Phonon-assisted luminescence by finite atomic displacements
In recent years, several articles have been published with Yambo, who calculated the phonon-assisted luminescence by means of finite atomic displacements[1][2][3][4].
In this tutorial we will show how to use YamboPy in combination with Yambo to perform these kind of calculations. For a general review of finite displacements calculations of vibrational properties we recommend this article[5].
Notice that calculation of phonon-assisted luminescence by finite atomic displacements are quite involved and expensive from a computational point of view, for this reason they are limited to relatively simple systems.
Locate the lowest indirect exciton (or indirect band gap)
In this tutorial as example we will consider the hexagonal-BN, that is an indirect insulator. The first step to calculate the phonon-assisted luminescence is to locate the lowest indirect exciton. The cleanest strategy to identify the lowest excitation would be to calculate the excitons along the whole Irreducible Brillouin zone(IBZ), then interpolate them as explained in Interpolate exciton dispersion and find the q point that correspond to the minimum.
A simpler approach is to use the GW (or Kohn-Sham) band structure to find the momentum responsible for the indirect band gap, in the major part of cases this correspond to the lowest exciton.
In the h-BN case we have:
The indirect gap is between a point close to K and the M point, see panel (a) of the figure above. We will approximate the momentum responsible for the indirect emission with q=K-M. Notice that then we should build supercells that contain this moment, so it is good to approximate it with fractions of integers that are not too large so as not to have giant supercells. In this case we get q=(1/3,-1/6, 0).
Notice that if you have a direct band gap material, the momentum q corresponding to the lowest transition is q=0 and you do not need to construct special supercells to sample the corresponding vibration, it will be sufficient to displace atoms in the primitive cell.
Calculate phonons at momentum q of the indirect transition
Now we need to calculate all atomic vibrations compatible with the momentum of the lowest indirect transition. In order to do so we first calculate the phonons with QE, here the inputs hBN_phonons.tgz, see panel (b) of Figure 1.
References
- ↑ Theory of phonon-assisted luminescence in solids: Application to hexagonal boron nitride, E. Cannuccia, B. Monserrat and C. Attaccalite, Phys. Rev. B 99, 081109(R) (2019)
- ↑ Exciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride, F. Paleari et al. PRL 122, 187401(2019)
- ↑ Excitons under strain: light absorption and emission in strained hexagonal boron nitride,P. Lechifflart, F. Paleari and C. Attaccalite (2022).
- ↑ Phonon-Assisted Luminescence in Defect Centers from Many-Body Perturbation Theory, F. Libbi, P. M. M. C. de Melo, Z. Zanolli, M. J. Verstraete, and N. Marzari, Phys. Rev. Lett. 128, 167401 (2022)
- ↑ Electron-phonon coupling from finite differences, Bartomeu Monserrat, J. Phys.: Condens. Matter 30 083001(2018)