Exciton-phonon coupling and luminescence: Difference between revisions

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In this advanced tutorial, we will calculate exciton-phonon interactions from first principles by interfacing DFPT (for phonon calculations) and BSE (for exciton calculations).
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 ($k$) and the transfer momenta ($Q$, $q$) of excitons and phonons, thus speeding up considerably the jobs while reducing the IO and memory load.
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>k</math>) and the transfer momenta (<math>Q</math>, <math>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.
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.
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'''Note:''' this tutorial will be updated when new exc-ph tools become available in Yambopy (including full-python postprocessing, Raman spectra, interpolated lifetimes, etc).
'''Note:''' this tutorial will be updated when new exc-ph tools become available in Yambopy (including full-python postprocessing, Raman spectra, interpolated lifetimes, etc).


== Knowledge requirements ==
== Requirements ==
This is an advanced topic: we assume that you already know something about the theory<ref name="Toyozawa" /><ref name="cudazzo" /><ref name="antonius" /><ref name="fulvio2" /><ref name="fulvio_thesis" /><ref name="pierre_thesis" /> and applications<ref name="zanfrognini" /><ref name="pierre" /><ref name="chan" /><ref name="chen" /><ref name="fulvio1" /><ref name="elena" /> 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.
This is an advanced topic: we assume that you already know something about the theory<ref name="toyozawa2003" /><ref name="antonius2017" /><ref name="cudazzo2020" /><ref name="paleari2019_PhD" /><ref name="paleari2022" /><ref name="lechifflart2023_PhD" /> and applications<ref name="paleari2019" /><ref name="cannuccia2019" /><ref name="chen2020" /><ref name="zanfrognini2023" /><ref name="lechifflart2023" /><ref name="chan2023" /><ref name="marini2024" /><ref name="murali2025" /> 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 <code>pw.x</code> and <code>ph.x</code>, we also use the yambo phonon-specific executable <code>yambo_ph</code> and the python utility '''Yambopy'''. The auxiliary code '''LetzElPhC''' (executable <code>lelphc</code>) will be used to obtain the electron-phonon matrix elements by reading the same electronic wavefunctions used by Yambo (and stored in the <code>SAVE</code> 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 <code>yambo_ph</code> or using Yambopy itself.
[[File:Workflow scheme.png|800px|center]]
== 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 <code>ecutwfc</code> 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 <code>pw.x</code> for Yambo. We stick with non-symmorphic symmetries. At the end, we will have the QE <code>save</code> directory.
INPUT
mpirun -np 4 pw.x -inp mos2.scf > scf.out


