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Register a new userGeneralized Wannier Functions
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Authors
Emil Prodan
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We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are exponentially localized a round a set of closed surfaces of monotonically increasing sizes. Estimates on the exponential dec ay rate and a discussion of the geometry of these surfaces is included.
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Localized Wannier functions provide an efficient and intuitive means by which to compute dielectric properties from first principles. They are most commonly constructed in a post-processing step, following total-energy minimization. Nonorthogonal generalized Wannier functions (NGWFs) [Skylaris et al., Phys. Rev. B 66, 035119 11 (2002); Skylaris et al., J. Chem. Phys. 122, 084119 (2005)] may also be optimized in situ, in the process of solving for the ground-state density. We explore the relationship between NGWFs and orthonormal, maximally localized Wannier functions (MLWFs) [Marzari and Vanderbilt, Phys. Rev. B 56, 12847 (1997); Souza, Marzari, and Vanderbilt, ibid. 65, 035109 (2001)], demonstrating that NGWFs may be used to compute electric dipole polarizabilities efficiently, with no necessity for post-processing optimization, and with an accuracy comparable to MLWFs.
Localized Wannier functions provide an efficient and intuitive framework to compute electric polarization from first-principles. They can also be used to represent the electronic systems at fixed electric field and to determine dielectric properties of insulating materials. Here we develop a Wannier-function-based formalism to perform first-principles calculations at fixed polarization. Such an approach allows to extract the polarization-energy landscape of a crystal and thus supports the theoretical investigation of polar materials. To facilitate the calculations, we implement a quasi-Newton method that simultaneously relaxes the internal coordinates and adjusts the electric field in crystals at fixed polarization. The method is applied to study the ferroelectric behavior of $mathrm{BaTiO_3}$ and $mathrm{PbTiO_3}$ in tetragonal phases. The physical processes driving the ferroelectricity of both compounds are examined thanks to the localized orbital picture offered by Wannier functions. Hence, changes in chemical bonding under ferroelectric distortion can be accurately visualized. The difference in the ferroelectric properties of $mathrm{BaTiO_3}$ and $mathrm{PbTiO_3}$ is highlighted. It can be traced back to the peculiarities of their electronic structures.
We review the formalisms of the self-consistent GW approximation to many-body perturbation theory and of the generation of optimally-localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave functions from such GW calculations can be used within this Wannier framework. These Wannier functions can be used to interpolate the many-body band structure from the coarse mesh of Brillouin zone points on which it is known from the initial calculation to the usual symmetry lines, and we demonstrate that this procedure is accurate and efficient for the self-consistent GW band structure. The resemblance of these Wannier functions to the bond orbitals discussed in the chemical community led us to expect differences between density-functional and many-body functions that could be qualitatively interpreted. However, the differences proved to be minimal in the cases studied. Detailed results are presented for SrTiO_3 and solid argon.
Superfluid to Mott-insulator transitions in atomic BEC in optical lattices are investigated for the case of number of atoms per site larger than one. To account for mean field repulsion between the atoms in each well, we construct an orthogonal set of Wannier functions. The resulting hopping amplitude and on-site interaction may be substantially different from those calculated with single-atom Wannier functions. As illustrations of the approach we consider lattices of various dimensionality and different mean occupations. We find that in three-dimensional optical lattices the correction to the critical lattice depth is significant to be measured experimentally even for small number of atoms. Finally, we discuss validity of the single band model.
We report on the implementation of the Wannier Functions (WFs) formalism within the full-potential linearized augmented plane wave method (FLAPW), suitable for bulk, film and one-dimensional geometries. The details of the implementation, as well as results for the metallic SrVO3, ferroelectric BaTiO3 grown on SrTiO3, covalently bonded graphene and a one-dimensional Pt-chain are given. We discuss the effect of spin-orbit coupling on the Wannier Functions for the cases of SrVO3 and platinum. The dependency of the WFs on the choice of the localized trial orbitals as well as the difference between the maximally localized and first-guess WFs are discussed. Our results on SrVO3 and BaTiO3, e.g. the ferroelectric polarization of BaTiO3, are compared to results published elsewhere and found to be in excellent agreement.
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