Periodic Zone Scheme - Bloch Theorem in Lattices

I am quite confused about the different representations of the dispersion relation in a lattice.

This image makes a lot of sense to me, since it only represents one dispersion curve and transforms it back to the 1st-Brillouin-Zone due to the periodicity of the lattice in the Bloch theorem.

But sometimes, the dispersion relation is also showed in the so called "periodic zone scheme" as follows:

In this one, there are a lot of dispersion curves, what would make me think there are infitenely many wave-functions with the same energy, but different reciprocal wave vectors $$k=k+n \cdot \frac{\pi}{a}$$, what would lead to an infinity number of possible states in each band. What am I getting wrong?

• Well, the next atom over sees that things look just the same as the first atom... Commented Feb 5 at 13:27
• Yes, but that is not in position space. It is in the fourier space. Commented Feb 5 at 16:46
• Indeed - the picture mixes up the bases, which makes it pretty useless. Commented Feb 5 at 17:02
• The states outside of the first Brillouin zone are the same states as those in the first Brillouin zone. That is, the state labeled by $k$ and $n$ (a band index) in the periodic zone scheme is the same as the one that has a value $k+G$, where $G$ is the reciprocal lattice vector that takes $k$ back into the first Brillouin zone. So there aren't more states. Instead, this picture can be useful for processes like Umklapp scattering, in which the scattering process results in a wave vector outside the first Brillouin zone. Commented Feb 5 at 17:22