# Symmetry breaking and band gaps?

Can the discontinuity in the E-K dispersion relation of a periodic lattice (at the boundary of a Brillouin zone) be understood as a consequence of breaking continuous translation symmetry into discrete translation symmetry? If yes, then what will be the logical progression of this argument?

• Yes. There are countless consequences. Almost the entire modern field of solid state physics starts with that fact. – garyp Nov 19 '14 at 13:48