Maximally-localized Wannier functions in perovskites: Cubic BaTiO3

The electronic ground state of a periodic crystalline solid is usually described in terms of extended Bloch orbitals; localized Wannier functions can alternatively be used. These two representations are connected by families of unitary transformations, carrying a large degree of arbitrariness. We have developed a localization algorithm that allows one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions. We apply this formalism here to the case of cubic BaTiO3. The purpose is twofold. First, a localized-orbital picture allows a meaningful band-by-band decomposition of the whole Bloch band complex. In perovskites, these Wannier functions are centered on the atomic sites and display clearly a s, p, d, or hybrid character. Second, since the centers of the Wannier functions map the polarization field onto localized point charges, the ground state dielectric properties become readily available. We study the Born effective charges of the paraelectric phase of BaTiO3. We are able to identify not only the contributions that come from a given group of bands, but also the individual contributions from the “atomic” Wannier functions that comprise each of these groups.