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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Basic questions about the Kitaev chain

I am trying to understand the first 5 pages of Introduction to topological superconductivity and Majorana fermions http://arxiv.org/abs/1206.1736 I read it 2-3 times and thought about it but a few ...
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Why is non-abelian property of Majorana fermion so difficult to observe experimentally?

Kouwenhoven's group observed experimental signatures consistent with the realization of Majorana bound states in semiconductor nanowire. (Mourik et al. 2012 Science 336, 1003, ...
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Question about Majorana spinor's property

I am reading the BBS, Exercise 5.1 This exercise is nothing but showing that two Majorana spinors $\Theta_1$ and $\Theta_2$ \begin{align} \bar{\Theta}_1 \Gamma_{\mu} \Theta_2 = -\bar{\Theta}_2 ...
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Plane wave solutions of the Majorana equation

Let u(p) and v(p) be the plane wave solutions of the Dirac equation with positive respectively negative energy. In case of a solution of the Majorana equation the charge-conjugated solution is ...
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Are there topological non-trivial states in zero dimension?

The periodic table of topological insulators and superconductors suggests that there can be topological non-trivial phases in zero dimension in non-interacting system with certain symmetries. A 0D ...
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About Majorana fermion in spin-orbit coupled quantum wires

Majorana mode has attracted great theoretical and experimental interest. The experimental evidence is obtained in quantum wires. The origin theoretical proposals of quantum wires are the papers: 1、R. ...
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Topological superconductors: what is the role of spin-orbit coupling? Are there topological non-trivial states without spin-orbit?

Let's say I have a one-dimensional system with particle-hole symmetry and with broken time-reversal symmetry. As a consequence, the chiral symmetry is also broken in this case (the chiral symmetry ...
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97 views

Dirac bracket for the Majorana Lagrangian

Note: See update below. Consider the Majorana Lagrangian $$\mathcal{L}=-\psi ^{\mathrm{T}}\mathrm{i}% \gamma ^{0}\left( \gamma ^{\rho }\partial _{\rho }+m\right) \psi ,\tag{1}$$ where $% \psi \in ...
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118 views

When was the first time that superconducting quasiparticles were called Majorana fermions?

Since a number of years, the field of superconductivity has a growing obsession with Majorana fermions. I wonder how far back we can go: When was the first time that superconducting quasiparticles ...
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commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, ...
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How the Vortex containing majorana bound state is non-abelian statistics

Recently,I read some papers about non-abelian statistics of majorana fermion, such as: Majorana Returns F. Wilczek http://www.nature.com/nphys/journal/v5/n9/full/nphys1380.html and Non-Abelian ...
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60 views

About recent experimental evidence of Majorana edge states in topological superconductors

I have a couple of question about the recent experimental evidence of Majorana edge states in topological superconductors. Which are the main differences between the experimental signatures of ...
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Anomaly for Majorana fermion?

In 4-spacetime dimension, is there U(1) gauge field chiral anomaly associated with Majorana fermion (or I am not sure if it is equivalent, majorana representation)? Besides, I have read from several ...
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How to calculate the ground states' Berry phases with doubly degeneracy, such as that due to the particle-hole symmetry or time reversal symmetry?

Suppose the ground states of a system are doubly degenerate due to an anti-unitary symmetry $K$, which are $|\psi>$ and $|K\psi>$. If the system is an one-dimensional Fermion system and ...
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356 views

What makes a superconductor topological?

I have read a fair bit about topological insulators and proximity induced Majorana bound states when placing a superconductor in proximity to a topological insulator. I've also read a bit about ...
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62 views

What are the quantum numbers of Majorana neutrinos?

I have a question about majorana neutrinos. Majorana particles are particles that are their own antiparticle. From this I would argue that they need to have all quantum numbers equal to zero. My ...
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74 views

Neutrino mass and the Majorana equation

I can't seem find this on the Internet. What does the Majorana equation predict neutrino masses to be (if they were their own antiparticle), and how? (I have little understanding of spinors, btw...) ...
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What is the number of fermions in Kitaev honeycomb model?

One way to solve the Kitaev honeycomb model: $$ H = J_x \sum_{\textrm{x links}, <ij> } \sigma^x_i \sigma^x_j + J_y \sum_{\textrm{y links}, <ij> } \sigma^y_i \sigma^y_j + J_z ...
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How are topological invariants constructed?

I've seen several different definitions for what are called topological invariants, for instance in the context of Majorana unpaired modes, by Kitaev: http://arxiv.org/abs/cond-mat/0010440 ...
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Can one define wavefunction for Bogoliubov quasiparticle excitation in a superconductor?

Wavefunction is essentially a single particle concept. It is easily extended to multiparticle system as follows- if one has say five electrons the wavefunction of this five electron state is any ...
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Axiom approach for majorana fermions

This is the usual way of introducing majorana operators. First we have $N$ fermionic modes. The corresponding operators satisfy the commutation relations $$ \{c_i, c_j \}= \{c_i^\dagger, c_j^\dagger ...
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braiding bosons or fermions around majorana fermion

Majorana fermions are described by their topological charge. My question is whether we can see the topological charge of Majorana fermions by braiding a boson or a fermion around it ? Is the only ...
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Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
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Why are Majorana fields usually used to introduce gravity in the Rarita-Schwinger Lagrangian?

When first introducing the gravitational interaction for a spin-3/2 Rarita-Schwinger field, Majorana fields are usually used (see for example here at chapter 4, or in Ramond, (6.4.112) ). Why is ...
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Why Majorana phases cannot be removed?

Why is the extra two Majorana phases in the PMNS matrix cannot be removed if neutrinos are Majorana fermions? Or in other words, why are the Majorana phases cannot be absorbed into the redefinition of ...
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Why aren't purely Dirac neutrinos ruled out?

It is common knowledge that in neutrinos can be Dirac particles without any Majorana masses as given a mass matrix, \begin{equation} \left( \begin{array}{cc}\nu _L & \nu _R \end{array} \right) ...
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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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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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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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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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Seesaw type-1 and integrating out heavy fields

Let's assume seesaw 1 type of generation of left neutrino Majorana mass: $$ L_{m} = -G_{ij}\begin{pmatrix} \bar{\nu}_{L}& \bar{l}_{L}\end{pmatrix}^{i}i\sigma_{2}\begin{pmatrix}\varphi_{1}^{*} \\ ...
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84 views

How to cancel infinite mass corrections for quantities without counterterms?

I'm trying to understand how infinite mass corrections are cancelled for a particle that is massless at tree level. In short the problem is that we have infinite diagrams, but we don't have a ...
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Double decay $\beta\beta$ observation and neutrino mass

If the double decay $\beta\beta$ will be detected this means the neutrino is a Majorana particle coincident with its antiparticle. At the moment the half life of this decay is put to ...
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Majorana Superfields

so apologies if this is a silly question... In the type 1 see saw model we add extra Majorana fermions to our model. These fermions have to be total gauge singlets in order to have a Majorana mass ...
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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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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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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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444 views

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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316 views

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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427 views

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 ...