Abstract
Low temperature photoluminescence spectra of the phonon sidebands of a color center in hexagonal boron nitride are compared to an independent boson model. We infer that the LA-phonon sideband is described by deformation coupling proportional to in-plane strain, resulting in a phonon bath that is effectively two-dimensional. For optical phonons, sharp resonances close to turning points in the phonon dispersion are observed. We infer that the TO-electron coupling is described by deformation coupling proportional to in-plane lattice displacement, resulting in a TO bath that is also effectively two-dimensional. By contrast, for the LO branches we infer that the Fr\"ohlich coupling depends on the interactions between adjacent layers, and propose that the 200-meV peak is a signature of a few-layer sample. This work highlights features of electron-phonon coupling that arise from the layered structure of h-BN.
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