Does it make any sense to calculate edge states for topological semimetals while they don't have any global gap?
Topological semimetals do have interesting edge states. Here I give two examples:
- Weyl semimetals. The edge states are called "Fermi arcs", which are constant-energy states that connect the projections of the Weyl points onto the surface. The Wikipedia article has a very nice depiction of Fermi arcs.
- Nodal line semimetals. The edge states are called "drumhead states", and again are relatively flat states that are contained within the projection of the bulk nodal line onto the surface.
Standard packages to calculate topological properties typically have the appropriate functionality to calculate these surface states of semimetals. For example, here is the descprition from WannierTools, which uses a Green's function approach.