# GaN¶

Author: Samuel Poncé

Warning

The following example aims at providing physically meaningful results. Calculations can therefore take a significant amount of time. For quick calculations, look at the `EPW/tests/`

folder.

## Running EPW on polar wurtzite GaN¶

The polar wurtzite GaN example is located inside the `EPW/examples/gan/`

directory. Within this directory there are three directories. `pp/`

contains the Pb pseudopotential, `phonon/`

contains the input files to calculate the phonons for GaN; `epw/`

contains the inputs to run `epw.x`

on GaN.

Once `pw.x`

, `ph.x`

and `epw.x`

have been compiled, we are ready to run the example.

## Calculating the phonons¶

The first step is to calculate the phonons in the irreducible wedge. For this example, we use a `6x6x6`

coarse grid.
First go inside the phonon directory

```
cd phonons
```

The phonon code from QE requires a ground-state self-consistent run

```
../../../../bin/pw.x < scf.in >& scf.out &
```

The electronic bandstructure of w-GaN is presented in Figure 1 below.

We will now continue in sequential. Let us compute the dynamical matrix, phonon frequencies and change of potential using the `ph.x`

code

```
../../../../bin/ph.x < ph.in >& ph.out &
```

This will give us the phonon frequency and dynamical matrices at 28 irreducibles q-points.
We then need to copy the `.dyn`

and `.dvscf`

as well as the `_ph0/diam.phsave`

folder inside the `save`

folder. Those are all the quantities produced by Quantum Espresso that EPW needs.
Because the files need to have a specific name and because there can be quite a few files, you can use the small python script to help you. Just issue

```
python pp.py
```

in the phonons folder. The script will ask you the prefix used for the QE calculations as well as the number of irreducible **q**-points computed. The script will place all the files in the `save`

folder. We are now done with QE and can move to the `epw`

folder.

The phonon bandstructure of w-GaN is presented in Figure 1 below.

## Calculating the electron-phonon matrix element using EPW¶

We first have to do a scf and nscf calculations. To do that, go inside the `epw`

directory and issue:

```
../../../../bin/pw.x < scf.in >& scf.out
```

```
../../../../bin/pw.x < nscf.in >& nscf.out
```

We can then run the EPW calculation. We will start by computing the phonon linewidth (imaginary part of the phonon self-energy). Note that we have set `phonselfen = .true.`

in the `epw.in`

input file.
Also you can notice that we are computing the interpolated electron-phonon matrix element along the high-symmetry **q**-point line. This is achieved by reading a data file using the `filqf = 'gan_band.qpt'`

input command.

You can then launch the EPW calculation:

```
../../../bin/epw.x < epw.in >& epw.out
```

Although the electron-phonon matrix elements as presented at the bottom of Figure 1 are not outputted directly (usually not relevant), you can easily print them by modifying the code. This should give you the correct red interpolation line as seen on the figure.