How can I distinguish degeneracy from band structure?

In summary, degeneracy refers to the situation where two or more quantum states have the same energy level, while band structure describes the range of energy levels that electrons can occupy in a solid. To distinguish between the two, one can analyze the energy dispersion relations in a material. If multiple states at a given energy level correspond to different quantum numbers or momenta, this indicates degeneracy. Conversely, band structure reveals the allowed and forbidden energy levels, showing how these states are grouped into bands due to the periodic potential in crystals. Understanding the interaction between these concepts is crucial for interpreting electronic properties in materials.
  • #1
Mohammad-gl
29
4
TL;DR Summary
I have a band structure plot and want to know if it is degenerated or non-degenerated. How can I realize that?
This is the band structure.
Untitled.png
 
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  • #2
Where the bands cross or touch at the gamma point, they are degenerate.
 
  • #3
Dr Transport said:
Where the bands cross or touch at the gamma point, they are degenerate.
In fact my question is that the degeneracy is related to cross the valence and the conduction band or that can be happen even in touching the valences or conduction bands too?
 
  • #4
Mohammad-gl said:
In fact my question is that the degeneracy is related to cross the valence and the conduction band or that can be happen even in touching the valences or conduction bands too?
I don't understand your response. The conduction bands are degenerate at the gamma point because they coalesce. The valence bands cross at the gamma point, because they cross. the conduction and valance bands are not degenerate in this case because they are completely separated by the band gap, plain and simple.
 
  • #5
Dr Transport said:
I don't understand your response. The conduction bands are degenerate at the gamma point because they coalesce. The valence bands cross at the gamma point, because they cross. the conduction and valance bands are not degenerate in this case because they are completely separated by the band gap, plain and simple.
I mean that generally can we call a band structure degenerate even if there be a cross in the valence bands? and is not crucial that valence and conduction bands cross each other?
 

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