[HN Gopher] What are Majorana zero modes?
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       What are Majorana zero modes?
        
       Author : ColinWright
       Score  : 66 points
       Date   : 2025-02-19 19:54 UTC (4 days ago)
        
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       | prof-dr-ir wrote:
       | > there's a chance neutrinos are Majorana particles.
       | 
       | Pet peeve: don't say "are Majorana particles", say "have a
       | Majorana mass term".
       | 
       | All spin 1/2 fermions in four spacetime dimensions can be
       | constructed from the chiral (or Weyl) representation. A Dirac
       | fermion is two independent chiral fermions. A Majorana fermion is
       | just a chiral fermion written in a funny way. And people saying
       | that chiral fermions cannot have mass are lying. (/rant)
       | 
       | By the way, a nicer explanation for the neutrino masses is the
       | so-called seesaw mechanism:
       | 
       | https://en.wikipedia.org/wiki/Seesaw_mechanism
       | 
       | In this wiki article the Majorana mass is denoted B'. However, as
       | the article explains, it must vanish by gauge invariance in the
       | standard model.
        
         | sigmoid10 wrote:
         | > And people saying that chiral fermions cannot have mass are
         | lying
         | 
         | People usually say that in the context of the vanilla Standard
         | Model. So far, experiments say we don't see right handed
         | neutrinos and we also don't see lepton number violation. So we
         | can't have masses there. This stuff only works if you start
         | with the assumption that the Standard Model is an effective
         | field theory and introduce higher dimension operators. Or if
         | you go full BSM. The most simple expansion of the standard
         | model that allows for Neutrino oscillations precisely needs
         | them to be (pure) Majorana particles. Though that doesn't
         | explain their weird masses as you say and the more complex
         | expansion that results in seesaw (which adds a Dirac mass)
         | seems a bit more natural. So your argument is mostly a case of
         | missing context.
        
           | noone_important wrote:
           | I kind of disagree on your statement about lepton violation.
           | The standard model predicts lepton violating processes
           | (sphalerons). The true symmetry of the standard model is B-L.
           | Of course you are right, that these topological effects will
           | not lead to majorana mass terms.
        
             | sigmoid10 wrote:
             | Well, while sphalerons theoretically break B+L in the non-
             | perturbative regime, they are exponentially suppressed at
             | the energy level of our colliders. At the same time,
             | irrelevant operators that also violate it are suppressed by
             | the GUT scale. So even if you take the minimal Standard
             | Model at face value, you're out of luck finding any sign of
             | the violation either way. But if Neutrinos get Majorana
             | masses, that would be an _additional_ explicit violation at
             | the perturbative level. That would be something we can
             | directly observe, as in neutrinoless double beta decay.
        
               | noone_important wrote:
               | I agree, that neutrinoless double beta decay would be
               | incredibly interesting, but it is very speculative (and
               | depending on the neutrino mass hierarchy not really
               | falsifiable).
               | 
               | My original point was just that lepton number is not a
               | good symmetry as it is broken by rhe chiral anomaly,
               | which is not speculative at all. Of course, the sphaleron
               | effects are negligible in collider settings, but for
               | cosmology they are crucial and might be indirectly
               | observable.
        
       | cmcconomy wrote:
       | Welcome to the era of Majoranal Computing
        
       | hackandthink wrote:
       | https://scottaaronson.blog/?p=8669
       | 
       | "Q2. What is a topological qubit?
       | 
       | A. It's a special kind of qubit built using nonabelian anyons,
       | which are excitations that can exist in a two-dimensional medium,
       | behaving neither as fermions nor as bosons. The idea grew out of
       | seminal work by Alexei Kitaev, Michael Freedman, and others
       | starting in the late 1990s. Topological qubits have proved harder
       | to create and control than ordinary qubits."
       | 
       | https://en.wikipedia.org/wiki/Anyon
        
         | random3 wrote:
         | The more relevant bit, beyond the paper
         | 
         | > I foresee exciting times ahead, provided we still have a
         | functioning civilization in which to enjoy them.
        
       | dr_dshiv wrote:
       | Aren't the 0 and 1 states of a qubit basically the zero mode
       | (ground state) and first mode of the quantum system? So, there
       | can be superposition of the modes, but when measured (with an EM
       | pulse), it either re-emits the pulse (producing a 1) or absorbs
       | it (producing a 0). Is that correct?
       | 
       | I recently learned there are qubits that have more than 2
       | modes... like a qutrit, with 3:
       | https://en.wikipedia.org/wiki/Qutrit
        
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