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superlattice brillouin zone and Symmetry points


I was trying to find the brillouin zone of a GaAs superlattice and their points of symmetry to use it in determing the bandstructure. I am using the [111] as the z direction and the structure is periodic in the x and y direction but none periodic in the z direction. I am still looking for my way in this field and i couldnt find a good textbook that explain this, especially how to find the symmetry points of a crystal whether it is in bulk stucture or superlattice. So i really would appreciate any help or guidance in this problem.

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