| We have applied first-principles calculations to investigate the topological insulator state of half-Heusler materials and the momentum density for overdoped cuprates. The specific topics addressed in this thesis are as follows.;1. Topological insulators are materials exhibiting a novel quantum state of matter; these insulators are characterized by a bulk excitation generated by the spin orbit interaction, and protected conducting states on their edge or surface. In this work we investigate in detail the electronic structure of a series of ternary half-Heusler compounds MM'X of MgAgAS-type with M = (Lu, La, Sc, Y) and M'X=(PtBi,AuPb,PdBi,PtSb,AuSn,NiBi,PdSb). The characteristic features of all half-Heusler compounds considered here are topological nontrivial semimetal, or nontrivial metal, or trivial insulator. The analysis of the relation among the band inversion strength (distance from the critical line), atomic number of constituents, and lattice constant could provide a methodology (a rule of thumb) to predict the topological order of hypothetical nonmagnetic half-Heusler compound more generally.;2. The bulk Fermi surface (FS) is observed in an overdoped ( x=0.3) single crystal of La2-xSrxCuO4 by using Compton scattering. A 2-D momentum density reconstruction from measured Compton profiles yields a clear FS signature in the third Brillouin zone along [100]. The quantitative agreement between density functional theory calculations and momentum density experiment suggests that Fermi-liquid physics is restored in the overdoped regime. The FS shows signs of a change topological of the FS found at lower doping. We find similar quantitative agreement between the measured 2D angular correlation of positron annihilation radiation (2D-ACAR) spectra and DFT simulations. However, 2D-ACAR does not give such a clear signature of the FS in the extended momentum space in either theory or experiment. |
