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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Mass scales in See-saw mechenism

Are both types of Majorana masses $$\mathcal{L}^L_M=-\frac{m_L}{2}[\overline{(\psi_L)^c}\psi_L + \overline{\psi_L}(\psi_L)^c]$$ and $$\mathcal{L}^R_M=-\frac{m_R}{2}[\overline{(\psi_R)^c}\psi_R + ...
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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}) ...
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Majorana Mass For Neutrinos In Standard Model

Neutrinos can't be given Dirac masses because there is no $SU(2)_L$ singlet right handed neutrinos in the standard model. But can neutrinos be given Majorana masses in the standard model? EDIT: Why ...
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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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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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Problem evaluating $C^{-1}M^\dagger C$

How can I show the following? $$\overline{\psi_L}M^\dagger (\psi_L)^c=\overline{\psi_L}CM^\dagger\overline{\psi_L}^T$$ where $\psi^c=C\overline{\psi}^T$ and ...
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Majorana mass vs Dirac Mass

Why is it said that the Dirac mass term conserves the fermion number but the Majorana mass term does not? Can someone explain this mathematically? Which breakdown of symmetry is responsible for ...
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Majorana equation in two forms

Let's have two forms of Majorana equation. First form (standart or spinor representations of gamma-matrices). $$ i\gamma^{\mu} \partial_{\mu}\Psi - m\Psi = 0, \quad \Psi = \Psi_{c} = \hat {C} \bar ...
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Non-vanishing commutator of potential and mass matrices for Majorana fermions interaction theory

Consider 2 different Majorana fermions $\Psi_{L}, \Psi_{R}$ (physically, neutrinos). In general case I can write the massive part of lagrangian of these fermions in the form $$ L_{m} = (\bar ...
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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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Topology and Majorana bound states

I'm working at the moment on Majorana Bound states and their topological properties. Now I have a question about it. The Altland-Zirnbauer symmetry classes says us how many topological different ...
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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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Determining spectra of edge states numerically

Normally we write a Bloch Hamiltonian $H(\mathbf{k})$ for the bulk and determine the spectrum which gives us various bands i.e we basically obtain $E=E(\mathbf{k})$ for the bulk only. Also in the ...
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What sorts of complications do massive neutrinos bring to the Standard Model?

Naively, I'd just think of considering them as any other massive fermions (but without electric charge), including the appropriate chiralities (and neutrino-higgs coupling when necessary). ...
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Question about Majorana fermions

I have a few questions about Majorana fermions. What is Majorana mass? Does it have a different value compared to the mass in the Dirac equation for an arbitrary fermion? How exactly do they differ? ...
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Vortices and chemical potential in topological superconductors

I am trying to read up some review articles about Majorana physics in topological material, but I am not really familiar with the condensed matter terminology (with condensed matter in general I ...
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Majorana wavefunction

I'm trying to compute the wavefunction for a Majorana state in an nanowire/superconductor hybrid system, like arXiv: Majorana Fermions and a Topological Phase Transition in ...
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Parity of the ground state of a Majorana chain

I work on the Kitaev toy model for Majorana fermions. He writes that in Majorana basis the Hamiltonian becomes in general $$ H = \frac{i}{4} \sum_{l,m} A_{l,m}\gamma_{l}\gamma_{m} $$ where $\gamma$ ...
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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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Is a single particle transition allowed between two superconductors having Majorana modes?

Sorry maybe I ask a very naive and stupid question. The motivation to ask it is as follows: I am considering the parity protection of Majorana qubit based on Kitaev's 1D model. As we know, in the ...
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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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What is the most natural new physics one can expect at the TeV scale: new (supersymmetric)particles or some new (non-commutative) spacetime structure?

Up to now, nothing else than one Standard Model (SM) Higgs boson-like resonance has been found at the LHC while many predictions based on effective theories using supersymmetry require several Higgs ...
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What is an anapolar moment?

I just read this: Anapolar Dark Matter I'm not sure i've heard the term 'anapolar' before, so i google and i found this: http://en.wikipedia.org/wiki/Toroidal_moment This confuses me, my ...
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Are majorana masses technically natural?

I understand that Dirac masses for fermions are "technically natural" (in the 't Hooft sense of technical naturalness) because they break chiral symmetry. In limit where the Dirac mass goes to zero, ...
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What is the importance of the Fermi energy $E_F$ or the chem. potential $\mu$ for topological superconductors

A lot of effort is put into shifting the Fermi energy of a topological insulator to exactly zero which then provides some advantages when this TI is coupled with a superconductor. I don't understand ...
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How is a Majorana fermion created when a s-wave superconductors is in proximity to a topological insulator (e.g. via an antidot)

Kane and Fu proposed a few geometries how to create Majorana zero modes using a s-wave superconductor in proximity to a 3D topological insulator (TI). -> ...
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What is a $p_x + i p_y$ superconductor? Relation to topological superconductors

I often read about s-wave and p-wave superconductors. In particular a $p_x + i p_y$ superconductor - often mentioned in combination with topological superconductors. I understand that the overall ...
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Basic questions in Majorana fermions

Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?
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Why is the majorana particle a fermion?

My knowledge of quantum mechanics is rather limited, but what I always understood was that Bosons have integer spins and Fermions have half-integer spins. My question is very simple: the Majorana ...
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229 views

Neutrino mass with Dirac and Majorana

Why both Dirac mass and Majorana mass terms are needed to explain the mass of a neutrino?
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How can one know if one has a Majorana fermion?

If the Majorana fermion is a fermion that is it's own antiparticle and exactly the same as its fermion counterpart, then how do they know that it's not just a fermion?
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How is this a condition for a Majorana zero mode?

EDIT: Nevermind, I figured it out. When you apply the expression on a state, you can clearly see what it does: The new state created by applying the Majorana operators must have the same energy as the ...
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Majorana particles statistics

What is the influence of Hermitian condition ($\psi=\psi^{\dagger}$) of Majorana fermions operators in their statistical behavior? A Majorana fermion gas must obey the Fermi-Dirac statistics, or ...
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Which symmetric pure qudit states can be reached within local operations?

There are two pure symmetric states $|\psi\rangle$ and $|\phi\rangle$ of $n$ qudits. Is there any known set of invariants $\{I_i:i\in\{1,\ldots,k\}\}$ which is equal for both states iff ...
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Is there a Majorana-like representation for singlet states?

I mean the Majorana representation of symmetric states, i.e., states of $n$ qubits invariant under a permutation of the qudits. See, for example, D. Markham, "Entanglement and symmetry in permutation ...