Optical transitions and momentum conservation in a one-dimensional crystal

Optical processes in semiconductors require conservation of momentum. An indirect gap semiconductor cannot emit light because the conduction band minimum does not have the same momentum as the valence band maximum. However, this conservation law can be relaxed through zone-folding. Increasing the size of the unit cell in a one-dimensional crystal leads to a reduction of the Brillouin zone. The energy bands are consequently folded to fit into the new zone. Momentum is now conserved but the optical matrix still forbids the transition. As every other atom is substituted with a different atom, translational symmetry is broken allowing optical transitions.