Talk:Majorana fermion

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

message: 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)
thread_title:  2016 

message: 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)
thread_title: How big?

message: 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)
thread_title:  unsourced content moved from main article: 

message: 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)
replies: text: 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)

text: 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)
thread_title:  particle-antiparticle in superconductor 

message: 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)
replies: text: 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)

text: 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)
thread_title: Majorana particle same thing?

message: 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)
thread_title:  the pronunciation is off 

message: 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)
thread_title:  Majorana braiding experiments 

message: 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)
thread_title:  Separating Majorana bound states 

message: In the section "Theory", the statement «For a Dirac fermion the operators \gamma^{\dagger}_j 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^\dagger_j 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)
thread_title:  Theory - Creation and annihilation operators 

message: 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)
thread_title:  spurious tag 

message: The article writes
 For a Dirac fermion the operators \gamma^{\dagger}_j 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)
thread_title:  Terminology