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2

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 ...

1

I think a good introduction are these two talks: Roman Jackiw: "Fractional charge, Majorana fermions: the Physics of isolated zero modes" - 1 and Fabian Hassler Lecture 1: Topological quantum computing A short summary is that for 1D systems Majorana bound states can exist at domain walls. Let say you have a long wire and you can divide it in two ...

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In both phases you have s-wave pairing in the bulk for the case of a nanowire with proximity induced superconducting correlations through an s-wave superconductor. What happens in the non-trivial phase is that the effective low-energy model is equal to a spin-polarized p-wave superconductor(see this Master thesis: Masterthesis and this paper arXiv: ...

2

In either cases the bulk is superconducting. I don't understand why you ask whether it is p-wave or Cooper pair. In this context, "p-wave" always means p-wave pairing, so always a superconductor to begin with. In the topological phase, if the Zeeman field is large the effective low-energy theory is the same as a spinless p-wave superconductor, so in a sense ...

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Comments to the question (v9): If we ignore the overall normalization, then OP correctly applies the Dirac-Bergmann$^1$ method, which leads to second-class constraints.$^2$ Normally the Majorana Lagrangian (1) is defined with a factor $\frac{1}{2}$ in front. Then there will be no factor $\frac{1}{2}$ in the anti-commutator relation (9), see e.g. Ref. 2. ...

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If you are interested what happens in the energy spectrum, then this two papers could be very helpful for you: arXiv:1206.1736 and arXiv:1205.7054. The spin-orbit coupling splits the two spin bands (see in arXiv:1206.1736 Fig. 5a) and the Zeeman term mix them (see in arXiv:1206.1736 Fig. 5b). This looks then in the end like a p-wave pairing in the ...

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