Strongly Correlated Electrons · arXiv:0912.4508 v4 · submitted 22 Dec 2009
Robustness of Majorana fermions in 2D topological superconductors
The paper says
“Here we show that when s-wave superconductivity is proximity-induced on the surface of a topological insulator or a spin-orbit-coupled semiconductor, as has been recently suggested, the mini-gaps of the resultant non-Abelian states can be orders of magnitude larger than in a chiral p-wave superconductor.”
from the abstract · picked out as the main claim by a classifier
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The paper
Abstract
In 2D chiral p-wave superconductors, the zero-energy Majorana fermion excitations trapped at vortex cores follow non-Abelian statistics which can be potentially exploited to build a topological quantum computer. The Majorana states are protected from the thermal effects by the mini-gap, Δ2/εF (Δ:bulk gap, εF: Fermi energy), which is the excitation gap to the higher-energy, non-topological, bound states in the vortex cores. Robustness to thermal effects is guaranteed only when T ≪ Δ2/εF ∼ 0.1 mK, which is a very severe experimental constraint. Here we show that when s-wave superconductivity is proximity-induced on the surface of a topological insulator or a spin-orbit-coupled semiconductor, as has been recently suggested, the mini-gaps of the resultant non-Abelian states can be orders of magnitude larger than in a chiral p-wave superconductor. Specifically, for interfaces with high barrier transparencies, the mini-gap can be as high as ∼ Δ ≫ Δ2/εF, where Δ is the bulk gap of the s-wave superconductor responsible for the proximity effect.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.99
What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.52 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.95 · mentions code or data availability 0.01
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v4). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| In 2D chiral p-wave superconductors, the zero-energy Majorana fermion excitations trapped at vortex cores follow non-Abelian statistics which can be potentially exploited to build a topological quantum computer. | background 1.00 | 0.05 | 0.04 | hedged possibility 0.53 |
| The Majorana states are protected from the thermal effects by the mini-gap, $\Delta^2/\epsilon_F$ ($\Delta$:bulk gap, $\epsilon_F$: Fermi energy), which is the excitation gap to the higher-energy, non-topological, bound states in the vortex cores. | background 1.00 | 0.10 | 0.04 | asserted 1.00 |
| Robustness to thermal effects is guaranteed only when $T \ll \Delta^2/\epsilon_F \sim 0.1$ mK, which is a very severe experimental constraint. | background 0.87 | 0.10 | 0.05 | asserted 1.00 |
| Here we show that when s-wave superconductivity is proximity-induced on the surface of a topological insulator or a spin-orbit-coupled semiconductor, as has been recently suggested, the mini-gaps of the resultant non-Abelian states can be orders of magnitude larger than in a chiral p-wave superconductor. | contribution 0.62 | 0.85 | 0.78 | asserted 0.99 |
| Specifically, for interfaces with high barrier transparencies, the mini-gap can be as high as $\sim \Delta \gg \Delta^2/\epsilon_F $, where $\Delta$ is the bulk gap of the s-wave superconductor responsible for the proximity effect. | result 1.00 | 0.81 | 0.32 | asserted 0.78 |
What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.63
What was examined, and what was not
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,645 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 1 Pith paper
Reviewed papers on Pith that cite this one. The full citation record
How later papers used it
56 later papers cite it
4 papers by the same authors are listed below: 1 built on it, 2 used its method or tool and 1 compared its own results with it.
Builds on it 1 of 2 papers with this label · 1 by the same authors
By the same authors
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Extended this paper's surprising result, previously obtained for the proximity-induced superconducting state on a topological insulator surface, to the spin-orbit coupled semiconductor.
Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems (2010) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Uses its method or tool 2 of 9 papers with this label · 2 by the same authors
By the same authors
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Followed this paper to obtain the renormalization factors analytically and plotted them with numerical solutions and static-limit approximations.
Effects of large induced superconducting gap on semiconductor Majorana nanowires (2015) (same authors) · 0.93 · paraphrased: the licence does not allow quoting
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Modeled the self-energy from the proximitized superconductor as in this paper, with the positive real part branch cut for omega below Delta and positive imaginary part otherwise.
Avoiding Dilution: Using Diffusion and Vision Transformers to resolve Majorana Features in Nanowires at High Temperature (2026) (same authors) · 0.94 · paraphrased: the licence does not allow quoting
Compares with it 1 of 4 papers with this label · 1 by the same authors
By the same authors
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Observed that in the weak-coupling and weak disorder limit the induced gap scales linearly with coupling, the same as previous calculations done with a clean superconductor in this paper.
Bulk disorder in the superconductor affects proximity-induced topological superconductivity (2015) (same authors) · 0.99 · paraphrased: the licence does not allow quoting
How the literature uses it
8 arXiv papers cite this in 11 sentences
Papers citing it · 8 sentences without a confident label
Builds on it 1 paper
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This surprising result, which was obtained previously for the proximity-induced superconducting state on the surface of a TI, [ref] is now extended to the spin-orbit coupled semiconductor in this paper.
Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems · Summary and Conclusion · 1.00
Uses its method or tool 1 paper
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The superconducting correlations in the TI are generated through the tunneling between the TI and the parent SC, and the effective Hamiltonian [ref] can be calculated by integrating out the SC degrees of freedom in the combined SC-TI system and computing the SC-TI interface self-energy [ref] . $Δ$ obtained in this way depends on the pairing potential in the parent SC as well as on the strength of the TI-SC coupling, and is in general a function of the spatial coordinate $$.
Influence of disorder on antidot vortex Majorana states in 3D topological insulators · Effective model of the proximitized TI surface · 0.81
Cites it as background 1 paper
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Recently, some exotic ordered states in condensed matter systems, such as the Pfaffian states in fractional quantum Hall (FQH) systems, [ref] $p$-wave superconductors/superfluids, [ref] theoretical models that can be potentially simulated in cold atom optical lattice systems, [ref] as well as the surface state of a topological insulator (TI) or related systems [ref] have been discussed as systems which can support Majorana fermions as the lowest energy excitations.
Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems · Introduction · 0.92
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