I am currently studying solid state physics and we just saw the construction of the Brillouin zones. My question is the following:
Does the sequence of the $n$th Brillouin zones converges to any particular geometrical form? From some figures I have seen, it seems to tend to a circle ( for different lattices ) but if this is true, I don't have any idea why and whether it is convergent whatever the form of the lattice at the beginning.
Does somebody have an idea?