Abstract by: Fulvio Paleari

Phonon-assisted optical transitions in bulk hexagonal boron nitride from first principles

The optical response of layered materials such as hexagonal boron nitride (hBN) is usually dominated by the presence of strongly bound excitons (interacting electron-hole pairs). In particular, bulk hBN has a wide, indirect single-particle band gap in the far-UV range. However, theoretical calculations show a direct exciton with a large binding energy of 700 meV lying below the indirect band gap. Therefore, the optical gap of this material was commonly assumed to be “direct”.

In contrast to this, recent photoluminescence experiments[1,2] have displayed a low-lying fine structure that is convincingly explained in terms of phonon-assisted recombination of indirect electron-hole pairs.

Here[3], we present a finite-difference approach to the computation of the phonon-assisted optical spectrum of bulk hBN. We first demonstrate the existence of a pair of indirect excitons lying 0.1 eV below the direct one. These excitons are dark for the equilibrium geometry of the lattice. However, these states become optically visible when coupled with the phonon modes with momentum q corresponding to the indirect band gap, if these phonons have the right symmetry.

In order to quantify this, the exciton-phonon coupling at q is expressed in terms of a product of the mean square displacement of the atoms and the second derivative of the excitonic optical response function with respect to atomic displacements along the phonon eigenvectors. Furthermore, we use detailed balance arguments to obtain the intensity ratio between emission and absorption processes.

We obtain an ab initio phonon-assisted optical spectrum that compares favourably with experimental results. We find that the fine structure seen in experiments results from the contributions of all transverse and longitudinal optical modes, which couple with various strengths to the indirect excitonic states.

References:

[1] G. Cassabois, P. Valvin and B. Gil, Nat. Photonics 10 (2016)

[2] T. Q. P. Vuong et al., Phys. Rev. B 95, 201202(R) (2017)

[3] F. Paleari, H. Miranda, A. Molina-Sánchez and L. Wirtz, arXiv:1810.08976