First-principle Wannier functions and effective lattice fermion models for narrow-band compounds

Abstract

We propose a systematic procedure for constructing effective lattice fermion models for narrow-band compounds on the basis of first-principles electronic structure calculations. The method is illustrated for the series of transition-metal (TM) oxides: SrVO${}_3$, YTiO${}_3$, V${}_2$O${}_3$, and Y${}_2$Mo${}_2$O${}_7$. It consists of three parts, starting from LDA. (i) construction of the kinetic energy Hamiltonian using downfolding method. (ii) solution of an inverse problem and construction of the Wannier functions (WFs) for the given kinetic energy Hamiltonian. (iii) calculation of screened Coulomb interactions in the basis of \textit{auxiliary} WFs, for which the kinetic-energy term is set to be zero. The last step is necessary in order to avoid the double counting of the kinetic-energy term, which is included explicitly into the model. The screened Coulomb interactions are calculated in a hybrid scheme. First, we evaluate the screening caused by the change of occupation numbers and the relaxation of the LMTO basis functions, using the conventional constraint-LDA approach, where all matrix elements of hybridization involving the TM $d$ orbitals are set to be zero. Then, we switch on the hybridization and evaluate the screening associated with the change of this hybridization in RPA. The second channel of screening is very important, and results in a relatively small value of the effective Coulomb interaction for isolated $t_{2g}$ bands. We discuss details of this screening and consider its band-filling dependence, frequency dependence, influence of the lattice distortion, proximity of other bands, and the dimensionality of the model Hamiltonian.

35 pages, 25 figures

References in corpus (8)

• Full orbital calculation scheme for materials with strongly correlated electrons
• Screening of Coulomb interactions in transition metals
• Orbital-Spin Structure and Coupling to Lattice in RTiO${}_3$ with R=La,Pr,Nd and Sm
• Quantum Versus Jahn-Teller Orbital Physics in YVO${}_3$ and LaVO${}_3$
• Electronic Structure of Strongly Correlated Systems Emerging from Combining Path-Integral Renormalization Group with Density Functional Approach
• Crystal-field splitting for low symmetry systems in ab initio calculations
• Lattice Distortion and Magnetic Ground State of YTiO${}_3$ and LaTiO${}_3$
• Optimized Effective Potential for Extended Hubbard Model

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