Theory of phonon-assisted luminescence in solids: Application to hexagonal boron nitride

We study the luminescence of hexagonal boron nitride $\left(h\text{−}\mathrm{BN}\right)$ by means of nonequilibrium Green's functions plus finite-difference electron-phonon coupling. We derive a formula for light emission in solids in the limit of a weak excitation that includes perturbatively the contribution of electron-phonon coupling at the first order. This formula is applied to study luminescence in bulk $h\text{−}\mathrm{BN}$. This material has attracted interest due to its strong luminescence in the ultraviolet region of the electromagnetic spectrum [K. Watanabe et al., Nat. Mater. 3, 404 (2004)]. The origin of this intense luminescence signal has been widely discussed, but only recently a clear signature of phonon-mediated light emission started emerging from the experiments [G. Cassabois et al., Nat. Photonics 10, 262 (2016)]. By means of our theoretical framework, we provide a clear and full explanation of light emission in $h\text{−}\mathrm{BN}$.

Figure 1

(a) Electronic band structure of $h\text{−}\mathrm{BN}$. The red arrow represents the scattering with a phonon between $M$ and $K$ and the blue one the emission of a photon. (b) Phonon band structure of $h\text{−}\mathrm{BN}$. The red vertical line marks the position of the phonon $\mathbf{q}$ point involved in the luminescence process [see the red arrow in (a)].

Figure 2

Blue continuous line: Luminescence spectra calculated using Eq. (4) for bulk $h\text{−}\mathrm{BN}$. The vertical lines represent the position of the $iX$ doublet that has zero dipole matrix elements. Orange dashed-dotted line: Experimental results taken Ref. [7]. We choose the normalization of both spectra in such a way as to have an optimal visualization in a single figure.