Isotopic Heft on the B_{1 l} Silent Mode in Ultra-Narrow Gallium Nitride Nanowires

Wurtzite semiconductor compounds have two silent modes, B_{1 l} and B_{1 h}. A silent mode is a vibrational mode that carries neither a dipole moment nor Raman polarizability. Thus, they are forbidden in both infrared reflectivity and Raman spectroscopy. Astonishingly, we detected the B_{1 l} mode in high-quality, ultra-narrow GaN nanowires using resonant Raman scattering, although the B_{1 h} was not observed, and there is no immediate explanation for this asymmetric finding. The Raman experiments were performed using several laser lines from 647 to 325 nm; the latter is a wavelength in which Raman becomes resonant. Actually, we observed the B_{1 l} mode only in resonance, indicating that the appearance of this mode is related to Fröhlich electron-phonon interactions; i.e., a dipole moment emerging in the B_{1 l} silent mode may not be present in the B_{1 h} mode. To shed light onto the physical origin of these observations, we performed density functional theory calculations of the lattice dynamics in GaN. We performed a careful analysis of the different physical mechanisms that allow the forbidden mode to appear to explain the physics underlying the nonzero dipole moment in the B_{1 l} mode, and the reason why this dipole moment is not present in the B_{1 h} mode.