== References ==
== References ==


<references>
<references>
<ref name="Toyozawa" >Optical processes in solids, Toyozawa, Yutaka, and Chris Oxlade. Cambridge University Press, (2003). </ref>
<ref name="toyozawa2003" >Optical processes in solids, Toyozawa, Yutaka, and Chris Oxlade. Cambridge University Press, (2003). </ref>
<ref name='pierre'>[https://arxiv.org/abs/2212.10407 First-principles study of luminescence in hexagonal boron nitride single layer: Exciton-phonon coupling and the role of substrate],  
<ref name='lechifflart2023'>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'',  
P Lechifflart, F Paleari, D Sangalli, C Attaccalite Phys. Rev. M, '''7''' (2), 024006 (2023)</ref>
[https://doi.org/10.1103/PhysRevMaterials.7.024006 Phys. Rev. M, '''7''' (2), 024006 (2023)]; [https://arxiv.org/abs/2212.10407 arXiv2212.1047]</ref>
<ref name='elena'>[https://arxiv.org/abs/1807.11797 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)</ref>
<ref name='cannuccia2019'>E. Cannuccia, B. Monserrat and C. Attaccalite, ''Theory of phonon-assisted luminescence in solids: Application to hexagonal boron nitride'', [https://doi.org/10.1103/PhysRevB.99.081109 Phys. Rev. B '''99''', 081109(R) (2019)]; [https://arxiv.org/abs/1807.11797 arXiv1807.11797]</ref>
<ref name='fulvio1'>[https://arxiv.org/abs/1810.08976 Exciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride], F. Paleari et al. PRL '''122''', 187401(2019) </ref>
<ref name='paleari2019'>F. Paleari et al., ''Exciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride'', [https://doi.org/10.1103/PhysRevLett.122.187401 Phys. Rev. Lett. '''122''', 187401 (2019)]; [https://arxiv.org/abs/1810.08976 arXiv1810.089776] </ref>
<ref name='chen'>[https://arxiv.org/abs/2002.08913 Exciton-Phonon Interaction and Relaxation Times from First Principles],
<ref name='chen2020'>[https://arxiv.org/abs/2002.08913 Exciton-Phonon Interaction and Relaxation Times from First Principles],
Hsiao-Yi Chen, Davide Sangalli, and Marco Bernardi, Phys. Rev. Lett. '''125''', 107401(2020)</ref>
Hsiao-Yi Chen, Davide Sangalli, and Marco Bernardi, Phys. Rev. Lett. '''125''', 107401(2020)</ref>
<ref name="pierre_thesis">[https://www.yambo-code.eu/wiki/images/5/54/These_final.pdf Exciton-phonon coupling and phonon-assisted luminescence in hexagonal Boron Nitride nanostructures], PhD Thesis, Pierre Lechifflart (2023)</ref>
<ref name="lechifflart2023_PhD">[https://www.yambo-code.eu/wiki/images/5/54/These_final.pdf Exciton-phonon coupling and phonon-assisted luminescence in hexagonal Boron Nitride nanostructures], PhD Thesis, Pierre Lechifflart (2023)</ref>
<ref name='fulvio_thesis'>[https://wwwen.uni.lu/research/fstm/dphyms/people/fulvio_paleari First-principles approaches to the description of indirect absorption and luminescence spectroscopy: exciton-phonon coupling in hexagonal boron nitride], PhD thesis, Fulvio Paleari (2019)</ref>
<ref name='paleari2019_PhD'>F. Paleari, ''First-principles approaches to the description of indirect absorption and luminescence spectroscopy: exciton-phonon coupling in hexagonal boron nitride'', [https://wwwen.uni.lu/research/fstm/dphyms/people/fulvio_paleari PhD thesis, University of Luxembourg (2019)]</ref>
<ref name='zanfrognini'>[https://arxiv.org/abs/2305.17554 Distinguishing different stackings in layered materials via luminescence spectroscopy], M. Zanfrognini et al. Phys. Rev. Lett. '''131''', 206902 (2023) </ref>
<ref name='zanfrognini2023'>[https://arxiv.org/abs/2305.17554 Distinguishing different stackings in layered materials via luminescence spectroscopy], M. Zanfrognini et al. Phys. Rev. Lett. '''131''', 206902 (2023) </ref>
<ref name='marini_g'>[https://arxiv.org/abs/2402.03826 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)</ref>
<ref name='marini2024'>[https://arxiv.org/abs/2402.03826 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)</ref>
<ref name='antonius'>[https://arxiv.org/abs/1705.04245 Theory of exciton-phonon coupling], G. Antonius, S. G. Louie, Phys. Rev. B, '''105''', 085111 (2022)</ref>
<ref name='antonius2017'>G. Antonius, S. G. Louie, ''Theory of exciton-phonon coupling'', [https://doi.org/10.1103/PhysRevB.105.085111 Phys. Rev. B, '''105''', 085111 (2022)]; [https://arxiv.org/abs/1705.04245 arXiv1705.04245 (2017)]</ref>
<ref name='fulvio2'>[https://arxiv.org/abs/2205.02783 Exciton-phonon interaction calls for a revision of the “exciton” concept], F. Paleari, A. Marini, Phys. Rev. B, '''106''', 125403 (2022)</ref>
<ref name='paleari2022'>[https://arxiv.org/abs/2205.02783 Exciton-phonon interaction calls for a revision of the “exciton” concept], F. Paleari, A. Marini, Phys. Rev. B, '''106''', 125403 (2022)</ref>
<ref name='cudazzo'>[First-principles description of the exciton-phonon interaction: A cumulant approach], P. Cudazzo, Phys. Rev. B, '''102''', 045136 (2020)</ref>
<ref name='cudazzo2020'> P. Cudazzo, ''First-principles description of the exciton-phonon interaction: A cumulant approach'', [https://doi.org/10.1103/PhysRevB.102.045136 Phys. Rev. B, '''102''', 045136 (2020)]; [https://orbilu.uni.lu/bitstream/10993/44769/1/main.pdf Open access pdf from Luxembourg University]</ref>
<ref name='chan'>[https://arxiv.org/abs/2212.08451 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)</ref>
<ref name='chan2023'>[https://arxiv.org/abs/2212.08451 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)</ref>
<ref name='murali2025'>[https://arxiv.org/abs/2407.16111 Origin of Interlayer Exciton–Phonon Coupling in 2D Heterostructures], M. Nalabothula, S. Reichardt, L. Wirtz, Nano Lett., '''25''', 15 (2025)</ref>
</references>
</references>

Latest revision as of 15:33, 18 September 2025

Tdgw-phonon-usc-01-1024x829.jpg

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.

Workflow scheme.png

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

  1. ↑ Optical processes in solids, Toyozawa, Yutaka, and Chris Oxlade. Cambridge University Press, (2003).
  2. ↑ G. Antonius, S. G. Louie, Theory of exciton-phonon coupling, Phys. Rev. B, 105, 085111 (2022); arXiv1705.04245 (2017)
  3. ↑ 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
  4. ↑ F. Paleari, First-principles approaches to the description of indirect absorption and luminescence spectroscopy: exciton-phonon coupling in hexagonal boron nitride, PhD thesis, University of Luxembourg (2019)
  5. ↑ Exciton-phonon interaction calls for a revision of the “exciton” concept, F. Paleari, A. Marini, Phys. Rev. B, 106, 125403 (2022)
  6. ↑ Exciton-phonon coupling and phonon-assisted luminescence in hexagonal Boron Nitride nanostructures, PhD Thesis, Pierre Lechifflart (2023)
  7. ↑ 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
  8. ↑ E. Cannuccia, B. Monserrat and C. Attaccalite, Theory of phonon-assisted luminescence in solids: Application to hexagonal boron nitride, Phys. Rev. B 99, 081109(R) (2019); arXiv1807.11797
  9. ↑ Exciton-Phonon Interaction and Relaxation Times from First Principles, Hsiao-Yi Chen, Davide Sangalli, and Marco Bernardi, Phys. Rev. Lett. 125, 107401(2020)
  10. ↑ Distinguishing different stackings in layered materials via luminescence spectroscopy, M. Zanfrognini et al. Phys. Rev. Lett. 131, 206902 (2023)
  11. ↑ 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
  12. ↑ 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)
  13. ↑ 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)
  14. ↑ Origin of Interlayer Exciton–Phonon Coupling in 2D Heterostructures, M. Nalabothula, S. Reichardt, L. Wirtz, Nano Lett., 25, 15 (2025)
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