Majorana fermions are the particles associated to the real representation (hence the real solution) of the Dirac equation, as established by the Italian physicist Ettore Majorana in the late 30's. By extension, a Majorana fermion will be any particle (emergent or fundamental) having the property to ...

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Why do the $1/2$ factor appear in the Majorana mass Lagrangian?

In case of Dirac neutrino there is no $1/2$ factor in the mass Lagrangian but for Majorana type neutrino there is a half factor in the mass Lagrangian.
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Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?

In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity $$ \overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}. $$ Here, I am using 4 ...
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Is the conjectured noncommutative heavy scalar “brother” of the already detected Higgs boson is a pseudo scalar?

This is a technical (may be trivial?) question about this sigma scalar field advertised by Chamseddine and Connes to improve the electroweak vacuum stability involved by the weak mass of the already ...
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Definition of 'Majorana Number' in the Kitaev Chain

I have some questions about the Kitaev toy model for Majorana fermions (arXiv:cond-mat/0010440). First of all, his proof for the definition of the 'Majorana number' is not so clear to me. $$P(H(L_{1} ...
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Fractional Josephson effect explained

I am confused by the fractional Josephson effect. I still don't know if there has to be parity conservation or not. Is the fractional Josepshon effect always connected to fermion parity anomaly ...
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Why is there a Majorana zero mode in the $\pi$ flux core of the p+ip superconductor?

In this review paper (http://arxiv.org/pdf/1202.1293.pdf), the author shows that threading a $\pi$ flux through a 2D $p_x+ip_y$ superconductor will trap a Majorana zero mode at the flux center. The ...
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Majorana equation and non-invariance of spinor representation under discrete Lorentz transformations

Here I asked about getting an equation for two-component spinor as the alternative for Dirac equation. It was found that it is called Majorana equation. It may be easily derived by using historical ...
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Oscillations and Majorana Neutrino

In neutrino oscillations, neutrinos can convert from one flavor to another. This implies individual lepton number is not conserved. Doesn't it also imply that, if the neutrinos have mass, the mass ...
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Josephson effect - fractional or not

It is well known that a current proportional to $J\propto\sin(\phi_1-\phi_2)$ flows when two superconductor with phases $\phi_1$ and $\phi_2$ are connected. Also, a current which depends on the ...
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Pedagogical introduction to vertex, domain wall, and kink

Recently, Majorana fermion becomes hot in condensed matter physics. The concepts: vertex, domain wall, and kink often appear in these articles about Majorana fermion. I have no idea about the ...
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Equivalence of derivation of Majorana fermions

Perhaps is this a stupid question but I have really no answer. To prove the emergence of Majorana bound states I search zero-energy solution of the Bogoliubov - de Gennes equation $$ ...
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Commutators of differential and field operators

In $p+ip$ superconductivity, a term in the Hamiltonian (in polar coordinates) is $$ H=\int \mathrm{d}^2\vec{r} \left[ \left( \partial_r -\frac{i}{r} \partial_{\theta} \right) \psi^\dagger(\vec{r}) ...