- #1
hokhani
- 483
- 8
Is it possible in the first brillouin zoon that two energy bands crossed?
DrDu said:In contrast to what physchem has stated, Pauli principle plays no role as the two bands which become degenerate still have different quantum numbers, so that energetic degeneracy is not forbidden.
PhysTech said:In a crystal you label the Bloch states using ##\textbf{k}##. Therefore ##\textbf{k}## is a quantum number (or numbers if you count the three components) (pg. 141 of Ashcroft and Mermin). So yes, at the intersection point the quantum numbers are in fact the same.
Also, can you please provide specific examples DrNo? I want to know which crystals permit band crossing.
DrDu said:The point I wanted to make is that k is not the only quantum number but the label of the bands is also a quantum number.
The crossing of bands which has created most furor in the last years are maybe the "diabolic points" in graphene.
Almost any material like e.g. Si will show plenty of intersections:
https://wiki.fysik.dtu.dk/gpaw/exercises/band_structure/bands.html
The concept refers to the phenomenon where two energy bands in the first Brillouin zone of a crystalline material intersect or overlap, resulting in a complex and unique electronic structure.
The interception of energy bands plays a crucial role in determining the electronic, magnetic, and optical properties of materials. It can also affect the material's conductivity, thermal properties, and response to external stimuli.
The interception of energy bands depends on the material's crystal structure, lattice parameters, and electronic interactions between atoms. It can also be influenced by external factors such as temperature, pressure, and strain.
Yes, the interception of energy bands can be controlled by altering the material's composition, doping, or applying external stimuli such as electric or magnetic fields. This allows for the tuning of material properties and the creation of new functionalities.
The interception of energy bands can result in a narrowing or widening of the band gap, depending on the specific electronic structure. This can have significant implications for a material's optical and electronic properties, making it a critical factor in material design and engineering.