= Solution
{c}
For ordinary one-phonon <infrared> <optical absorption>, both an energy and a momentum selection rule must hold. The optical <photon> has negligible <crystal momentum> on the scale of the <Brillouin zone>, so <crystal momentum conservation> selects $\mathbf q\simeq0$ modulo a genuine <reciprocal lattice vector>. In addition, the mode must change the macroscopic <electric polarization>, with a component along the incident <polarization of an electromagnetic wave>.
In terms of atomic displacements $\mathbf u_j$ and <Born effective charge> tensors $Z_j^*$, the relevant derivative is proportional to $\sum_jZ_j^*\mathbf u_j$ per <primitive unit cell>. Thus an <optical phonon> at $\mathbf q=0$ is not automatically infrared active: its dipole contributions may cancel. Disorder-assisted and multiphonon processes relax these simple first-order selection rules.
Back to article page
