Talk:Majorana fermion

& Neutrinos, et al

I added a bit about Majorana/Dirac neutrinos and the neutralino. HEL 17:53, 30 September 2006 (UTC)

Please check this artical: http://www.nature.com/news/quest-for-quirky-quantum-particles-may-have-struck-gold-1.10124 Rick Smit (talk) 14:33, 1 March 2012 (UTC)

I already linked to it. Brienanni (talk) 17:34, 1 March 2012 (UTC)

Discovery

The news says that physicists at Delft university have discovered "the Majorana particle". 84.86.56.119 (talk) 19:22, 12 April 2012 (UTC)

The news is wrong. They discovered evidence for a Majorana quasiparticle. That's not the same thing, and is discussed in the quasiparticle section of the article. Modest Genius ^talk 13:41, 16 April 2012 (UTC)

The news is wrong. "the Majorana particle" and the Majorana fermion has already been discovered as quasiparticle in any superconductors long time ago. The Delft group was looking for protect zero-energy modes (or "Majorana zero modes"), which are not Majorana fermions. — Preceding unsigned comment added by 99.254.174.25 (talk) 16:32, 26 May 2012 (UTC)

Ahem. Evidence?

"the Majorana particle" and the Majorana fermion has already been discovered as quasiparticle in any superconductors long time ago.

--Thnidu (talk) 19:48, 21 December 2012 (UTC)

The thing is that quasiparticle fermionic excitations in superconductors are actually Majorana fermions. This is not contested, and while there may be no experiment dedicated to observe pairwise annihilation of those, this is rooted in the modern theory of superconductivity. I think the difference between Majorana fermions and Majorana bound states/zero modes is explained fairly well in the corresponding section. Anton.akhmerov (talk) 14:27, 27 December 2012 (UTC)--

Guys, please try to make this article readable for non-experts. We all know that for getting fame, news articles are unclear on purpose. The wording that should be used everywhere here is truly "quasiparticle fermionic excitations" or so. The wording particle is missleading as it implicitely refers to as fundamental particles. — Preceding unsigned comment added by 85.28.86.7 (talk) 20:48, 4 October 2014 (UTC)

This is not correct, please see the discussion in Majorana fermion#Majorana bound states as well as discussion below; both clarify the terminology matters quite accurately. In particular, it isn't appropriate to use "fermionic" when referring to Majorana zero modes/bound states. As far as particle/quasiparticle goes, I believe the article it quite accurate. If you see any place where the terms are not used correctly, fix it (but do keep in mind the fermion/bound state distinction) Anton.akhmerov (talk) 21:00, 4 October 2014 (UTC)

With regards the recent "Detection" section, I suggest the following changes:

1. "In 2014, Majorana bound states were observed for the first time by the Princeton University scientists using a low-temperature scanning tunneling microscope" --> "In 2014, evidence of Majorana Bound States was observed for the first time using a low-temperature scanning tunneling microscope, by scientists at Princeton University".

2. "Physicist Jason Alicea of California Institute of Technology, not involved in the research, said the study offered "compelling evidence" for Majorana fermions" --> "Physicist Jason Alicea of California Institute of Technology, not involved in the research, said the study offered "compelling evidence" for Majorana fermions but that "we should keep in mind possible alternative explanations—even if there are no immediately obvious candidates"".

I feel these alterations would lend the article a more objective tone, which is particularly important given its recent inclusion in Wikipedia's front page news segment. By all means, if anyone has any objections I would be happy to hear them.95.145.178.230 (talk) 13:41, 5 October 2014 (UTC)

This is very reasonable. I would suggest an even further modification, which would make the descriptions of the Princeton and the earlier Delft experiments more comparable. Both experiments received comparable amount of attention, both provide rather detailed and very high quality measurements, but neither allows to conclude with full certainty that the observed conductance peak is due to Majoranas. Also the detection subsection shouldn't really be separate from the preceding discussion. Anton.akhmerov (talk) 17:41, 5 October 2014 (UTC)

