Past exam of the condensed matter physics major option course of the University of Oxford / 2019 / 1 / d / iii

$P_1$ has primitive coordinates $(1/2,1/2)$ and therefore fails the first-order optical momentum condition; its local $V_1$ pattern also has zero dipole derivative. $P_2$ is a zone-centre mode with the dipole-active $V_2$ pattern, so its molecular dipole changes add coherently.The allowed absorption for $P_2$ uses an polarization of an electromagnetic wave with an out-of-plane component. At normal incidence on an ideal free-standing layer the electric field is in the plane, so that specific measurement geometry would suppress it despite the mode's intrinsic vibrational infrared activity.