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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: ...


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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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There is an important distinction here which I feel the other answers have not addressed. One can check that the unitary $U$ as given in the question is indeed symmetric in the sense that $[U,W(g)] = 0$, where $W(g)$ is the representation of the symmetry. It is also a local unitary, in the sense that one can find a local (possibly time-dependent) Hamiltonian ...



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