Reduced Zone Scheme of Free Electron Gas

[exciton]

Hi,

I was just wondering if there is any reason why the reduced zone scheme of the
free electron gas is looking like here (and in all other textbooks):

http://www.pha.jhu.edu/~jeffwass/2ndYrSem/slide19.html

I mean I could add any reciprocal lattice vector which moves
the particular energy branch in the 1. brillouin-zone.


thanks in advance

 

[kanato]

The reduced zone scheme is where all the bands have been translated into the first Brillouin zone. I don't really understand the question you are asking? You can't add a reciprocal lattice vector to a band to move it around in the zone, because the zone is the size of the reciprocal lattice vectors. Have a look at the extended zone scheme; the branches are periodic. if you add a reciprocal lattice vector to one of the bands, you translate it by exactly its period.

 

[exciton]

Edit: Yeah, you're right. There is only one possibility to move a branch in the 1. brillouin-zone.
Thanks.