Data and post-processing scripts for Phys. Rev. Research 3, 023027 (2021)
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Oxygen vacancies in strontium titanate: A DFT+DMFT study
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DOI: doi.org/10.1103/PhysRevResearch.3.023027
J. Souto-Casares, N. A. Spaldin, C. Ederer
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Abstract:
We address the long-standing question of the nature of oxygen vacancies in
strontium titanate, using a combination of density functional theory and
dynamical mean-field theory (DFT+DMFT) to investigate in particular the effect
of vacancy-site correlations on the electronic properties. Our approach uses a
minimal low-energy electronic subspace including the Ti-t2g orbitals plus an
additional vacancy-centered Wannier function, and it provides an intuitive and
physically transparent framework to study the effect of the local electron-
-electron interactions on the excess charge introduced by the oxygen vacancies.
We estimate the strength of the screened interaction parameters using the
constrained random phase approximation, and we find a sizable Hubbard U parameter
for the vacancy orbital. Our main finding, which reconciles previous experimental
and computational results, is that the ground state is either a state with double
occupation of the localized defect state or a state with a singly occupied
vacancy and one electron transferred to the conduction band. The balance between
these two competing states is determined by the strength of the interaction both
on the vacancy and the Ti sites, and on the Ti-Ti distance across the vacancy.
Finally, we contrast the case of vacancy doping in SrTiO3 with doping via La
substitution, and we show that the latter is well described by a simple
rigid-band picture.
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The compressed tar archive contains a jupyter notebook (https://jupyter.org/) that
will read the data produced by VASP, wannier90, and the triqs DMFT framework
(https://triqs.github.io/triqs/2.1.x/) and post-process it to the figures found
in our publication, after proper redirection of the paths to the needed output files.
All input data is also contained in the archives.
Note: Due to license reasons we had to remove all VASP POTCAR files.
Figures 1 and 2 were done using the visualization program VESTA light Inkscape
postprocessing for labelling and highlighting.
Basic workflow:
-1-DFT calculation: VASP + Wannier90 to create a wannier90_hr.dat file, containing the
tight-binding-like Hamiltonian of the correlated orbitals (Ti-t2g or Ti-t2g+OV).
VASP bandstructure is extracted from the output files using the script bands.py;
Wannier90 DOS files are calculated individually and later manipulated with the
script merge_wannier_dos.py.
-2-DMFT calculation: Use the Wannier90 converter to create the h5 input file. Define
the DMFT calculation on the param.py file, and run dmft_cthyb.py. The main output
files are called 'observables_imp#.dat'. To calculate the spectral functions we use
Bryan's maxent algorithm as implemented in
https://bitbucket.org/lewinboehnke/maxent/src/master
Quasiparticle weights are extracted from the h5 output files.
-3-cRPA calculation, in three steps: (1[DFT]) starting normal DFT calculation,
(2[EXACT]) where optical properties are calculated, (3[CRPA]) to obtain the U tensors.
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