Chiral edge state as topological properity of bulk state

Question

As far as I know, quantum hall effect and quantum spin hall effect has chiral edge state. Chiral edge state is usually closely related with delocalization, since back scattering is forbidden. However, some topological nontrivial state does not have chiral state, such as majorana bound state in topological superconductor.

I am quite interested whether the existance of chiral edge state is determined by bulk topological properity?

Thanks in advance

Answer 1

The Majorana bound state inside a vortex of a topological superconductor is, indeed, not a chiral edge state. It does not follow that the topological superconductor does not have a chiral edge state. It does! Solve, for example, the BdG equations for a p+ip superconductor with open boundary conditions, and you'll see it.

The existence of edge modes is typically argued to be tied to the fact that if you have a state with a nontrivial topological invariant, you need to close the excitation gap to change it. So, if you have an interface between a topological state and vacuum (which is topologically trivial) there are gapless edge modes to accommodate the change in topological invariant that necessarily occurs across the interface.