Pith. sign in

REVIEW 3 major objections 5 minor 56 references

Fermion parity and quantum capacitance oscillation with partially separated Majorana and quasi-Majorana modes

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Parity-dependent quantum capacitance oscillations in disordered nanowires are not unique evidence of topological Majorana zero modes; trivial quasi-Majorana modes produce the same signal.

desk verdict A solid existence proof that q-MZMs and partially separated Majoranas reproduce the capacitance parity signature, though the 'generic' prevalence claim is ahead of the evidence. read the letter →

arxiv 2505.23741 v1 pith:E23VSQWT submitted 2025-05-29 cond-mat.mes-hall quant-ph

Tudor D. Stanescu , Sumanta Tewari This is my paper
classification cond-mat.mes-hallquant-ph
keywords Majoranazeromodesquantumcapacitancefermionparitydisorderquasi-MajoranapartiallyseparatedAndreevboundstatesnanowiredotfluxoscillations
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

This paper argues that flux-induced oscillations of the quantum capacitance in a semiconductor–superconductor nanowire coupled to a quantum dot are not a unique signature of topologically protected Majorana zero modes. Across a disordered 3-micron wire model, parity-shifted capacitance oscillations with period $h/e$ and amplitude near 1 fF appear not only for well-separated Majorana modes but also for partially overlapping Majorana modes and for topologically trivial quasi-Majorana modes (Andreev bound states whose constituent Majorana wave functions are slightly displaced). The result matters because such oscillations have been proposed as a fermion-parity readout and fusion mechanism in a recent experiment, and the paper shows that the same signal can arise without any topological protection.

What carries the argument

The argument is carried by three pieces. (1) A tight-binding model of a 3 $\mu$m InAs wire with Rashba spin-orbit coupling, Zeeman field, and a Gaussian disorder potential of amplitude $V_0$, proximity-coupled to a superconductor and connected end-to-end through a single-level quantum dot, with magnetic flux $\Phi$ entering as phases $\phi = (\pi/2)\Phi/\Phi_0$ in the dot–wire couplings. (2) The quantum capacitance, taken as the zero-frequency limit of the linear-response expression in Eq. (7), which converts the parity-dependent low-energy spectrum into the measured signal. (3) The Majorana overlap $O$ defined in Eq. (6), which measures the spatial separation of the two constituent Majorana wave functions ($O=1$ perfect overlap, $O=0$ perfect separation) and provides the operational distinction between 'topological' (well-separated) and 'quasi-Majorana' (strongly overlapping) states. A winding-number invariant for the periodically repeated disordered wire is used to classify parameter regions as topologically trivial or nontrivial.

What would settle it

Compute the flux-dependent quantum capacitance for an ensemble of dozens of independent disorder realizations at $V_0 = 1.2$ meV, classifying each realization by its winding number and the overlap $O$ of its lowest-energy mode; if a large fraction of topologically trivial realizations fail to show $h/e$-periodic, parity-shifted capacitance oscillations near 1 fF, the genericity claim would be falsified, whereas if trivial realizations produce the same oscillations with comparable probability, the claim stands.

Watch

Extended reading notes

Core claim

The central claim is that in a disordered nanowire–quantum-dot interferometer, the parity-dependent quantum capacitance as a function of magnetic flux $\Phi$ oscillates with period $h/e$ and amplitude ~1 fF regardless of whether the underlying near-zero-energy states are topologically protected Majorana zero modes, partially separated Majorana modes with overlap as high as $O = 0.63$, or a topologically trivial quasi-Majorana mode. The authors demonstrate this by computing the quantum capacitance from a linear-response formula for four representative low-energy states of a strongly disordered ($V_0 = 1.2$ meV) 3 $\mu$m wire: one clearly trivial q-MZM with $O = 0.63$ and three partially separated Majorana pairs with $O = 0.046$, $0.066$, and $0.23$. The resulting flux-dependent capacitance curves (Fig. 8) are qualitatively and even quantitatively similar to the low-disorder 'ideal' case with well-separated Majoranas ($O = 5.6\times10^{-4}$). The paper concludes that observing such oscillations indicates the presence of partially separated or trivial quasi-Majorana modes and does not constitute evidence of topological Majorana zero modes.

