Crucially, for intermediate state energies >3.0 eV the dispersion of the SSs (Surface States) in our data changes again and the SSs disperse faster to larger momentum values with increasing energy above EF (Fermi Energy). To our knowledge, such a strong deviation from the free-electron-like behaviour was not observed yet for SSs on fcc(111) noble metal surfaces. This observation can be explained by assuming that the SSs disperse into the bulk bands for intermediate state energies >3.0 eV to connect the valence and conduction bands.
Source: Topological states on the gold surface
Call it a hunch, but I think that despite its nature the problem can potentially be simplified through topological/bulk approach. Though, I won't deny that it's somewhat 'blegh' regardless of the change in regime. ;)