9: Cubic BaTiO\(_3\)¶

Outline: Obtain MLWFs for a perovskite
Directory: tutorials/tutorial09/ Files can be downloaded from here
Input Files
- batio3.scf The pwscf input file for ground state calculation
- batio3.nscf The pwscf input file to obtain Bloch states on a uniform grid
- batio3.pw2wan Input file for pw2wannier90
- batio3.win The wannier90 input file

To start with, we are going to obtain MLWFs for the oxygen 2p states. From the bandstructure ¹, these form an isolated group of bands. We use the wannier90 keyword exclude_bands to remove all but the 2p bands from the calculation of the overlap and projection matrices (we don't have to do this, but it saves time).

Run pwscf to obtain the ground state of BaTiO\(_3\)
Terminal
```
pw.x < BaTiO3.scf > scf.out
```
Run pwscf to obtain the Bloch states on a uniform k-point grid
Terminal
```
pw.x < BaTiO3.nscf > nscf.out
```
Run wannier90 to generate a list of the required overlaps (written into the BaTiO3.nnkp file).
Terminal
```
wannier90.x -pp BaTiO3
```
Run pw2wannier90 to compute the overlap between Bloch states and the projections for the starting guess (written in the BaTiO3.mmn and BaTiO3.amn files).
Terminal
```
pw2wannier90.x < BaTiO3.pw2wan > pw2wan.out
```
Run wannier90 to compute the MLWFs.
Terminal
```
wannier90.x BaTiO3
```

Inspect the output file BaTiO3.wout.

Plot the second MLWF, as described in Section 1, by adding the following keywords to the input file BaTiO3.win

Input file

wannier_plot = true
restart = plot
wannier_plot_list = 2
wannier_plot_supercell = 3

and re-running wannier90. Visualise it using XCrySDen,

Terminal

xcrysden `--`xsf BaTiO3_00002.xsf

We can now simulate the ferroelectric phase by displacing the Ti atom. Change its position to

Input file

Ti 0.505 0.5 0.5

and regenerate the MLWFs (i.e., compute the ground-state charge density and Bloch states using pwscf, etc.) and look at the change in the second MLWF.

Further ideas¶

Look at MLWFs for other groups of bands. What happens if you form MLWFs for the whole valence manifold?
Following Ref. ¹, compute the Born effective charges from the change in Wannier centres under an atomic displacement.

Nicola Marzari and David Vanderbilt. Maximally-localized Wannier functions in perovskites: Cubic BaTiO3. AIP Conference Proceedings, 436(1):146–155, 06 1998. ↩↩