2D p+ip superconductors have zero energy mid-gap modes localized at the boundaries as well as in the vortex cores as pointed out in several places such as Read, Green and Ivanov. The modes result in non-Abelian statistics and a non-trivial counting for the vortex excitations.
All these calculations, as far as I can understand, use a BdG equation to arrive at the above mentioned results. Is it clear that the mid-gap states and vortex structure predicted by BdG equation will be self-consistent ?
ie For a 4-fermion interaction Hamiltonian that results in a p-wave order parameter, will a self consistent calculation for the structure of a vortex give us the same properties that BdG equation gives ?