I have made the above changes as well as "The Majorana bound states appeared..." -> "It was suggested that Majorana bound states appeared...". I also agree with Anton that it is unnatural to have the separate "Detection" section for Yazdani et al.'s work, perhaps we could get some comments on this before merging it with the section which mentions the Delft work.95.145.178.230 (talk) 18:09, 5 October 2014 (UTC)

2016

Referencing this edit:

   A proof of the existence of Majorana fermions in a solid state material as quasiparticles was announced by researchers at Oak Ridge National Laboratory, working in collaboration with Max Planck Institute and University of Cambridge on 4 April 2016.

There has been no discovery. The only mention of this on Oak Ridge National Laboratory's website is an abstract for a paper published this year. ORNL has not issued any news releases, however. Adraeus (talk) 12:35, 27 June 2016 (UTC)

How big?

Where on this scale are the Majorana fermion? — Preceding unsigned comment added by 99.21.254.133 (talk • contribs) 19:43, 17 April 2012

Since no Majorana fermions have been discovered, nowhere. Modest Genius ^talk 13:48, 18 April 2012 (UTC)

unsourced content moved from main article:

In fact, if we define Majorana fermions as fermions that are identical to their antiparticle, then the quasi-particles in any superconductors will be Majorana fermions (even without vortex). This is because the quasi-particles in any superconductors are fermions that can annihilate with itself. Such kind of "Majorana fermion" (ie the one that is actually introduced by Majorana) has already been found in superconductors. What people are looking for recently is actually Majorana zero mode inside of a vortex or other defects of a superconductor. The Majorana zero mode, as a zero-dimensional object, does not have Bose/Fermi statistics as defined by exchange and braiding. A vortex that carries a Majorana zero mode has a non-Abelian statistics, which is also not a fermion. So the "Majorana zero modes" are very different from the Majorana fermions introduced by Majorana. Refering "Majorana zero modes" as "Majorana fermions" can be very confusing. 63.255.24.6 (talk) 13:48, 18 April 2012 (UTC)

particle-antiparticle in superconductor

In a conventional superconductor, electrons are paired from opposite spin bands. The quasiparticles are then electrons and holes from opposite spin bands, so they are not each others antiparticle. Mathematically, the creation and annihilation operators in a conventional superconductor are related by γ_up(E) = γ^†_down(-E), so even at E=0 one has γ_up=γ^†_down, which is not the required Majorana relation γ=γ^†. (The subscripts "up" and "down" refer to the spin bands.) This is why the discovery of Majorana fermions in a superconductor is a highly unusual event, and nothing something common, as was suggested in a recent edit of the article. — Preceding unsigned comment added by Brienanni (talk • contribs) 16:24, 26 May 2012 (UTC)

The fermions that Majorana actually introduced carry spin-1/2. So Majorana fermions carry spin-1/2. It is well known that the anti-particle of a spin-up Majorana fermions is a spin-down Majorana fermions. This is exactly the property the quasiparticles in spin-singlet superconductors. So the quasiparticles in spin-singlet superconductors are the real Majorana fermions introduced by Majorana. Since the complex conjugate of spin-1/2 representation of SO(3) is the same spin-1/2 representation, we may regard the spin-1/2 Majorana fermions as their own anti-particles. The "Majorana relation γ=γ^†" defines the Majorana zero mode, which is not the Majorana fermions introduced by Majorana. The real Majorana fermions can propagate in space, while Majorana zero mode cannot propagate. So please do not confuse a zero mode with Majorana fermions. Majorana fermions is defined very nicely in the first a few lines of this article. The second half of the article really confuses the matter, and is inconsistent with the nice definition in beginning of the article. The second half of the article should belong to a new Wiki article under a name such as "topologically protected zero-energy mode". Although such a notion was not introduced by Majorana, we can still call it Majorana zero-mode. — Preceding unsigned comment added by 99.254.174.25 (talk) 16:58, 26 May 2012 (UTC)

Let me try to clarify things a bit without math. There is a simple way to see if a particle is a Majorana fermion or not: take two of them, and ask if they can annihilate each other. In a spin-singlet superconductor, the quasiparticle excitations are a superposition of an electron from one spin band and a hole from the other spin band. Two of these excitations cannot annihilate each other, simply because you cannot fill a hole in one spin band with an electron from the other spin band. So the quasiparticle excitations of a spin-singlet superconductor are not Majorana fermions.