Load-bearing premise

The paper's claim that the mimicry is generic rests on a single disorder profile (at $V_0 = 1.2$ meV) and a few chosen parameter points, with no disorder-ensemble averaging or probability estimate, so the assertion that trivial quasi-Majorana modes typically produce the same oscillations is not quantified.

Editorial extensions

If this is right

  • Parity-dependent capacitance oscillations with period $h/e$ and amplitude ~1 fF can no longer be read as standalone evidence for topological Majorana zero modes in hybrid nanowire devices.
  • In strongly disordered wires, generic low-energy delocalized states are partially separated Majorana modes with characteristic length scales of 1–3 $\mu$m, comparable to the wire length, making protection by spatial separation unlikely.
  • A near-zero-energy state can satisfy the operational test of being a delocalized low-energy mode while being topologically trivial, as the q-MZM example shows.
  • The parameter regions that produce experimental-looking oscillations do not generally satisfy the topological gap protocol (gap closing and reopening), so requiring that protocol does not resolve the ambiguity.
  • The probability that the low-energy modes behind the oscillations are topologically protected decreases strongly with disorder strength, so the interpretation of such measurements depends sensitively on disorder conditions.

Reading between the lines

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

  • If the mimicry is generic, then an experiment claiming topological protection needs a second, independent observable—such as exponential suppression of the mode splitting with wire length or a nonlocal response to a perturbation at the wire middle—rather than the capacitance oscillation alone.
  • A quantitative disorder-ensemble study (for example, the percentage of realizations at $V_0 = 1.2$ meV that show ~1 fF $h/e$-periodic oscillations while being topologically trivial by the winding number) would convert the demonstration from case studies into a statistical claim; such a calculation is a natural follow-up that this paper does not report.
  • The same capacitance formalism could be used to test other proposed Majorana signatures, such as two-terminal conductance teleportation or the $4\pi$ Josephson effect, for their vulnerability to quasi-Majorana mimics.
  • The overlap $O$ defined here could serve as a practical screening figure of merit: devices whose low-energy states have $O$ above a threshold like $0.1$ should be excluded from parity-readout or fusion experiments intended to probe topological physics.
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 paper studies an interferometric device consisting of a one-dimensional semiconductor-superconductor nanowire coupled end-to-end through a quantum dot, and computes the quantum capacitance as a function of magnetic flux. After benchmarking a low-disorder case with well-separated topological Majorana zero modes (MZMs), the authors consider a strongly disordered wire and identify low-energy states that are either partially separated Majorana modes with significant overlap or topologically trivial quasi-Majorana modes. They show that in both cases the parity-resolved quantum capacitance exhibits flux oscillations with period h/e and amplitude around 1 fF, qualitatively similar to the ideal Majorana case. The paper concludes that such capacitance oscillations are not a unique signature of topologically protected Majorana zero modes.

Significance. If the central claim holds, this is a valuable cautionary result for the interpretation of recent interferometric parity-readout experiments: a finite-size, disordered Majorana wire can produce the same capacitance signature from partially overlapping Majorana modes or from topologically trivial quasi-Majorana modes. The numerical work is direct and transparent: the capacitance is computed from the BdG eigenstates of the coupled nanowire-dot model, with no fitting to the experimental oscillations and no parameter extracted from the target signature. The explicit benchmark against a clean, well-separated MZM case (Fig. 2) and the systematic overlap measure O provide a useful framework. The main significance is in sharpening the distinction between the existence of a mimicry mechanism and the prevalence of such mimics in realistic disordered devices.

