Exciton-phonon coupling and luminescence

This tutorial works only with Yambo version > 6.x

The exciton-phonon part of Yambo does not support symmetries yet!!!

This an advanced tutorial, in order to calculate exciton-phonon coupling and phonon-assisted absorption/emission you need a deep knowledge of the theory and of the Yambo code.
In this tutorial we will calculate phonon-assisted absorption and luminescence including the scattering between exciton and phonon.

We will consider as example bulk silicon. Notice that parameters of the present tutorial are not at convergence, but are just as a possible example.
The tutorial includes several steps and the calculations can be quite expensive.

Electron-phonon matrix elements

First of all we calculate electron-phonon matrix elements as explained in the section: Electron-phonon matrix elements but in the last passage of the tutorial we expand the electron-phonon matrix elements in all the Brillouin Zone. In order to do so, when we read the electron-phonon matrix elements from QE with the command ypp_ph -g g we turn on the flag GkkpExpand

gkkp                             # [R] gkkp databases
gkkp_db                          # [R] GKKP database
#GkkpReadBare                  # Read the bare gkkp
DBsPATH= "../elph_dir/"                     # Path to the PW el-ph databases
PHfreqF= "none"                  # PWscf format file containing the phonon frequencies
PHmodeF= "none"                  # PWscf format file containing the phonon modes
GkkpExpand                    # Expand the gkkp in the whole BZ
#UseQindxB                     # Use qindx_B to expand gkkp (for testing purposes) 

if everything worked fine in the log you will find:

....
<---> :: Uniform sampling      :yes
<---> :: Symmetry expanded     :yes
.....

Notice that in the calculation of the electron-phononn coupling you need a number of conduction bands as large as the one that will be used in the Bethe-Salpeter Equation.

Remove all symmetries

Now we remove all symmetries with the command ypp_ph -y

fixsyms                          # [R] Remove symmetries not consistent with an external perturbation
% Efield1
 0.000000 | 0.000000 | 0.000000 |        # First external Electric Field
%
% Efield2
 0.000000 | 0.000000 | 0.000000 |        # Additional external Electric Field
%
BField= 0.000000           T     # [MAG] Magnetic field modulus
Bpsi= 0.000000             deg   # [MAG] Magnetic field psi angle [degree]
Btheta= 0.000000           deg   # [MAG] Magnetic field theta angle [degree]
RmAllSymm                     # Remove all symmetries
#RmTimeRev                     # Remove Time Reversal
#RmSpaceInv                    # Remove Spatial Inversion
#KeepKGrid                     # Do not expand the k-grid

the code will expand the electronic wave-function and copy the gkkp_expanded databases in the new folder.

BSE at finite momentum

Go in the folder without symmetries, run the setup, perform the GW calculation if required from your system,
and then run the BSE for all momentum q as explained in the tutorials: BSE basic, BSE convergence, BSE for 2D Do not forget to turn on the flag WRbsWF to write the excitonic wave-functions.

Exciton-phonon matrix elements and optics

Now that you have the BSE for all momentum and the gkkp_expanded databases you can create the exciton-phonon matrix elements, according to the equation:

and calculate optical response as:

with the command: yambo_ph -excph o

excph                            # [R] Exction-phonon
ExcGkkp                          # [R][EXCPH] Exciton-Phonon Matrix Elelements
ExcPhOptics                      # [R][EXCPH] Exciton-Phonon Optics
BoseTemp=-1.000000         eV    # Bosonic Temperature
% ELPhExcStates
 1 | 2 |                             # [EXCPH] Incoming (external) exciton states
%
% ELPhExcSum
 1 | 6 |                             # [EXCPH] Outgoing (virtual) exciton states
%
LoutPath= "none"                 # [EXCPH] Path of the outgoing L
EXCTemp= 0.000000          eV    # [EXCPH] Excitonic Temperature (for luminescence spectra)
#PlotLum                       # [EXCPH] Plot luminescence spectra
#DiagExcph                     # [EXCPH] Use only Diagonal Exciton-phonon matrix elements
#DBGSigmaOnly                  # [EXCPH] Double-grid only for Sigma
% EnRngeXd
  0.00000 | 10.00000 |         eV    # [Xd] Energy range
%
% DmRngeXd
 0.100000 | 0.100000 |         eV    # [Xd] Damping range
%
ETStpsXd= 100                    # [Xd] Total Energy steps