In the experiment mentioned in the article a spin-triplet pairing is induced, so that the quasiparticle excitations combine an electron and hole from the same spin band. Two such excitations can annihilate. In that sense one can call them Majorana fermions, even though this is a very different object than the fundamental particle introduced by Majorana. Brienanni (talk) 19:33, 26 May 2012 (UTC)

Thank you for the explanation. My point is that the fermion introduced by Majorana does carry spin-1/2. For such kind of particle, a spin-up fermion cannot annihilate a spin-up fermion. So according to your reasoning, the fermions introduced by Majorana (just like the quasiparticle excitations of a spin-singlet superconductor) are not Majorana fermions. I do agree with you that, in the presence of spin-orbital coupling, spin is not conserved and quasiparticles in superconductor can always annihilate with themselves. We may also call those fermions Majorana fermions, despite that they do not carry spin-1/2 while the fermions introduced by Majorana do carry spin-1/2. In any case, the thing described by the Majorana relation γ=γ^† at E=0 is a zero-mode. It is not the propagating Majorana fermion. — Preceding unsigned comment added by 99.254.174.25 (talk) 20:54, 26 May 2012 (UTC)

Majorana particle same thing?

I've just read about the Dartmouth research on what they call "majoranas" or "majorana particles". Are these the same thing as described in this article? If not, I think there needs to be a new article to treat these separately. Tmangray (talk) 16:11, 1 August 2012 (UTC)

same thing Brienanni (talk) 21:15, 1 August 2012 (UTC)

Okay, thanks. I've added these alternate names to the article. Tmangray (talk) 02:25, 3 August 2012 (UTC)

Some times, "majoranas" refers to the majorana zero-modes, which are not "majorana particles" and are not "majorana fermions". So we should remove "majoranas". Also, we should have two articles: this article about "majorana fermions" and another article about "majorana zero mode". — Preceding unsigned comment added by 95.242.109.225 (talk) 09:13, 18 September 2012 (UTC)

You are doing it wrong. This is a right way. And make edit summaries please, 95.242.109.225, I already asked you. Incnis Mrsi (talk) 15:11, 18 September 2012 (UTC)

While I definitely agree that Majorana zero mode is not a fermion, and should technically not be called a Majorana fermion, I would like to note that the Majorana zero modes are most frequently called Majorana fermions both in specialized as well as in popular literature. At least as it stands recently, Majorana zero mode is the most relevant meaning of 'Majorana fermion' (check e.g. google news). Due to this, I think the most reasonable decision would be to keep the articles not split, with the difference between the two closely related concepts clearly explained. --Anton.akhmerov (talk) 08:38, 30 September 2012 (UTC)

I concur: splitting the articles into two separate ones would create more confusion than clarification. It's better to just explain the different meanings of the word in one article. We already have separate articles for Majorana fermion, equation, and spinor, and merging would seem to make more sense than splitting. Brienanni (talk) 09:56, 30 September 2012 (UTC)

We should split this article into two. "Majorana fermion" and "Majorana zero mode" are not closely related concepts. If we compare "Majorana fermion" to an "apple", "Majorana zero mode" will be a "lake". We should not try to explain to people that an "apple" is a "lake" in this wiki page, as well as in other publications. — Preceding unsigned comment added by 99.237.13.87 (talk) 06:50, 5 October 2012 (UTC)