major comments (3)
  1. [Abstract and Section IV] The abstract and conclusion claim that capacitance oscillations arise 'generically' from partially separated Majorana modes and quasi-Majorana modes, and that the probability of topologically protected modes 'decreases strongly' with disorder. These prevalence statements are not supported by the numerical evidence: the strong-disorder calculation uses a single disorder realization, namely the profile shown in Fig. 1(b), and four hand-picked low-energy states selected from that same profile. There is no disorder ensemble average, no distribution of overlaps or capacitance amplitudes, and no fraction of trivial or partially overlapping realizations that produce h/e oscillations. The demonstrated result is an existence proof, not a generic or probabilistic statement. I recommend either adding disorder-ensemble statistics that quantify the fraction of low-energy states yielding parity-dependent oscillations similar to Fig. 8, or tempering the language to avoid claims about genericity and probability.
  2. [Section III.B and Fig. 4] The topological/trivial classification relies on an unpublished finite-system topological invariant [55], defined by periodically repeating the finite disordered wire. Because the invariant is not presented in the manuscript, the assertion that the state in Fig. 6(a) is 'definitely topologically trivial' cannot be independently checked. The paper also acknowledges large finite-size effects and fragmented topological regions, so the classification is central to distinguishing q-MZMs from partially separated topological modes. I ask the authors to provide the explicit definition and computation of the invariant, or to use a published and accessible criterion, or to clearly mark these classifications as provisional pending the companion paper.
  3. [Section III.B, Figs. 5-8] The selection of the four representative states is explicitly conditioned on the modes being delocalized and nearly zero energy (Fig. 4 right panel), and the dot potential VQD and couplings λL, λR are tuned separately for each case (Fig. 7 caption). The conclusion that there are no qualitative differences among the four panels of Fig. 8 may therefore reflect favorable state selection rather than a generic property of disordered nanowires. I suggest reporting a broader scan, for example including states with larger overlaps, localized low-energy states, and varying VQD and coupling parameters within a resonance window, and stating how often the h/e capacitance oscillation actually appears and with what amplitude.
minor comments (5)
  1. [Section III.B, caption of Fig. 6] Typo: 'partially-seperated' should be 'partially-separated'.
  2. [Eq. (2)] The Zeeman term is written as Γ Σ_i (c†_{i↑} c_{i+1↓} + c†_{i↓} c_{i+1↑}), involving nearest-neighbor sites; the standard Zeeman term is on-site (c†_{i↑} c_{i↓}). Please check whether this is a typographical error or an intentional spin-flip hopping term.
  3. [Eq. (7)] The summation constraint is marked with a star, but the text describes it only in prose. Please define the ranges of n and m explicitly in the equation or immediately around it.
  4. [Section IV] The phrase 'flux h/2e-periodic bimodality' is confusing because the capacitance oscillations shown in Fig. 8 have period h/e for a given parity; the h/2e periodicity is a combined statement about the two parity sectors. Please clarify this wording.
  5. [References] Reference [55] is cited as 'to be published' and is used for a load-bearing classification. If it remains unpublished, the manuscript should either include the necessary details in an appendix or be updated once the companion paper is available.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the capacitance oscillations are computed from the BdG model without fitting, with only a minor caveat about an unpublished same-author topological invariant used for labeling.

full rationale

The derivation chain is self-contained at its core. The flux-dependent capacitance is obtained by numerically diagonalizing the effective BdG Hamiltonian (Eq. (4)) together with the quantum-dot coupling (Eq. (5)) and applying the linear-response capacitance formula (Eq. (7)). No parameter is fitted to the experimentally observed capacitance oscillations in Ref. [53]; the h/e period and ~1 fF amplitude emerge from the model, and the experiment serves as an external benchmark. The disorder profile in Fig. 1(b) is fixed before the state selection, and the overlap measure (Eq. (6)) is descriptive rather than an input to the dynamics. The paper's negative conclusion—that such oscillations do not uniquely identify topological MZMs—is supported by explicit calculation for a trivial quasi-Majorana example. The one caveat is that the classification of Fig. 6(a) as 'definitely topologically trivial' uses the finite-system winding-number invariant of Ref. [55], an unpublished manuscript by the same authors; this is a support gap and a self-citation, and it should be independently checked, but it is not a circular reduction because the capacitance calculation does not use the invariant as an input and the existence of trivial quasi-Majorana states has independent prior support. The 'generic' prevalence claim is based on a single disorder profile and selected low-energy states rather than an ensemble average; that is a statistical-scope concern, not circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central numerical demonstration introduces several hand-chosen model parameters, especially a single disorder profile, and relies on an unpublished topological-invariant method from the authors' own group. No new physical entities are introduced. The core claim is qualitative and likely robust, but the word 'generically' is supported by selected examples rather than an ensemble.

