Exciton-phonon coupling and luminescence
In this advanced tutorial, we will calculate exciton-phonon interactions from first principles by interfacing DFPT (for phonon calculations) and BSE (for exciton calculations).
The DFTP calculations are run with Quantum ESPRESSO, while the many-body GW-BSE calculations are run with Yambo. Finally, the exciton-phonon interaction will be obtained by combining and postprocessing the databases computed in the two previous runs. The great advantage of this workflow is that the calculations can be run in the irreducible Brillouin zones both for the electronic momenta ([math]\displaystyle{ k }[/math]) and the transfer momenta ([math]\displaystyle{ Q }[/math], [math]\displaystyle{ q }[/math]) of excitons and phonons, thus speeding up considerably the jobs while reducing the IO and memory load.
We will first compute the exciton-phonon coupling matrix elements: these are the building blocks needed to construct experimental observables such as phonon-assisted optical spectra (such as luminescence), Raman spectra and exciton lifetimes. We will do this in the case of monolayer MoS2, a 2D system with large spin-orbit interaction.
As an example of application, we will consider the case of phonon-assisted luminescence. We will do this in the case of bulk hBN, a layered indirect insulator with strong electron-phonon coupling.
Note: this tutorial will be updated when new exc-ph tools become available in Yambopy (including full-python postprocessing, Raman spectra, interpolated lifetimes, etc).
Requirements
This is an advanced topic: we assume that you already know something about the theory[1][2][3][4][5][6] and applications[7][8][9][10][11][12][13][14] of exciton-phonon physics.
Also, we assume that you already know how to run both a basic Yambo GW-BSE calculation and a DFPT phonon calculation with Quantum ESPRESSO.
Besides the QE executables pw.x and ph.x, we also use the yambo phonon-specific executable yambo_ph and the python utility Yambopy. The auxiliary code LetzElPhC (executable lelphc) will be used to obtain the electron-phonon matrix elements by reading the same electronic wavefunctions used by Yambo (and stored in the SAVE directory), while also making full use of crystal symmetries. LetzElPhC (link) will be run by Yambopy, but it must nonetheless be installed. Finally, the exciton-phonon properties can be computed either using yambo_ph or using Yambopy itself.
Step 0: Pseudopotentials, equilibrium structure and convergence
In a real calculation, it is important to ensure that both the pseudopotential and the lattice parameters that we are using are compatible and perform well for the electronic excited states and for the lattice vibrations simultaneously. Furthermore, you have to make sure that the wave function cutoff ecutwfc is converged with respect to the DFPT step and not just to the DFT one. This is in addition to the other customary convergence tests for DFT, DFPT, GW and BSE calculations.
This is often the most time-demanding step when starting on a new system.
For the sake of this tutorial, we assume that we have already done all these tests and we are starting the final workflow to get the exciton-phonon properties.
Step 1: scf calculation
First of all, we run a standard scf calculation with pw.x for Yambo. We stick with non-symmorphic symmetries. At the end, we will have the QE save directory.
INPUT
mpirun -np 4 pw.x -inp mos2.scf > scf.out
References
- ↑ Optical processes in solids, Toyozawa, Yutaka, and Chris Oxlade. Cambridge University Press, (2003).
- ↑ P. Cudazzo, First-principles description of the exciton-phonon interaction: A cumulant approach, Phys. Rev. B, 102, 045136 (2020) Open access pdf from Luxembourg University
- ↑ Theory of exciton-phonon coupling, G. Antonius, S. G. Louie, Phys. Rev. B, 105, 085111 (2022)
- ↑ Exciton-phonon interaction calls for a revision of the “exciton” concept, F. Paleari, A. Marini, Phys. Rev. B, 106, 125403 (2022)
- ↑ First-principles approaches to the description of indirect absorption and luminescence spectroscopy: exciton-phonon coupling in hexagonal boron nitride, PhD thesis, Fulvio Paleari (2019)
- ↑ Exciton-phonon coupling and phonon-assisted luminescence in hexagonal Boron Nitride nanostructures, PhD Thesis, Pierre Lechifflart (2023)
- ↑ Distinguishing different stackings in layered materials via luminescence spectroscopy, M. Zanfrognini et al. Phys. Rev. Lett. 131, 206902 (2023)
- ↑ P. Lechifflart, F. Paleari, D. Sangalli, C. Attaccalite, First-principles study of luminescence in hexagonal boron nitride single layer: Exciton-phonon coupling and the role of substrate, Phys. Rev. M, 7 (2), 024006 (2023) arXiv2212.1047
- ↑ Optical absorption and photoluminescence of single layer boron nitride from a first principles cumulant approach, G. Marini, M. Calandra, P. Cudazzo, Nano Lett., 24, 20, 6017 (2024)
- ↑ Exciton Lifetime and Optical Line Width Profile via Exciton–Phonon Interactions: Theory and First-Principles Calculations for Monolayer MoS2, Y-h Chan, J. B. Haber, M. H. Naik, J. B. Neaton, D. Y. Qiu, F. H. da Jornada, S. G. Louie, Nano Lett., 23, 9 (2023)
- ↑ Origin of Interlayer Exciton–Phonon Coupling in 2D Heterostructures, M. Nalabothula, S. Reichardt, L. Wirtz, Nano Lett., 25, 15 (2025)
- ↑ Exciton-Phonon Interaction and Relaxation Times from First Principles, Hsiao-Yi Chen, Davide Sangalli, and Marco Bernardi, Phys. Rev. Lett. 125, 107401(2020)
- ↑ F. Paleari et al., Exciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride, Phys. Rev. Lett. 122, 187401 (2019) arXiv1810.089776
- ↑ 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)