99.237.13.87, please take a look into WP:What_Wikipedia_is_not. Wikipedia articles are not intended to be read like a textbook or a scientific journal, and article titles should reflect common usage of the words. Majorana zero modes were popularized under the name 'Majorana fermions' by the media. Additionally this term is used by Kitaev, and by many after him. Regarding your remark, I agree that we shouldn't explain that an apple is a lake. We should however also not rename the "jellyfish" Wikipedia article into "Cnidaria" just because jellyfish are not fish. We might want to explain how a koala bear differs from a bear. --Anton.akhmerov (talk) 02:46, 16 October 2012 (UTC)

the pronunciation is off

it says maɪəˈrɒnə referring to the video (where an american researcher pronounces it like that). italian vowels sound differently and english speakers have difficulty with vowels anyway. especially the o and final a are not pronounced the same way (here both are ə) and more importantly, all a's are pronounced the same way. this articles suggests they are all pronounced differently. it's majoˈraːna (the vowels are fa'ther, awe, father, father) https://en.wikipedia.org/wiki/Help:IPA_for_Italian 92.196.32.203 (talk) 12:59, 1 January 2016 (UTC)

Majorana braiding experiments

I added details of two experiments braiding Majoranas, but these were reverted.

For my own experiment, there are two issues at play. One is self-citation. The other is that the way of realizing Majoranas that this experiment uses is not discussed in the article. There is little I can do about the former. But for the latter, at least I can add a section. So I have! I hope the experiment can be added to this section in future. Maybe we can wait until it is published and gets a DOI, though.

For the other experiment, it is a simulation of superconducting systems. So it should go in the section for superconducting experiments.

Woottonjames (talk) 21:01, 1 February 2017 (UTC)

Hi James! I have reverted the edits because of several concerns. Firstly, the original description merely stated "Two experiments that exchange Majoranas where carried out independently in 2016" without explaining that those were simulations and did not have a relation to the rest of the section. This you have corrected in the new version. However even with you having corrected that, I still have strong doubts whether the citations are appropriate:

• The N. Comm. paper is about Jordan-Wigner transformation of a spin chain, and is unrelated to the twist defects.
• Your preprint is about a system that has no spatial separation of degrees of freedom, and therefore it is hard for me to assess whether it realizes twist defects, as opposed to merely the same unitary transformation.
• Finally the reference "Demonstrating non-Abelian statistics of Majorana fermions using twist defects" is rather technical, but also it appears to be better suited to e.g. Toric code.

In addition to these issues, please keep in mind that self-citation in an encyclopedia is a clear conflict of interest. Wikipedia policites Wikipedia:Conflict_of_interest#Citing_yourself suggest to propose such an edit on a talk page, and only apply it if it is approved. If you believe that your paper is important, please ask others whether they also agree. Anton.akhmerov (talk) 23:51, 1 February 2017 (UTC)

I agree about the N. Comm paper being unrelated to the twists. I suggested that it be added to the superconducting section, since I believe the mathematics simulated is that of Kitaev's wires. I will not do so myself as I don't want this to become an edit war.

I take the point about the conflict of interest, though the suggestion you mention is to be done 'when in doubt'. I was not in doubt that these two experimental papers on Majoranas, one published and the other accepted for publication, were suitable for this article. They were relevant and did not place undue emphasis on my work, since I was citing all papers that I know of on experimentally braiding Majoranas.

Furthermore, my paper does have spatial separation of the degrees of freedom. But this isn't a talk page for my paper. I'll just resign myself to the fact that it isn't going in to the article any time soon.

