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Questions tagged [majorana-fermions]

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 be its own anti-particle.

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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 ...
Mike's user avatar
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Is there an elegant proof of the existence of Majorana spinors?

Almost all standard sources on the existence of Majorana spinors (e.g. Appendix B.1 to Polchinski's "String Theory", Vol. 2) do so in a way I consider inherently ugly: A priori, we are dealing with ...
ACuriousMind's user avatar
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32 votes
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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?
Timothy's user avatar
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Why do or don't neutrinos have antiparticles?

This was inspired by this question. According to Wikipedia, a Majorana neutrino must be its own antiparticle, while a Dirac neutrino cannot be its own antiparticle. Why is this true?
Peter Shor 's user avatar
26 votes
2 answers
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Dirac, Weyl and Majorana Spinors

To get to the point - what's the defining differences between them? Alas, my current understanding of a spinor is limited. All I know is that they are used to describe fermions (?), but I'm not sure ...
Phibert's user avatar
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22 votes
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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=...
Piotr Migdal's user avatar
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22 votes
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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 ...
Tom Rylands's user avatar
20 votes
3 answers
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Why do people say that neutrinos are either Dirac or Majorana fermions?

The question of whether a given particle "is" a Dirac or Majorana fermion is more subtle than is sometimes presented. For example, if we just consider the "old" Standard Model with massless neutrinos, ...
tparker's user avatar
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Is the Ising CFT different from the Majorana CFT?

If by 'Ising CFT' I mean the conformal field theory describing the critical quantum Ising chain $ H = \sum_n \left( \sigma^z_n - \sigma^x_n \sigma^x_{n+1} \right)$ and by 'Majorana CFT' I mean the ...
Ruben Verresen's user avatar
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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 ...
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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 ...
sintetico's user avatar
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14 votes
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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 ...
SRS's user avatar
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13 votes
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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 ...
FraSchelle's user avatar
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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 ...
Leandro Seixas's user avatar
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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? ...
Andrew McAddams's user avatar
9 votes
1 answer
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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). -> http://www.physics.upenn.edu/~kane/pubs/p56....
Mike's user avatar
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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}...
Adonai Cruz's user avatar
9 votes
1 answer
580 views

Eigenvalues of Majorana fermions

I have a somewhat naive question about Majorana fermions. Typically, two Majorana fermion modes $\gamma_{i,1}$ and $\gamma_{i,2}$ are defined by writing a single ordinary fermion $c_i$ in terms of &...
Zack's user avatar
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9 votes
1 answer
967 views

Ising anyon topological order and its edge $c=1/2$ CFT

We know that conformal field theories are closely related to two-dimensional topological orders via edge-boundary correspondence. An Ising topological order can be obtained by gauging the fermion ...
pathintegral's user avatar
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9 votes
1 answer
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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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9 votes
1 answer
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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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9 votes
3 answers
712 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 ...
laboussoleestmonpays's user avatar
8 votes
3 answers
820 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) \...
JeffDror's user avatar
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8 votes
2 answers
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Why is the notion of neutrinos as possiblly Majorana fermions still promoted given the observation of neutrino oscillations?

A Majorana particle is a fermion whose antiparticle is itself. In other words, a Majorana fermion has only two components, rather than 4 components for a Dirac fermion. Neutrinos are alleged as ...
MadMax's user avatar
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8 votes
2 answers
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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 $\tau\ge10^{25}$...
Riccardo.Alestra's user avatar
8 votes
1 answer
3k 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 ...
Michiel's user avatar
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8 votes
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Difference between $c=1$ Dirac CFT and two copies of $c=\frac{1}{2}$ Majorana CFT?

The $c = \frac{1}{2}$ (non-chiral) Majorana CFT has six primary fields: the vacuum 1, the two Majorana fields $\eta, \bar \eta$ $\left( \Delta_\eta = \Delta_{\bar \eta} = \frac{1}{2}\right)$, the ...
Ruben Verresen's user avatar
8 votes
1 answer
678 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 ...
Carlo Beenakker's user avatar
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1 answer
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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 ...
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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.
Sabya's user avatar
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1 answer
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How are Majorana zero-modes protected against fermionic operators?

