Does each band have multiple allowed E-values for th same k?

[philip1201]

So every theoretical resource I've been able to find seems to map bands to lines for a 1D crystal, surfaces for a 2D crystal, and hypersurfaces for a 3D crystal. But then there are images like the ARPES data below (fig. 1a, 1b, 2) where the density of states is a lot higher within the valence band energy range even if there isn't a band-line nearby. ARPES should restrict k to one axis, so I don't think it can be explained by variance from k in the other directions.

Many explanatory images also show the bands as if the valence band has states below the band-line and the conduction band has states above the band-line, like fig. 3.

fig. 1

fig. 2

fig. 3

 

[BigJDubs]

The explanation for this phenomenon is that the band structure of a crystal is actually composed of many subbands that are split due to the presence of symmetry in the crystal lattice. The splitting of the bands is known as band splitting, and it occurs when two or more energy levels overlap, resulting in multiple subbands with different energies. This is illustrated in figure 4 below.The higher density states observed in the valence band range can be explained by the fact that the electrons occupy multiple subbands in the valence band, leading to an increase in the number of available states. Similarly, the same effect can be observed in the conduction band, where the electrons occupy multiple subbands, resulting in an increased density of states in the conduction band range. fig. 4