Woottonjames (talk) 09:32, 14 February 2017 (UTC)

Separating Majorana bound states

Right now the article becomes progressively more confusing because of mixing together Majorana fermions and Majorana bound states in condensed matter. While a couple of years ago the contents were minimal and straightforward, there are now more and more references added, some about Majorana fermions, some about Majorana bound states (all in addition to the high energy part of the article). This makes the article progressively harder to maintain. I propose to separate out the Majorana bound states to offload part of complexity and to make it easier to validate the content. Anton.akhmerov (talk) 02:16, 31 July 2017 (UTC)

I think this is an excellent idea. I do notice a very recent paper by Xiao-Gang Wen (arXiv:1708.06214) that also laments this confusion surrounding Majorana fermions and Majorana bound states (which are not fermions), and making a clear separation of the two concepts would be beneficial. Brienanni (talk) 14:20, 22 August 2017 (UTC)

This article is becoming a complete mess. The Majorana bound state section now has been expanded to include original research on "majorana surface modes in lattice quantum field theory for the simulation of gauginos in supersymmetric Yang Mills theories", which has absolutely nothing to do with Majorana bound states: These "gauginos" are fermions, while the Majorana bound states are non-Abelian anyons. Can someone please take the courage and clean up the confusion. The suggestion given above to split off the Majorana bound states into a separate article seems the way to go. Brienanni (talk) 14:17, 3 February 2018 (UTC)

Theory - Creation and annihilation operators

In the section "Theory", the statement «For a Dirac fermion the operators $\gamma _{j}^{\dagger }$ and $\gamma _{j}$ are distinct, whereas for a Majorana fermion they are identical.» is not correct.
Instead, for a Majorana fermion the creation operator of the particle $\gamma _{j}^{\dagger }$ is identical to the annihilation operator of the corresponding antiparticle, but is the complex conjugate of the annihilation operator of the particle $\gamma _{j}$ (which, in turn, is identical to the creation operator of the antiparticle). That is clear also from the notation and is correctly stated in the previous sentence. — Preceding unsigned comment added by Szunino81 (talk • contribs) 07:34, 18 December 2017 (UTC)

spurious tag

Moreover, the lede of this article is far more accessible than others of its kind, the math in the body of the article relatively light. 98.4.124.117 (talk) 01:46, 31 July 2018 (UTC)

Contradiction about neutrinos

The second paragraph says, The nature of neutrinos is not settled – they may turn out to be either Dirac or Majorana fermions. I take this to refer to the known neutrinos
ν
_e,
ν
_μ,
ν
_τ. But in section "Elementary particles" the possibility that these are majorana is excluded because they have weak isospin and are thus not sterile. Which is it? Or was the sentence in the second paragraph intended to mean that some neutrinos could hypothetically be majorana (although the known ones aren't)? Then it should be rewritten. 2.204.227.211 (talk) 14:14, 25 January 2024 (UTC)

Yeah, it is an unfortunate tendency to not cite something when something is not settled. Also happens in research. However, I just was reading about Majorana fermions in the context TQC and the article https://www.nature.com/articles/nphys1380 was linked (F. Wilczek, 2009).

I do not know the current status of this debate and I haven't cited on Wiki yet, so I don't feel like messing that up right now. If someone would like to add that citation, that would be great. 2001:9E8:89B9:A300:A5FB:3796:8EF7:BB93 (talk) 18:42, 28 February 2024 (UTC)

Terminology

The article writes

For a Dirac fermion the operators $\gamma _{j}^{\dagger }$ and $\gamma _{j}$ are distinct, whereas for a Majorana fermion they are identical. The ordinary fermionic annihilation and creation operators $f$ and $f^{\dagger }$ can be written in terms of two Majorana operators $\gamma _{1}$ and $\gamma _{2}$ by...

Dirac fermions and ordinary fermions are the same I suppose? Why are they called differently and why does the notation swap from $\gamma$ to $f$ from one sentence to the next?

Also the indices are confusing, particularly because we had given Dirac fermions indices when they were $\gamma$ and dropped them when we moved on to $f$.

The notation of this article (https://iopscience.iop.org/article/10.1088/0268-1242/27/12/124003) and Fig. 1 are helpful. It also restates the expressions I just added (which were simply re-expressed from the existing text). 2001:9E8:89B9:A300:A5FB:3796:8EF7:BB93 (talk) 19:04, 28 February 2024 (UTC)