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There may be some language confusion here. The "Majorana representation" refered to in the question has nothing to do with Majorana fermions. Rather it is about the so-called "Majorana stellar representation" of spin J pure quantum states (which can be thought of as the generalization for J>1/2 of the Bloch representation of spin 1/2 pure states). See e.g. ...

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In short, what makes a superconductor topological is the nontrivial band structure of the Bogoliubov quasiparticles. Generally one can classify non-interacting gapped fermion systems based on single-particle band structure (as well as symmetry), and the result is the so-called ten-fold way/periodic table. The topological superconductivity mentioned in the ...

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A prototypical example of an intrinsic topological superconductor is the so-called $p$-wave superconductor [more details there: What is a $p_x + i p_y$ superconductor? Relation to topological superconductors, also, Meng-Cheng wrote the spinless $p$-wave model in 2D somewhere else on this page, and comment it carefully]. You can also induce topological ...

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You say about Majorana fermions: "From this I would argue that they need to have all quantum numbers equal to zero." which is not true. Charge conjugation is defined on Dirac spinors as $\psi^c := \mathrm{i}\gamma^0\gamma^2\bar\psi^T$. Being Majorana means $\psi^c = \psi$. While this would imply the spinor has zero electric charge (and zero all other ...

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There is no well established theory predicting the neutrino mass (even if of Majorana type). A particle is its own anti-particle if the field describing the particle is a real field. That means obviously that the electric charge is 0 but not necessarily that other charges are zero. For instance, if the neutrinos are Majorana neutrinos, they would still have ...

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