# 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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### Expanding a density matrix in terms of operators

In Lukasz's paper: https://arxiv.org/pdf/0909.2654.pdf He writes "consider a density matrix ρ, written as a polynomial of the 2N Majoranas cj in such a way that each cj occurs to the power 0 or 1 in ...
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### Topological superconductors

I have been reading a lot about quantum computation by using topological materials and I could see that the standard approach is to engineer a p-wave superconductor by using a 1-D semiconductor wire ...
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### How to plot Majorana energies for Kitaev chain as function of mu?

My first attempt was, using the Python library Kwant, getting the lowest eigenvalues for the 1D p-wave superconductor as a function of the chemical potential mu (In the image below I show what I got). ...
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### Connection between $2n$ real fermions and $SO(2n)$

In section 11.4 of "Basic Concepts of String Theory" by Blumenhagen et al, they say: Consider a system of $2n$ two-dimensional real fermion (...) transforming as a vector of $SO(2n)$. I guess they ...
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### What are the fermions in the SYK model doing?

The Hamiltonian of the SYK model is \begin{equation} H = \mathcal{N}\sum_{ijkl}^N J^{ijkl} \chi_i \chi_j \chi _k \chi _l \end{equation} where $\mathcal{N}$ is some normalization to make the energy ...
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### What mechanism will generate Dirac neutrinos?

Giving mass to neutrinos is not a problem. The problem is to explain its smallness. Once right-handed neutrinos $\nu_R$'s are included in the Standard Model (SM), the Majorana mass for $\nu_R$ must ...
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### Spin 1/2 Fermion With Both Majorana and Dirac Masses?

I will use Van der Waerden notation in the following: It is easy to construct both Majorana and Dirac mass terms in the lagrangian of a Dirac spinor with left-handed component $\phi_{\alpha}$ and ...
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### Kitaev's reason for looking at p-wave superconductors

I would really like to understand the thought process that lead Kitaev to proposing the Kitaev chain but most expositions really just start from the Hamiltonian and derive the Majoranas without any ...
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### The logic behind a specific step of SUSY variation

I'm following Neil Lambert's Supersymmetry notes, and there's a step in equation 5.67 which has me stumped. He says he uses the fact that "$C\gamma_\mu$ is symmetric". I don't see how that helps, and ...
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### What's the difference between cylindrical geometry and disk with a hole for topological chiral $p_x\!+\!i p_y$ superconductor?

We know that for a topological chiral p-wave superconductor with a cylindrical geometry, i.e. one conserved momentum $k$ and one open boundary direction, there exists edge modes with opposite ...
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### Fermionizing the Gell-Mann Algebra

In condensed matter physics one often solves a spin Hamiltonian by transcribing the Pauli matrices into fermionic operators. For instance, in the Kitaev model you can introduce four Majorana modes for ...
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### How many dimensions has a Majorana Fermion state space?

For an exercise question, I'm wondering on how I can determine the dimensionality of a state space spanned by Majorana fermions. A (Dirac) fermionic excitation ($f , f^\dagger$) has a state space of ...
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### Majorana Fermion Coherent States

I was wondering if there are coherent states for Majorana operators, so, states that fulfill the relation \begin{align} \hat{\gamma}_A |a,b\rangle &= a |a,b\rangle \\ \hat{\gamma}_B |a,b\...
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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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### Real Majorana wavefunction / field: What is the big deal?

It is known that there is a set of gamma matrices that can be purely imaginary (called Majorana basis), thus one can solve the 1st quantized Majorana wave function in terms of real wave function. ...
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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 ...
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### Can neutrino oscillates into antineutrino?

Unlike antineutron, an antineutrino aren't made up of antiquarks so how do we tell an antineutrino from ordinary neutrino? Can majorana particle oscillates between matter particle and antiparticle?
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### How to get the Green's function of free modes in the Sachdev-Ye-Kitaev (SYK) model?

In studying this paper "Remarks on the Sachdev-Ye-Kitaev (SYK) model" (http://arXiv.org/abs/1604.07818), I have no idea how to get the free Majorana fermion Green's function (Eq. (2.5) in the above ...
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### What is a Higgs Portal Scale?

I am reading about the prospective decay of Higgs into Majorana fermions (possibly sterile neutrinos). In the image the branching ratio of Higgs to a pair of Majorana fermions is given for different ...
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### What is the order of magnitude of the energy released in Majorana fermions collision/annihilation?

Majorana fermion experiment It has been observed a quantum state in a one atom thick wire which in a certain energy range behaves like a Majorana fermion. It is a quasiparticle that arises out of the ...
The Kitaev $p$-wave spinless superconductor model has Hamiltonian as $$H = \sum_{j=1}^{N-1} tc_j^\dagger c_{j+1} + \Delta c_jc_{j+1} + h.c. + \sum_{j=1}^N \mu c_j^\dagger c_j$$ which has topological ...