Yambopy tutorial: electron-phonon coupling

In this tutorial we will cover the handling of electron-phonon coupling matrix elements by Yambopy. The electron-phonon calculation follows two steps: 1. Quantum Espresso calculation of phonon energies, eigenmodes and variations of the self-consistent potential via ph.x. 2. Electron-phonon matrix element calculation, symmetry expansion and conversion by the LetzElPhC.

For more information on the LetzElPhC and how you should run step 1., please see the related documentation [| here].

• Electron-phonon matrix elements (Yambo databases: ndb.elph_gkkp*, Yambopy class: YamboElectronPhononDB).

Command line: importing electron-phonon matrix elements

You may have seen how to calculate and import electron-phonon matrix elements in yambo in the electron-phonon tutorial.

With Yambopy, we can generate a yambo SAVE folder and import the matrix elements with a single command. Typing

$yambopy gkkp

will print the necessary documentation:

Produce a SAVE folder including elph_gkkp databases

Arguments are:
  -nscf, --nscf_dir  -> <Optional> Path to nscf save folder
  -elph, --elph_dir  -> Path to elph_dir folder
  -y, --yambo_dir    -> <Optional> Path to yambo executables
  -e, --expand       -> <Optional> Expand gkkp databases

The necessary quantum espresso databases are stored in ELPH_SAVES/QE_SAVES/hBN.save (nscf calculation) and ELPH_SAVES/QE_SAVES/elph_dir (matrix elements from the dfpt calculation). For this tutorial we also need to expand the electron-phonon matrix elements to the full Brillouin zone. Since this is a different calculation with respect to the previous section, please generate this SAVE in a different directory than the one you used for the previous SAVE, which should be the current directory. For example:

$mkdir yambo-with-elph
$cd yambo-with-elph

Now we can run yambopy as in the instructions:

$yambopy gkkp -nscf ../ELPH_saves/QE_saves/hBN.save -elph ../ELPH_saves/QE_saves/elph_dir --expand

This should generate a yambo SAVE folder which contains the ndb.elph_gkkp_expanded* databases.

Electron-phonon intro: plots of el-ph matrix elements on k-BZ and q-BZ

In this section we will use the script elph_plot.py and read the electron-phonon databases that you generated in the previous section.

In order to read the ndb.elph_gkkp_expanded* databases in python we use the Yambopy class YamboElectronPhononDB, which can be instanced like this:

yelph = YamboElectronPhononDB(ylat,folder_gkkp='path/to/elph/folder',save='path/to/SAVE')

(notice that it requires a previous instance of YamboLatticeDB).

Now, the yelph object contains phonon frequencies, phonon eigenvectors, qpoint information and, of course, the electron-phonon matrix elements g_{nm\nu}(k,q) where n, m are electron band states, \nu is a phonon branch, and k and q are the electronic and transfer momenta.

We can print the docstring of the YamboElectronPhononDB class with

print(yelph.__doc__)

to get an idea of the information stored and of its capabilities.

Now check the elph_plot.py script. You will see that it performs two plots:

• Plot of |g(k)| in the k-BZ for selected n,m,\nu and q [Kspace_Plot=True].
• Plot of |g(q)| in the q-BZ for selected n,m,\nu and k [Qspace_Plot=True].

You can change the electronic, phononic and momentum indices to see what happens.