36: Silicon — Valence and low-lying conduction states¶

Marzari-Vanderbilt functional¶

Outline: Obtain MLWFs for the valence and low-lying conduction-band states of Si by minimizing the Marzari-Vanderbilt functional. Plot the interpolated bandstructure.
Directory: tutorial/tutorial36/
Input Files
- silicon.scf The pwscf input file for ground state calculation
- silicon.nscf The pwscf input file to obtain Bloch states on a uniform grid
- silicon.pw2wan Input file for pw2wannier90
- silicon.win The wannier90 input file
Run pwscf to obtain the ground state of silicon
Terminal
```
pw.x < silicon.scf > scf.out
```
Run pwscf to obtain the Bloch states on a uniform k-point grid. Note that we request the lower 4 (valence) bands
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 and the projections for the starting guess (written in the silicon.mmn and silicon.amn files).
Terminal
```
pw2wannier90.x < silicon.pw2wan > pw2wan.out
```
Run wannier90 to compute the MLWFs.
Terminal
```
wannier90.x silicon
```
Plot the bandstructure by adding the following commands to the input file silicon.win
Input file
```
restart = plot

bands_plot = true
```
and re-running wannier90. The files silicon_band.dat and silicon_band.gnu are created. To plot the bandstructure using gnuplot
Terminal
```
gnuplot
```
Gnuplot shell
```
load 'silicon_band.gnu'
```
The k-point path for the bandstructure interpolation is set in the kpoint_path block. Try plotting along different paths.

Stengel-Spaldin functional¶

Outline: Obtain MLWFs for the valence and low-lying conduction-band states of Si by minimizing the Stengel-Spaldin functional. Plot the interpolated bandstructure.
Directory: tutorial/tutorial36/
Input Files
- silicon.scf The pwscf input file for ground state calculation
- silicon.nscf The pwscf input file to obtain Bloch states on a uniform grid
- silicon.pw2wan Input file for pw2wannier90
- silicon.win The wannier90 input file
To run, the procedure is the same as the MV functional case.

Further ideas¶

Compare the spreads obtained by both functionals. Increase the grid and find out that the two functionals converges to the same behavior.
Compare the Wannier-interpolated bandstructure with the both functionals. Find out that the interpolated bandstructures are almost the same.