Solid State Physics: Constructing Brillouin Zones & Fermi Surfaces

[pengseanghor]

Dear every body. I have one problem of my homeworks that I can solve. Please help me!
Thank you.

Construct in k-spaceof the first 4 Brilloun zones of a square lattice in the extended zone scheme & show that the 1st, 2nd, 3rd, 4th Brilloun zones have all the same area.

Construct these pieces in the reduced zone scheme & the rough shape of the Fermi surface for the system with 4 free electrons/atom.

 

[graphene]

this could help

[URL]http://www.sjsu.edu/faculty/watkins/brillouin.htm

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radius of the fermi sphere is related to the number density.
u'll have to take care about the shape near the BZ boundaries