free parameters (5)
  • Disorder amplitude V0 = 1.2 meV (strong disorder case); 0.3 meV (clean benchmark)
    Chosen by hand to represent weakly and strongly disordered regimes; no scan or ensemble over disorder strengths.
  • Specific disorder profile Vdis(i) = Fig. 1(b)
    A single fixed realization; the paper does not average over disorder samples, so 'generically' rests on one instance.
  • Selected control parameters mu and Gamma = e.g., mu=3.92 meV, Gamma around 0.6 to 0.9 meV for the q-MZM state; see Fig. 6 panels
    Picked to show representative low-energy states; selection may bias the observed mimicry.
  • QD coupling parameters lambda_L, lambda_R and gate voltage VQD = e.g., lambda_L=0.02, lambda_R=0.01, VQD=3.922 meV in panel (a)
    Tuned to resonance windows where capacitance differences are large; the qualitative claim is likely robust, but the quantitative amplitude is coupling dependent.
  • Capacitance prefactor kappa and broadening eta = kappa=0.032 fF*meV, eta=2 meV
    Chosen constant and phenomenological broadening; not fitted to the experiment, but affects absolute amplitudes.
assumptions (4)
  • domain assumption Static approximation for the superconducting self-energy: sqrt(Delta0^2 - omega^2) approximately Delta0(Gamma), valid for low-energy physics.
    Invoked before Eq. (4) to replace the full self-energy with an effective BdG Hamiltonian; standard for low-energy Majorana studies but an approximation.
  • domain assumption Single-level quantum dot approximation.
    Section II assumes the QD level spacing is large and keeps only state n0 with energy 0; discards multi-level effects.
  • ad hoc to paper Topological invariant defined by periodically repeating the finite disordered wire.
    Ref [55] is cited as 'to be published' by overlapping authors; the classification of regions as topological or trivial rests on this unpublished method.
  • domain assumption BdG linear response capacitance formula Eq. (7) correctly describes the measured quantum capacitance.
    The zero-frequency limit of the dynamical capacitance with phenomenological broadening eta=2 meV is assumed to match the experimental observable.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Fermion parity and quantum capacitance oscillation with partially separated Majorana and quasi-Majorana modes." pith.science (2026). https://pith.science/paper/E23VSQWT

@misc{pith2026250523741,
  author       = {Pith},
  title        = {Pith review of: Fermion parity and quantum capacitance oscillation with partially separated Majorana and quasi-Majorana modes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E23VSQWT}},
  note         = {Machine review of arXiv:2505.23741}
}
read the original abstract

In a recent experiment, flux dependent oscillations of the quantum capacitance were observed in a one dimensional spin-orbit coupled semiconductor superconductor heterostructure connected end to end via a quantum dot and threaded by a magnetic flux. In the topological superconducting phase of the heterostructure, the oscillations corresponding to different fermion parity sectors are shifted by half a period and can serve as a mechanism for fermion parity readout or fusion operations involving a pair of localized, well separated Majorana modes. In this work, we demonstrate that flux induced fermion parity dependent oscillations of the quantum capacitance in a disordered semiconductor superconductor quantum dot system can originate not only from topologically protected, spatially well separated Majorana zero modes (MZMs) localized at the wire ends, but also, generically, from partially separated Majorana modes with significant overlap, as well as from quasi-Majorana modes in the topologically trivial phase, which can be viewed as Andreev bound states whose constituent Majorana wave functions are slightly shifted relative to each other and have nonzero amplitude at opposite ends of the wire. Therefore, while the detection of flux dependent oscillations of quantum capacitance marks an important experimental advance, such observations alone do not constitute evidence of the presence of topological Majorana zero modes.

