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Majorana mode has attracted great theoretical and experimental interest. The experimental evidence is obtained in quantum wires. The origin theoretical proposals of quantum wires are the papers: 1、R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Phys. Rev. Lett.105, 077001 (2010). 2、Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010)

I have a few questions about this topological superconductor system:

1、In topological nontrivial phase, the Majorana fermion is at the ends, what is the bulk states? Is it a p-wave states or s-wave states? What magnitude is the gap?

2、In topological trivial phase, what is the bulk states? Is it a insulator or superconductor? If in superconducting phase, the electron pairing is s-wave or p-wave pairing? What magnitude is the gap?

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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 it is p-wave. The excitation gap is derived in these papers.

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  • $\begingroup$ Thank you very much. I just study the Majorana fermion and have little knowledge about is. In trivial phase, the effective low-energy theory is s-wave superconductor? $\endgroup$ – ZuoYou Jun 19 '15 at 0:16
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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: 1006.4395).

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