Overtones of interlayer shear modes in the phonon-assisted emission spectrum of hexagonal boron nitride

We address the intrinsic optical properties of hexagonal boron nitride in deep ultraviolet. We show that the fine structure of the phonon replicas arises from overtones involving up to six low-energy interlayer shear modes. These lattice vibrations are specific to layered compounds since they correspond to the shear rigid motion between adjacent layers, with a characteristic energy of about 6-7 meV. We obtain a quantitative interpretation of the multiplet observed in each phonon replica under the assumption of a cumulative Gaussian broadening as a function of the overtone index, and with a phenomenological line broadening taken identical for all phonon types. We show from our quantitative interpretation of the full emission spectrum above 5.7 eV that the energy of the involved phonon mode is 6.8 +/- 0.5 meV, in excellent agreement with temperature-dependent Raman measurements of the low-energy interlayer shear mode in hexagonal boron nitride. We highlight the unusual properties of this material where the optical response is tailored by the phonon group velocities in the middle of the Brillouin zone.