I am learning about Majorana fermions in topological quantum computation, and more particularly about the Kitaev chain, described by $$ H = -\mu \sum_{i=1}^N c_i^\dagger c_i - \sum_{i=1}^{N-1} \left(t ...
Ronan's user avatar
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6 votes
2 answers
7k 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 ...
Thomas Elliot's user avatar
6 votes
1 answer
3k views

Transpose of fermion bilinears

TL;DR When we take the transpose of two Grassmann-valued spinors (fermions), should we add a minus sign because we end up anticommutating the two spinors? More details. I'm studying the behavior of ...
Jasmeru's user avatar
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6 votes
1 answer
745 views

Ground state of AKLT chain invariant under time-reversal?

The AKLT chain is an example of an SPT phase protected by time-reversal symmetry. The Hamiltonian of the system has time-reversal symmetry. The ground state wave function can be pictured as follows (...
John's user avatar
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6 votes
2 answers
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Can a Majorana field $\psi$ be charged under some $U(1)$ with a charge other than zero?

I know Majorana particles have to be electrically neutral because electric charged is conserved. My question, however, is whether at all a Majorana field $\psi$ be charged under any $U(1)$ (other ...
SRS's user avatar
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6 votes
1 answer
877 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 ...
alxandernashzhang's user avatar
6 votes
1 answer
510 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 ...
ZuoYou's user avatar
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6 votes
1 answer
210 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 ...
JeffDror's user avatar
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6 votes
1 answer
778 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 ...
SRS's user avatar
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6 votes
1 answer
673 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-...
user avatar
6 votes
1 answer
292 views

Zero modes $a_j\sim e^{-\kappa j}$ in a semi-infinite quantum Ising chain?

As a way of analyzing the performance of quantum annealing, I've been studying quantum diffusion in fermionizable lattice models with zero modes. In particular, the 1+1D quantum Ising model, semi-...
David Roberts's user avatar
5 votes
3 answers
3k views

Majorana Mass For Neutrinos In Standard Model

Neutrinos cannot have Dirac masses because there are no $SU(2)_L$ singlet right-handed neutrinos in the Standard Model (SM). But can neutrinos be given Majorana masses in the SM? I heard that Majorana ...
SRS's user avatar
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5 votes
2 answers
570 views

Are the two definitions of a Majorana fermion equivalent?

There seems to be two definitions of a Majorana fermion and I can't work out how to show they are equivalent. The first definition, which is on Wikipedia, is that a Majorana fermion is described by ...
Hermitian_hermit's user avatar
5 votes
2 answers
2k 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 ...
Noob Rev B's user avatar
5 votes
1 answer
2k 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 ...
S9G's user avatar
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5 votes
1 answer
591 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 ...
user avatar
5 votes
1 answer
1k 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, ...
Pengpeng Xu's user avatar
5 votes
1 answer
1k views

Neutrino mass with Dirac and Majorana

Why both Dirac mass and Majorana mass terms are needed to explain the mass of a neutrino?
Curious's user avatar
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5 votes
1 answer
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Plugging Majorana Spinor into Dirac Lagrangian does not give Majorana Lagrangian?

This seems like it should be simple but somehow I do not see how. The Majorana Lagrangian can be written in terms of a left handed Weyl spinor $\psi_L$ as $$ \mathcal{L}_M= i \psi_L^\dagger \bar{\...
user1379857's user avatar
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5 votes
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Why two different spinors are Grassmann quantities?

In Rydberg Quantum Field Theory page 441 (this edition, unfortunately page 441 is not in the link) it says If $\xi$ and $\eta$ are Majorana spinors [...] and since $\xi$ and $\eta$ are Grassmann ...
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