23: Silicon — \(G_0W_0\) bands structure interpolation¶

Note: This tutorial requires a recent version of the ypp post-processing code of yambo.

Outline: Interpolate the bands structure of silicon obtained from many-body perturbation theory at the \(G_0W_0\) level. Using the yambo code, the quasi-particle corrections (QP) are summed to Kohn-Sham eigenvalues, while the wavefunctions remain the same.
Directory: tutorials/tutorial23/ Files can be downloaded from here
Input Files
- silicon.scf The pwscf input file for the ground state calculation
- silicon.nscf The pwscf input file to obtain Bloch states on a uniform grid
- silicon.gw.nscf The pwscf input file to obtain Bloch states on a reduced grid with many empty bands
- silicon.pw2wan The input file for pw2wannier90
- silicon.win The wannier90 input file
- silicon.gw.win The wannier90 input file (for the \(G_0W_0\) step)
- yambo.in The yambo input file
- ypp.in The ypp input file
Copy the input files from the INPUT directory into a working directory (e.g. WORK)
Run pwscf to obtain the ground state charge of silicon
Terminal
```
pw.x < silicon.scf > scf.out
```
Run pwscf to obtain the Bloch states reduced grid. We use a 8x8x8 with many bands (many empty bands are needed to perform a \(G_0W_0\) with yambo)
Terminal
```
pw.x < silicon.gw.nscf > nscf.gw.out
```
Use the k_mapper.py utility to find the indexes of a 4x4x4 uniform grid into the 8x8x8 reduced grid
Terminal
```
./k_mapper.py 4 4 4 "..tutorials/tutorial23/WORK/nscf.gw.out"
```
Use the output to complete the yambo.in input file (you also need to specify how many bands you want to compute the QP corrections, here you can use all the bands from 1 to 14). Then, you should have obtained something like:
Output file
```
 1| 1| 1|14|
3| 3| 1|14|
5| 5| 1|14|
13| 13| 1|14|
...
```
Enter the si.save directory and run p2y. A SAVE folder is created, you can move it up in the /WORK/ directory.
Run a \(G_0W_0\) calculation from the /WORK/ directory (remember, we are using a 8x8x8 grid but computing QP corrections only on a 4x4x4 grid)
Terminal
```
yambo
```
Run pwscf to obtain the Bloch states on a uniform k-point grid
Terminal
```
pw.x < silicon.nscf > nscf.out
```
Run wannier90 to generate a list of the required overlaps (written into the silicon.nnkp file).
Terminal
```
wannier90.x -pp silicon
```
Run pw2wannier90 to compute the overlap between Bloch states, the projections for the starting guess (written in the silicon.mmn and silicon.amn respectively).
Terminal
```
pw2wannier90.x < silicon.pw2wan > pw2wan.out
```
Run wannier90 to compute the MLWFs.
Terminal
```
wannier90.x silicon
```
At this point, you should have obtained the interpolated valence bands for silicon at the DFT level.
Run a ypp calculation (just type ypp)
Terminal
```
ypp
```
You should obtain a file silicon.gw.unsorted.eig which contains the QP corrections on a uniform 4x4x4 grid.
Run the gw2wannier90.py script to reorder, align and correct all matrices and files using the QP corrections
Terminal
```
../../../utility/gw2wannier90.py silicon mmn amn
```
Run wannier90 to compute the MLWFs.
Terminal
```
wannier90.x silicon.gw
```
At this point, you should have obtained the interpolated valence bands for silicon at the \(G_0W_0\) level.

After you completed the tutorial for the valence bands only, you can repeat the final steps to interpolate also some conduction bands using disentanglement (the code is already present as comments in the input files).