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A few less technical details than the ones you can find in Meng Cheng answer on this page are perhaps welcome. For practical applications, we are not interested in Majorana modes, since they are a simple mathematical rewriting of the fermionic creation and annihilation operators. Say differently, to any creation $c^{\dagger}$ and annihilation $c$ operators ...

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You should forget about the name "Majorana fermions", although people have been using it (unfortunately) a lot in the literature on topological superconductivity. A much better terminology is "Majorana zero modes". "Majorana fermions" is more appropriate when you have propagating modes like chiral edge modes of a 2D topological superconductor, but not for ...

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First of all, a majorana fermion does not "possess non-abelian statistics", it is predicted to obey non-abelian braiding statistics which may serve as a building block for fault-tolerant quantum computation. There have been studies that indicate the presence of a Majorana end states for example in semiconductor quantum wires coupled to a conventional ...

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The relation you ask about is just a reshuffling of the components. Writing out the indices we have $$\Theta_1^T C \, \Gamma_{\mu} \Theta_2 = (\Theta_1^T)_a C_{ab} \, (\Gamma_{\mu})_{bc} (\Theta_2)_c = - (\Theta_2)_c (\Gamma_{\mu})_{bc} C_{ab} (\Theta_1^T)_a = - (\Theta_2^T)_c (\Gamma_{\mu}^T)_{cb} (C^T)_{ba} (\Theta_1)_a$$ where the minus sign in the ...

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