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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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 $|\phi\rangle=...
18
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2answers
5k views

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?
16
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1answer
6k views

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 ...
15
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4answers
215 views

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 ...
10
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1answer
295 views

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 ...
9
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3answers
341 views

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 ...
8
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2answers
947 views

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 ...
8
votes
1answer
611 views

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? ...
8
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3answers
553 views

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 ...
7
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1answer
1k views

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 ...
6
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3answers
2k 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 ...
6
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3answers
292 views

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) \...
6
votes
2answers
230 views

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 $\tau\ge10^{25}$...
6
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1answer
4k views

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 ...
6
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1answer
932 views

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 $\gamma$ ...
6
votes
1answer
746 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 ...
5
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3answers
520 views

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 ...
5
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1answer
536 views

Neutrino mass with Dirac and Majorana

Why both Dirac mass and Majorana mass terms are needed to explain the mass of a neutrino?
5
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1answer
292 views

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 ...
5
votes
1answer
103 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 ...
5
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2answers
271 views

Unpaired Majoranas in the Kitaev chain

How can we see unpaired Majoranas for a Kitaev chain in topological non-trivial phase? By looking at the equation below (obtained by making $c_{j}=\frac{e^{-i\phi/2}}{2}\left(\gamma_{B,j}+i\gamma_{A,j}...
5
votes
1answer
152 views

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). ...
5
votes
1answer
150 views

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 anti-...
5
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0answers
110 views

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 ...
4
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2answers
1k views

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 ...
4
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2answers
584 views

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 ...
4
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1answer
97 views

Photons are self-conjugate but neutrinos may or may not: why is that?

Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified. Although the neutrinos are ...
4
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1answer
384 views

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, ...
4
votes
1answer
653 views

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). -> http://www.physics.upenn.edu/~kane/pubs/p56....
4
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1answer
470 views

Majorana bound states in the Bogoliubov-de Gennes (BdG) formalism

I have the Kitaev chain tight-binding Hamiltonian into the BdG formalism (like the one in the "Bulk-edge correspondence in the Kitaev chain" section of Week 1 of this course http://www.topocondmat.org/...
4
votes
2answers
317 views

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.
4
votes
1answer
398 views

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 Semiconductor-...
4
votes
1answer
181 views

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 ...
4
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0answers
112 views

About the $Z_2$ topological invariant

In Kitaev 2001 it is shown that the topological invariant $Z_2$ in a topological superconductor (Class D or BDI, one dimensional) can be defined as $$ (-1)^\nu={\rm sign\, Pf} [ A ]={\rm sign\, Pf}[ \...
4
votes
1answer
241 views

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 ...
4
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0answers
94 views

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 ...
3
votes
1answer
175 views

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 ...
3
votes
1answer
134 views

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}^{*} \\ \...
3
votes
1answer
321 views

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 ...
3
votes
1answer
78 views

If a neutrino and his antineutrino has different helicity how can it be a possibility that it is a Majorana particle?

All antineutrinos observed thus far possess right-handed helicity (i.e. only one of the two possible spin states has ever been seen), while neutrinos are left-handed. Notwithstanding that it is said ...
3
votes
1answer
207 views

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 ...
3
votes
0answers
51 views

Majorara zero mode in Ising chain, not exactly zero subtlety

We know the transverse field Ising model with N sites(open boundary), can be mapped into N free fermions(there are 2N modes if including the negative energy counterparts) With property: $$\gamma^\...
3
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0answers
136 views

Edge states of Kitaev chain [closed]

I am reading paper about Kitaev chain of electrons, which can exhibit famous Majorana fermions at ends of wire. The Hamiltonian (his Eq. (6)) reads $H = \frac{i}{2} \sum_j - \mu c_{2j-1}c_{2j} +(w+|\...
3
votes
0answers
71 views

Is the right-handed antineutrino the CPT conjugate of the left-handed neutrino?

I am working from the book Massive Neutrinos in Physics and Astrophysics by Mohapatra and Pal (which is available here). On page 66, the authors claim that $\psi_{L}$ is the $\mathcal{CPT}$ conjugate ...
3
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0answers
122 views

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 \...
3
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0answers
707 views

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} ...
2
votes
2answers
253 views

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 ...
2
votes
1answer
95 views

Is a Weyl fermion its own antiparticle?

Majorana fermions are their own antiparticles, and Weyl fermions are just Majorana fermions without mass. However, I haven't been able to find any source that says whether a Weyl fermion is its own ...
2
votes
2answers
499 views

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 ...
2
votes
1answer
45 views

What experimental measurement could be used to show that a neutrino is a Majorana and not a Dirac particle?

I've just been reading something on the concept that neutrinos could be Majorana particles and not Dirac fermions. I was wondering what experimental measurement could show/prove that neutrinos are in ...