Figures

Figures reproduced from arXiv: 2505.23741 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic representation of a semiconductor [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Spatial profiles of Majorana modes supported by a three [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 5
Figure 5. FIG. 5. Low-energy spectra as functions of the applied Zeeman field [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Spatial profiles of the Majorana modes associated with the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Flux-dependent oscillations of the capacitance correspond [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

56 extracted references · 48 canonical work pages

  1. [55]

    Eissele, B

    R. Eissele, B. Roy, S. Tewari, and T. D. Stanescu, Topological invariant for finite systems in the presence of disorder (2025), to be published

    work page 2025

  2. [1]

    Read and D

    N. Read and D. Green, Paired states of fermions in two di- mensions with breaking of parity and time-reversal symmetries and the fractional quantum hall effect, Phys. Rev. B 61, 10267 (2000)

    work page 2000

  3. [2]

    A. Y . Kitaev, Unpaired majorana fermions in quantum wires, Physics-Uspekhi 44, 131 (2001)

    work page 2001

  4. [3]

    A. Y . Kitaev, Annals. Phys.303, 2 (2003)

    work page 2003

  5. [4]

    Majorana, Nuovo Cimento 14, 171 (1937)

    E. Majorana, Nuovo Cimento 14, 171 (1937)

    work page 1937

  6. [5]

    Wilczek, Quantum mechanics of fractional-spin particles, Physical review letters 49, 957 (1982)

    F. Wilczek, Quantum mechanics of fractional-spin particles, Physical review letters 49, 957 (1982)

    work page 1982

  7. [6]

    Moore and N

    G. Moore and N. Read, Nucl. Physics B 360, 362 (1991)

    work page 1991

  8. [7]

    Nayak and F

    C. Nayak and F. Wilczek, Nucl. Physics B 479, 529 (1996)

    work page 1996

Show all 56 references
  1. [8]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008)

    2008

  2. [9]

    J. D. Sau, R. M. Lutchyn, S. Tewari, and S. D. Sarma, Generic new platform for topological quantum computation using semi- conductor heterostructures, Physical review letters104, 040502 (2010)

    2010

  3. [10]

    J. D. Sau, S. Tewari, R. M. Lutchyn, T. D. Stanescu, and S. D. Sarma, Non-abelian quantum order in spin-orbit-coupled semi- conductors: Search for topological majorana particles in solid- state systems, Physical Review B 82, 214509 (2010)

    2010

  4. [11]

    Y . Oreg, G. Refael, and F. von Oppen, Helical liquids and ma- jorana bound states in quantum wires, Physical review letters 105, 177002 (2010)

    2010

  5. [12]

    R. M. Lutchyn, J. D. Sau, and S. D. Sarma, Majorana fermions and a topological phase transition in semiconductor- superconductor heterostructures, Physical review letters 105, 077001 (2010)

    2010

  6. [13]

    Mourik, K

    V . Mourik, K. Zuo, S. M. Frolov, S. Plissard, E. P. Bakkers, and L. P. Kouwenhoven, Signatures of majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336, 1003 (2012)

    2012

  7. [14]

    M. T. Deng, C. L. Yu, G. Y . Huang, M. Larsson, P. Caroff, and H. Q. Xu, Anomalous zero-bias conductance peak in a nb–insb nanowire–nb hybrid device, Nano Letters 12, 6414 (2012)

    2012

  8. [15]

