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note
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The generalized gradient functional was used, which typically overestimates lattice constants and gives 3.9445 Å as the bulk lattice constant of STO. Therefore, all lattice constants were rescaled by 3.9445/3.905 in the calculations. Projector augmented wave potentials and a plane-wave cut off of 400 eV were used. We used. 4 × 4 × M Monkhorst-Pack sampling of the Brillouin zone, where M≥6/N for a supercell with N layers.
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