  Quantum emitters in two-dimensional hexagonal boron nitride (h-BN) have
generated significant interest due to observations of ultra-bright emission
made at room temperature. The expectation that solid-state emitters exhibit
broad zero-phonon lines at elevated temperatures has been put in question by
recent observations of Fourier transform (FT) limited photons emitted from h-BN
flakes at room temperature. The mechanism responsible for the narrow lines has
been suggested to be a mechanical decoupling from in-plane phonons due to an
out-of-plane distortion of the emitter's orbitals. All decoupled emitters
produce photons that are directed in-plane, suggesting that the dipoles are
oriented perpendicular to the h-BN plane. Motivated by the promise of an
efficient and scalable source of indistinguishable photons that can operate at
room temperature, we have developed an approach using density functional theory
(DFT) to determine the electron-phonon coupling for defects that have in- and
out-of-plane transition dipole moments. Our DFT calculations reveal that the
$\text{C}_2 \text{C}_\text{N}$ defect has an in-plane transition dipole moment,
and that of the $\text{V}_\text{N} \text{N}_\text{B}$ defect is perpendicular
to the plane. We exploit the two-dimensional framework recently implemented in
\texttt{QUANTUM ESPRESSO} to determine both the phonon density of states and
the electron-phonon matrix elements associated with the h-BN defective
structures. We find no indication that an out-of-plane transition dipole is
sufficient to obtain FT-limited photons at room temperature. Our work also
provides direction to future DFT software developments and adds to the growing
list of calculations relevant to researchers in the field of solid-state
quantum information processing.