    A. Das, Y . Ronen, Y . Most, Y . Oreg, M. Heiblum, and H. Shtrik- man, Zero-bias peaks and splitting in an al–inas nanowire topo- logical superconductor as a signature of majorana fermions, Na- ture Physics 8, 887 (2012)

    2012

  9. [16]

    L. P. Rokhinson, X. Liu, and J. K. Furdyna, The fractional ac josephson effect in a semiconductor–superconductor nanowire as a signature of majorana particles, Nature Physics 8, 795 (2012)

    2012

  10. [17]

    Churchill, V

    H. Churchill, V . Fatemi, K. Grove-Rasmussen, M. Deng, P. Caroff, H. Xu, and C. M. Marcus, Superconductor-nanowire devices from tunneling to the multichannel regime: Zero-bias oscillations and magnetoconductance crossover, Physical Re- view B 87, 241401 (2013)

    2013

  11. [18]

    Finck, D

    A. Finck, D. J. Van Harlingen, P. Mohseni, K. Jung, and X. Li, Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device, Physical review letters 110, 126406 (2013)

    2013

  12. [19]

    M. Deng, S. Vaitiek ˙enas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nyg˚ard, P. Krogstrup, and C. M. Marcus, Ma- jorana bound state in a coupled quantum-dot hybrid-nanowire system, Science 354, 1557 (2016). 9

    2016

  13. [20]

    Zhang, ¨O

    H. Zhang, ¨O. G ¨ul, S. Conesa-Boj, M. P. Nowak, M. Wimmer, K. Zuo, V . Mourik, F. K. De Vries, J. Van Veen, M. W. De Moor, et al., Ballistic superconductivity in semiconductor nanowires, Nature communications 8, 16025 (2017)

    2017

  14. [21]

    J. Chen, P. Yu, J. Stenger, M. Hocevar, D. Car, S. R. Plissard, E. P. Bakkers, T. D. Stanescu, and S. M. Frolov, Experimen- tal phase diagram of zero-bias conductance peaks in supercon- ductor/semiconductor nanowire devices, Science advances 3, e1701476 (2017)

    2017

  15. [22]

    Nichele, A

    F. Nichele, A. C. Drachmann, A. M. Whiticar, E. C. O’Farrell, H. J. Suominen, A. Fornieri, T. Wang, G. C. Gardner, C. Thomas, A. T. Hatke, et al., Scaling of majorana zero-bias conductance peaks, Physical review letters119, 136803 (2017)

    2017

  16. [23]

    Albrecht, E

    S. Albrecht, E. Hansen, A. P. Higginbotham, F. Kuemmeth, T. Jespersen, J. Nyg ˚ard, P. Krogstrup, J. Danon, K. Flensberg, and C. Marcus, Transport signatures of quasiparticle poison- ing in a majorana island, Physical review letters 118, 137701 (2017)

    2017

  17. [24]

    O Farrell, A

    E. O Farrell, A. Drachmann, M. Hell, A. Fornieri, A. Whiticar, E. Hansen, S. Gronin, G. Gardner, C. Thomas, M. Man- fra, et al. , Hybridization of subgap states in one-dimensional superconductor-semiconductor coulomb islands, Physical re- view letters 121, 256803 (2018)

    2018

  18. [25]

    J. Shen, S. Heedt, F. Borsoi, B. Van Heck, S. Gazibegovic, R. L. O. het Veld, D. Car, J. A. Logan, M. Pendharkar, S. J. Ra- makers, et al., Parity transitions in the superconducting ground state of hybrid insb–al coulomb islands, Nature communica- tions 9, 4801 (2018)

    2018

  19. [26]

    Sherman, J

    D. Sherman, J. Yodh, S. M. Albrecht, J. Nyg ˚ard, P. Krogstrup, and C. M. Marcus, Normal, superconducting and topological regimes of hybrid double quantum dots, Nature nanotechnology 12, 212 (2017)

    2017

  20. [27]

