About Majorana fermion in spin-orbit coupled quantum wires

Question

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?

Answer 1

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.

Answer 2

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).