Modeling electronic structure and spectroscopy in correlated materials and topological insulators

Current major topics in condensed matter physics mostly focus on the investigation of materials having exotic quantum phases. For instance, Z 2 topological insulators have novel quantum states, which are distinct from ordinary band insulators. Recent developments show that these nontrivial topological phases may provide a platform for creating new types of quasiparticles in real materials, such as Majorana fermions. In correlated systems, high-T c superconducting cuprates are complicated due to the richness of their phase diagram. Surprisingly, the discovery of iron pnictides demonstrates that high-Tc superconductivity related phenomena are not unique to copper oxide compounds. Many people believe that the better the understanding of the electronic structure of cuprates and iron pnictides, the higher chances to unveil the high temperature superconductivity mystery. Despite the fact that silicon is a fundamental element in modern semiconductor electronics technology, the chemical bonding properties of liquid silicon phase still remain a puzzle.;A popular approach to investigate electronic structure of complex materials is combining the first principles calculation with an experimental light scattering probe. Particularly, Compton scattering probes the many body electronic ground state in the bulk of materials in terms of electron momentum density projected along a certain scattering direction, and inelastic x-ray scattering measures the dynamic structure factor S(q, ω) which contains information about electronic density-density correlations.;In this thesis, I study several selected materials based on first principles calculations of their electronic structures, the Compton profiles and the Lindhard susceptibility within the framework of density functional theory. Specifically, I will discuss the prediction of a new type of topological insulators in quaternary chalcogenide compounds of compositions I2-II-IV-VI 4 and in ternary famatinite compounds of compositions I3-V-VI 4. I will present the electronic structure, Fermi surface topology and the interlayer coupling strength of the iron-based superconductor Ca 10(Pt3As8)(Fe2As2) 5. In the study of iron-pnictide LaOFeAs and cuprate La2−x SrxCuO4, I will discuss the Fermi surface topology and the related orbital characters near the Fermi energy from the aspect of Compton profiles and electron momentum density. The Compton scattering related study also includes the effect of disorder and chemical bonding in liquid silicon. I will describe the extension of the Lindhard susceptibility calculation to multiple Brillouin zones and illustrate the zone dependent susceptibility of the electron doped cuprate Nd2−xCexCuO 4. I also extend this study to the time-resolved response function of solids in real space.