    Vaitiek ˙enas, A

    S. Vaitiek ˙enas, A. Whiticar, M.-T. Deng, F. Krizek, J. Ses- toft, C. Palmstrøm, S. Marti-Sanchez, J. Arbiol, P. Krogstrup, L. Casparis, et al. , Selective-area-grown semiconductor- superconductor hybrids: A basis for topological networks, Physical review letters 121, 147701 (2018)

    2018

  21. [28]

    S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nyg˚ard, P. Krogstrup, and C. Marcus, Expo- nential protection of zero modes in majorana islands, Nature 531, 206 (2016)

    2016

  22. [29]

    P. Yu, J. Chen, M. Gomanko, G. Badawy, E. P. A. M. Bakkers, K. Zuo, V . Mourik, and S. M. Frolov, Non-majorana states yield nearly quantized conductance in proximatized nanowires, Na- ture Physics 17, 482–488 (2021)

    2021

  23. [30]

    Zhang, M

    H. Zhang, M. W. A. de Moor, J. D. S. Bommer, D. Xu, G. Wang, N. van Loo, C.-X. Liu, S. Gazibegovic, J. A. Logan, D. Car, R. L. M. O. het Veld, P. J. van Veldhoven, S. Koelling, M. A. Verheijen, M. Pendharkar, D. J. Pennachio, B. Shojaei, J. S. Lee, C. J. Palmstrøm, E. P. A. M....

    2021 arXiv

  24. [31]

    Aghaee, A

    M. Aghaee, A. Akkala, Z. Alam, R. Ali, A. Alcaraz Ramirez, M. Andrzejczuk, A. E. Antipov, P. Aseev, M. Astafev, B. Bauer, J. Becker, S. Boddapati, F. Boekhout, J. Bommer, T. Bosma, L. Bourdet, S. Boutin, P. Caroff, L. Casparis, M. Cassidy, S. Chatoor, A. W. Christensen, N. Cla...

    2023

  25. [32]

    Kells, D

    G. Kells, D. Meidan, and P. Brouwer, Near-zero-energy end states in topologically trivial spin-orbit coupled superconduct- ing nanowires with a smooth confinement, Physical Review B 86, 100503 (2012)

    2012

  26. [33]

    Bagrets and A

    D. Bagrets and A. Altland, Class d spectral peak in majorana quantum wires, Physical review letters 109, 227005 (2012)

    2012

  27. [34]

    D. I. Pikulin, J. Dahlhaus, M. Wimmer, H. Schomerus, and C. Beenakker, A zero-voltage conductance peak from weak an- tilocalization in a majorana nanowire, New Journal of Physics 14, 125011 (2012)

    2012

  28. [35]

    Prada, P

    E. Prada, P. San-Jose, and R. Aguado, Transport spectroscopy of n s nanowire junctions with majorana fermions, Physical Re- view B 86, 180503 (2012)

    2012

  29. [36]

    C.-X. Liu, J. D. Sau, T. D. Stanescu, and S. Das Sarma, An- dreev bound states versus majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial ver- sus topological zero-bias conductance peaks, Phys. Rev. B 96, 075161 (2017)

    2017

  30. [37]

    Pan and S

    H. Pan and S. D. Sarma, Physical mechanisms for zero-bias conductance peaks in majorana nanowires, Physical Review Research 2, 013377 (2020)

    2020

  31. [38]

    Moore, T

    C. Moore, T. D. Stanescu, and S. Tewari, Two-terminal charge tunneling: Disentangling majorana zero modes from partially separated andreev bound states in semiconductor- superconductor heterostructures, Physical Review B 97, 165302 (2018)

    2018

  32. [39]

    Moore, C

    C. Moore, C. Zeng, T. D. Stanescu, and S. Tewari, Quantized zero-bias conductance plateau in semiconductor- superconductor heterostructures without topological majorana zero modes, Phys. Rev. B 98, 155314 (2018)

    2018

  33. [40]

    A. Vuik, B. Nijholt, A. R. Akhmerov, and M. Wimmer, Repro- ducing topological properties with quasi-majorana states, arXiv preprint arXiv:1806.02801 (2018)

