. B111, 195416 (2025). 3 Device E [100][010] ⨂ B S D (a) TG1 PG TG2(b) [010][001] PbTe CdTe Au Ti AlO(c) -2 -...

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