9: Cubic BaTiO₃¶
- Outline: Obtain MLWFs for a perovskite.
1-5. Compute the MLWFs.
Converged values for the total spread functional and its components are shown in Table 1.
Table 1. Converged values of the components of spread functional and their sums for cubic BaTiO₃ in Å\(^2\).
| \(\Omega\) | \(\Omega_{\text{I}}\) | \(\Omega_{\text{OD}}\) | \(\Omega_{\text{D}}\) | \(N_{\mathrm{iter}}\) |
|---|---|---|---|---|
| 12.7187 | 12.5662 | 0.1525 | 0.000 | 50 |
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Plot the second MLWF.
The result is shown in Figure 2.
Top-view (a) and side-view (b) of the second MLWF in BaTiO₃. -
We can now simulate the ferroelectric phase by displacing the Ti atom. 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.
The result is shown in Figure 3.
Top-view (a) and side-view (b) of the second MLWF in BaTiO₃ with the Ti atom displaced.
Further ideas¶
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Look at MLWFs for other groups of bands.
Plots of MLWFs for other group of bands are shown in Figure 4.
MLWFs for other group of bands: a. Ti 3s (exclude bands = 2-20), b. Ti 3p (exclude bands = 1,5-20), c. Ba 5s (exclude bands = 1-4,6-20), d. O 2s (exclude bands = 1-5,9-20), e. Ba 5p (exclude bands = 1-8,12-20), f. O 2p (exclude bands = 1-11). -
What happens if you form MLWFs for the whole valence manifold?
Some representative MLWFs from the wannierisation of the whole valence bands are shown in Figure 5.
MLWFs formed from the whole valence manifold, i.e. from 20 bands: a. Ti 3s, b. Ti 3p, c. Ba 5s, d. O 2s, e. Ba 5p, f. O 2p.