| In recent years novel materials with unusual properties have continued to be discovered, with examples being graphene, iron pnictide superconductors, topological insulators, and heavy fermion superconductors. First principle methods based on density functional theory (DFT) are ideally suited to address and help to understand the physical mechanisms underlying the remarkable phenomena emerged in these materials.;The local spin density approximation extended to account for strong intra-atomic repulsion (LSDA+U method) within DFT is now a standard approach to study strongly correlated materials. It employs orbital-dependent potentials for the spatially localized, strongly correlated, and partially filled d and f orbitals, thus greatly improve predictions over LSDA. I have applied this LSDA+U method to (1) elemental Gd under pressure, (2) the class of tetraborides RB4 (R = rare earth), and (3) the heavy fermion metal YbRh2Si2 displaying quantum critical behavior. My results have added considerably to the understanding of the behavior in these materials.;Surprisingly high superconducting temperature Tc (20--25 K) are found in a few metal elements under pressure in the past few years. The electronic structures and lattice dynamics of two such elements, yttrium and calcium under pressure, are studied using DFT and linear response calculations. The calculated strong electron-phonon (EP) coupling (lambda > 1) can account for the observed Tc in both of them, a result that extends the understanding for the EP mechanism. In addition, possible crystal structures of Ca under pressure are studied, with new understanding of unusual observations being explained.;First principle calculations are performed to address several questions in the newly discovered iron pnictide superconductors. I have studied the basic electronic structures and the effects of a few influential factors. I predict the structures and properties of LaFeNO and LaFeSbO, two members that have not yet been synthesized. Antiphase magnetic boundary (with different densities) imposed on the stripe antiferromagnetic phase is investigated to explore possible spin fluctuations. The interplay of the structural and magnetic transitions and possible orbital fluctuations in these compounds are studied by a combination of first principle calculations, constructing Wannier functions for Fe 3d orbitals and comparing the resulting electron hopping amplitudes. |