    2018 arXiv

  34. [41]

    T. D. Stanescu and S. Tewari, Robust low-energy andreev bound states in semiconductor-superconductor structures: Im- portance of partial separation of component majorana bound states, Physical Review B 100, 155429 (2019)

    2019

  35. [42]

    C. Reeg, O. Dmytruk, D. Chevallier, D. Loss, and J. Klinovaja, Zero-energy andreev bound states from quantum dots in prox- imitized rashba nanowires, Phys. Rev. B 98, 245407 (2018)

    2018

  36. [43]

    San-Jose, J

    P. San-Jose, J. Cayao, E. Prada, and R. Aguado, Majorana bound states from exceptional points in non-topological super- conductors, Scientific reports 6, 21427 (2016)

    2016

  37. [44]

    Avila, F

    J. Avila, F. Pe ˜naranda, E. Prada, P. San-Jose, and R. Aguado, Non-hermitian topology as a unifying framework for the an- dreev versus majorana states controversy, Communications 10 Physics 2, 10.1038/s42005-019-0231-8 (2019)

    2019 doi

  38. [45]

    O. A. Awoga, J. Cayao, and A. M. Black-Schaffer, Supercurrent detection of topologically trivial zero-energy states in nanowire junctions, Phys. Rev. Lett. 123, 117001 (2019)

    2019

  39. [46]

    Prada, P

    E. Prada, P. San-Jose, M. W. A. de Moor, A. Geresdi, E. J. H. 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 Re- views Physics 10.1038/s42254-020-0228-y (2020)

    2020 doi

  40. [47]

    Cayao and A

    J. Cayao and A. M. Black-Schaffer, Distinguishing trivial and topological zero-energy states in long nanowire junctions, Physical Review B 104, 10.1103/physrevb.104.l020501 (2021)

    2021 doi

  41. [48]

    A. M. Turner, F. Pollmann, and E. Berg, Topological phases of one-dimensional fermions: An entanglement point of view, Phys. Rev. B 83, 075102 (2011)

    2011

  42. [49]

    Bonderson, M

    P. Bonderson, M. Freedman, and C. Nayak, Measurement-only topological quantum computation, Phys. Rev. Lett.101, 010501 (2008)

    2008

  43. [50]

    J. D. Sau, B. Swingle, and S. Tewari, Proposal to probe quan- tum nonlocality of majorana fermions in tunneling experiments, Phys. Rev. B 92, 020511 (2015)

    2015

  44. [51]

    A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Electri- cally detected interferometry of majorana fermions in a topo- logical insulator, Phys. Rev. Lett. 102, 216404 (2009)

    2009

  45. [52]

    J. D. Sau, S. Tewari, and S. Das Sarma, Probing non-abelian statistics with majorana fermion interferometry in spin-orbit- coupled semiconductors, Phys. Rev. B 84, 085109 (2011)

    2011

  46. [53]

    Aghaee, A

    Microsoft Azure Quantum, M. Aghaee, A. A. Ramirez, Z. Alam, R. Ali, M. Andrzejczuk, A. Antipov, M. Astafev, A. Barzegar, B. Bauer, J. Becker, U. K. Bhaskar, A. Bocharov, S. Boddapati, D. Bohn, J. Bommer, L. Bourdet, A. Bousquet, S. Boutin, L. Casparis, B. J. Chapman, ..., and ...

    2025

  47. [54]

    J. D. Sau and S. D. Sarma, Capacitance-based Fermion parity read-out and predicted Rabi oscillations in a Majorana nanowire (2024), arXiv:2406.18080

    2024 arXiv

  48. [56]

    B. B. Roy, R. Jaiswal, T. D. Stanescu, and S. Tewari, Stabilizing topological superconductivity in disordered spin-orbit coupled semiconductor-superconductor heterostructures, Phys. Rev. B 110, 115436 (2024)

    2024

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.