Abstract:
An effective low-energy model describing magnetic properties of alkali-cluster-loaded sodalites is derived by {\em ab initio} downfolding. We start with constructing an extended Hubbard model for maximally localized Wannier functions. {\em Ab initio} screened Coulomb and exchange interactions are calculated by constrained random phase approximation. We find that the system resides in the strong coupling regime and thus the Heisenberg model is derived as a low-energy model of the extended Hubbard model. We obtain antiferromagnetic couplings $\sim$ $O$(10 K), being consistent with the experimental temperature dependence of the spin susceptibility. Importance of considering the screening effect in the derivation of the extended Hubbard model is discussed.

Abstract:
Effective Hamiltonians for LaFeAsO and LaFePO are derived from the downfolding scheme based on first-principles calculations and provide insights for newly discovered superconductivity in the family of LnFeAsO$_{1-x}$F$_x$, Ln = La, Ce, Pr, Nd, Sm, and Gd. Extended Hubbard Hamiltonians for five maximally localized Wannier orbitals per Fe are constructed dominantly from five-fold degenerate iron-3$d$ bands. They contain parameters for effective Coulomb and exchange interactions screened by the polarization of other electrons away from the Fermi level. The onsite Coulomb interaction estimated as 2.2-3.3 eV is compared with the transfer integrals between the nearest-neighbor Fe-3$d$ Wannier orbitals, 0.2-0.3 eV, indicating moderately strong electron correlation. The Hund's rule coupling is found to be 0.3-0.6 eV. The derived model offers a firm basis for further studies on physics of this family of materials. The effective models for As and P compounds turn out to have very similar screened interactions with slightly narrower bandwidth for the As compound.

Abstract:
We derive an effective low-energy Hamiltonian for potassium loaded zeolite A, a unique ferromagnet from non-magnetic elements. We perform ab initio density functional calculations and construct maximally localized Wannier functions for low-energy states made from potassium s electrons. The resulting Wannier orbitals, spreading widely in the alminosilicate cage, are found to be the superatomic s and p orbitals in the confining potential formed by the host cage. We then make a tight-binding model for these superatomic orbitals and introduce interaction parameters such as the Hubbard U. After mean-field calculations for the effective model, we find that ab initio spin density functional results are well reproduced by choosing appropriate sets of the interaction parameters. The interaction parameters turn out to be as large as the band width, $\sim$ 0.5 eV, indicating the importance of electron correlation, and that the present system is an interesting analog of correlated multi-orbital transition metal oxides.

Abstract:
To investigate the possibility whether electron-phonon coupling can enhance orbital fluctuations in iron-based superconductors, we develop an ab initio method to construct the effective low-energy models including the phonon-related terms. With the derived effective electron-phonon interactions and phonon frequencies, we estimate the static part (\omega=0) of the phonon-mediated effective on-site intra- or inter-orbital electron-electron attractions as ~ -0.4 eV and exchange or pair-hopping terms as ~ -0.02 eV. We analyze the model with the derived interactions together with the electronic repulsions within the random phase approximation. We find that the enhancement of the orbital fluctuations due to the electron-phonon interactions is small, making the spin fluctuations dominant. As a result, the superconducting state with the sign reversal in gap functions ($s_\pm$-wave) is realized.

Abstract:
By using variational Monte Carlo method, we examine an effective low-energy model for LaFeAsO derived from an ab initio downfolding scheme. We show that quantum and many-body fluctuations near a quantum critical point largely reduce the antiferromagnetic (AF) ordered moment and the model not only quantitatively reproduces the small ordered moment in LaFeAsO, but also explains the diverse dependence on LaFePO, BaFe2As2 and FeTe. We also find that LaFeAsO is under large orbital fluctuations, sandwiched by the AF Mott insulator and weakly correlated metals. The orbital fluctuations and Dirac-cone dispersion hold keys for the diverse magnetic properties.

Abstract:
In order to clarify the mechanism of spin polarization in potassium-loaded zeolite A, we perform {\em ab initio} density-functional calculations. We find that (i) the system comprising only non-magnetic elements (Al, Si, O and K) can indeed exhibit ferromagnetism, (ii) while the host cage makes a confining quantum-well potential in which $s$- and $p$-like states are formed, the potassium-4$s$ electrons accommodated in the p-states are responsible for the spin polarization, and (iii) the size of the magnetic moment sensitively depends on the atomic configuration of the potassium atoms. We show that the spin polarization can be described systematically in terms of the confining potential and the crystal field splitting of the p-states.

Abstract:
We present a systematic ab initio study based on density-functional calculations to understand impurity effects in iron-based superconductors. Effective tight-binding Hamiltonians for the d-bands of LaFeAsO with various transition-metal impurities such as Mn, Co, Ni, Zn, and Ru are constructed using maximally-localized Wannier orbitals. Local electronic structures around the impurity are quantitatively characterized by their onsite potential and transfer hoppings to neighboring sites. We found that the impurities are classified into three groups according to the derived parameters: For Mn, Co, and Ni, their impurity-3d levels measured from the Fe-3d level are nearly 0.3 eV, -0.3 eV, and -0.8 eV, respectively, while, for the Zn case, the d level is considerably deep as -8 eV. For the Ru case, although the onsite-level difference is much smaller as O(0.1) eV, the transfer integrals around the impurity site are larger than those of the pure system by 20% \sim 30%, due to the large spatial spread of the Ru-4d orbitals. We also show that, while excess carriers are tightly trapped around the impurity site (due to the Friedel sum rule), there is a rigid shift of band structure near the Fermi level, which has the same effect as carrier doping.

Abstract:
We present a systematic study for understanding the relation between electronic correlation and superconductivity in C60 and aromatic compounds. We derived, from first principles, extended Hubbard models for twelve compounds; fcc K3C60, Rb3C60, Cs3C60 (with three different lattice constants), A15 Cs3C60 (with four different lattice constants), doped solid picene, coronene, and phenanthrene. We show that these compounds are strongly correlated and have a similar energy scale of the bandwidth and interaction parameters. However, they have a different trend in the relation between the strength of electronic correlation and superconducting transition temperature; while the C60 compounds have a positive correlation, the aromatic compounds exhibit negative correlation.

Abstract:
We predict that iron-based superconductors discovered near d6 configuration (5 Fe 3d orbitals filled by 6 electrons) is located on the foot of an unexpectedly large dome of correlated electron matter centered at the Mott insulator at d5 (namely, half filling). This is based on the many-variable variational Monte-Carlo results for ab initio low-energy models derived by the downfolding. The d5 Mott proximity extends to subsequent emergence of incoherent metals, orbital differentiations due to the Mott physics and Hund's-rule coupling, followed by antiferromagnetic quantum criticality, in quantitative accordance with available experiments.

Abstract:
We present ab initio two-dimensional extended Hubbard-type multiband models for EtMe_3Sb[Pd(dmit)_2]_2 and \kappa-(BEDT-TTF)_2Cu(NCS)_2, after a downfolding scheme based on the constrained random phase approximation (cRPA) and maximally-localized Wannier orbitals, together with the dimensional downfolding. In the Pd(dmit)_2 salt, the antibonding state of the highest occupied molecular orbital (HOMO) and the bonding/antibonding states of the lowest unoccupied molecular orbital (LUMO) are considered as the orbital degrees of freedom, while, in the \kappa-BEDT-TTF salt, the HOMO-antibonding/bonding states are considered. Accordingly, a three-band model for the Pd(dmit)_2 salt and a two-band model for the \kappa-(BEDT-TTF) salt are derived. We derive single band models for the HOMO-antibonding state for both of the compounds as well.