>>10891680topological states of matter are not new. it goes back decades to the work of Laughlin and others in the 80s.
basically the naive concept is that you can classify a state of matter by how the electrons in it are ordered. in a insulating solid they are all stuck on the lattice points centered on the atoms/molecules, in a conducting solid the electrons spread between molecules and can flow nicely from place to place but knock a bit against the other electrons, in a superconducting solid they pair up into one very coordinated state that knocks into nothing, etc. topological superconductors get a new sort of order along the boundaries/edges of the solid that don’t appear in ordinary solids. like for example a quantum hall state has a eing of electrons that all order with one another around the edge of a strip. if it weren’t a strip, but instead a tube, then that ordered layer of electrons wouldn’t form so the topology is the strip matters, hence why they’re called topological states of matter.
a topological superconductor probably also has that strip of electrons around the edge pair up so they can get into an even more ordered state and flow without hitting anything
