I am trying to read up some review articles about Majorana physics in topological material, but I am not really familiar with the condensed matter terminology (with condensed matter in general I should say) since I come from a high-energy background, so I come across quite a lot of vocabulary and visualization issues.
From the little that I know from semi-conductor physics, a gap is an energy difference between two bands such that a particle cannot go from one band to the other without being given at least that amount of energy. With that picture of band structure in mind, I don't really know what a gap potential is, nor how it can have vortices in it. For instance, in a $p_x + i p_y$ superconductor in 2D, it is said that Majorana fermions appear in vortices in the superconducting pairing potential, or when the gap is closed by variations in the chemical potential. I am wondering if there is an intuitive picture of what a "pairing potential vortex" is, without getting into solving the BdG equations for the superconductor, and on how Majorana fermions actually appear in them?
Moreover, another question that pops into mind is related to the use of chemical potential in the Hamiltonians describing superconductors. Statistical mechanics tells us that the chemical potential is the energy necessary to add one particle to a system from a reservoir, and also conveniently describes the energy costs related to diffusion processes in solutions. How does one interpret the chemical potential in a superconductor then? I have read somewhere that a non-homogeneous chemical potential $\mu(x)$ is a sign of an electric field $E(x) \sim \mu'(x)$, so it seems there would be a relation between $\mu$ and the electrostatic potential, but I don't find anything information that explains the relations between all these quantities in superconductors.