Development and application of first-principles-based methods for correlated electron materials with strong spin-orbit coupling

Abstract

The first-principles studies within the density functional theory (DFT) framework have been successfully applied to a wide range of materials in condensed matter physics. Despite the success of DFT, there exists a class of materials for which DFT fails to describe, even qualitatively. Most of these materials contain localized d and f electrons with strong Coulomb interactions. Beyond DFT methods are essential to account for electron-electron interactions of the localized orbitals correctly. DFT+U and DFT+dynamical mean field theory (DMFT) are widely used. In the +U and +DMFT frameworks, Kohn-Sham Hamiltonian is corrected by the local self-energy terms in static and dynamical mean-field level, respectively. In this thesis, we present the theoretical backgrounds, practical implementations, and its applications of the first-principles based methods. Focusing on the metal-insulator transition for strongly correlated materials, we analyze the role of the spin-orbit coupling and degeneracy of the bands near the Fermi level. Firstly, for systematic study, we have implemented full band DFT+DMFT based on OpenMX, a non-orthogonal pseudo-atomic orbital basis DFT code. While the different projection methods are tested, the natural atomic orbital orthogonalization is stable to basis set change. We also have developed new analytic continuation methods, so-called maximum quantum entropy method. This continuation method is developed to obtain spectral functions for the case of multi-band Hamiltonian and real material research.

Second, We also suggest the newly developed method and physical concept based on first-principles calculation. These methods are introduced to compare the calculation results with the experimental data and to provide useful insights to understand the results, e.g., metal-insulator transition. The DFT+U and +DMFT calculations are performed to apply our method to real materials. The calculation results for iridate and other transition-metal oxides are presented. The calculation results for $Sr_2IrO_4$, a prototype $j_{eff} = 1/2$ Mott insulator, and $SrIrO_3/SrTiO_3$ superlattice shows the importance of the interplay between the spin-orbit coupling and electronic correlations for the 5d orbitals. In this regards, we applied a simple technique to calculate spin-orbit coupling and branching ratio measured in x-ray absorption spectroscopy. Calculated <L.S> and branching ratio of the several different iridates are in good agreement with experimental data. We also suggest a way to quantify the `effective degeneracy' relevant to metal-insulator transition by introducing entropy-like terms. Calculating effective degeneracy, we show that the degeneracy lifting due to the spin-orbit coupling plays a central role in stabilizing `spin-orbit coupling assisted Mott insulator'. This quantified `effective degeneracy' concept is applied to not only 5d iridate but also 3d titanates, namely $LaTiO_3/LaAlO_3$ superlattice, suggesting a novel `degeneracy control' metal-insulator transition.