In this thesis we focus on two problems. First we propose a numerical method for generating optimized Wannier functions with desired properties. Second we perform the state of the art density functional plus dynamical mean-field calculations in pyrochlore iridates, to investigate the physics induced by the cooperation of spin-orbit coupling and electron correlation. We begin with the introduction for maximally localized Wannier functions and other related extensions. Then we describe the current research in the field of spin-orbit coupling and its interplay with correlation effects, followed by a brief introduction of the `hot' materials of iridates. Before the end of the introduction, we discuss the numerical methods employed in our work, including the density functional theory; dynamical mean-field theory and its combination with the exact diagonalization impurity solver. Then we propose our approach for constructing an optimized set of Wannier functions, which is a generalization of the functionality of the classic maximal localization method put forward by Marzari and Vanderbilt. Our work is motivated by the requirement of the effective description of the local subspace of the Hamiltonian by the beyond density functional theory methods. In extensions of density functional theory such as dynamical mean-field theory, one may want highly accurate description of particular local orbitals, including correct centers and symmetries; while the basis for the remaining degrees of freedom is unimportant. Therefore, we develop the selectively localized Wannier function approach which allows for a greater localization in the selected subset of Wannier functions and at the same time allows us to fix the centers and ensure the point symmetries. Applications in real materials are presented to demonstrate the power of our approach. Next we move to the investigation of pyrochlore iridates, focussing on the metal-insulator transition and material dependence in these compounds. We perform combined density functional plus dynamical mean-field calculations in Lu$_2$Ir$_2$O$_7$, Y$_2$Ir$_2$O$_7$, Eu$_2$Ir$_2$O$_7$, with spin-orbit coupling included and both single-site and cluster approximations appiled. A broad range of Weyl metal is predicted as the intervening phase in the metal-insulator transition. By comparing to experiments, we find that the single-site approximation fails to predict the gap values and substantial difference between the Y and Eu-compound, demonstrating the inadequacy of this approximation and indicating the key role played by the intersite effects. Finally, we provide a more accurate description of the vicinity of the metal-insulator and topological transitions implied by density functional plus cluster dynamical mean-field calculations of pyrochlore iridates. We find definitive evidence of the Weyl semimetal phase, the electronic structure of which can be approximately described as ``Weyl rings" with an extremely flat dispersion of one of the Weyl bands. This Weyl semimetal phase is further investigated by the $k\cdot p$ analysis fitting to the numerical results. We find that this unusual structure leads to interesting behavior in the optical conductivity including a Hall effect in the interband component, and to an enhanced susceptibility.

Thesis (Ph. D.)--University of Chicago, Department of Physics, 2001. / Includes bibliographical references. Also available on the Internet.

Density functional theory is a successful theory used in physics, chemistry and nanoscience to describe the ground state properties of solids and molecules. It calculates ground state energies and related properties by using the density of the valence electrons as a fundamental variable. In a system of interacting electrons, the electrons will correlate due to the Pauli exclusion principle, as well as their coulomb repulsion. This interaction energy is known as the exchange-correlation energy and is approximated in density functional theory because it is the only unknown in the energy as a functional of density. The simplest model to approximate this exchangecorrelation energy is the local density approximation, which only relies on the local density of the valence electrons at every point. Generalized gradient approximations are approximations which build upon the local density approximation by also using the gradient of the local density. Recently, many new versions of the generalized gradient approximation have been developed to attempt to obtain better energetic and structural properties either at the same time, or at the expense of the other. In this study, we examine the performance of these models by calculating the atomization energy of the AE6 test set. The cohesive energy, lattice constant and bulk modulus of a four solid test set was also calculated. These calculations were done using ABINIT, a density functional theory code that uses a pseudopotential model with plane waves to examine molecules and solids. One of the more recently developed generalized gradient approximation models, the SOGGA, is tested to compare with the standard models. The accuracy of using a pseudopotential model is also tested. It was found that by using a generalized gradient approximation that was better for energy calculations, the structural property calculations would not be as accurate. The SOGGA is a functional that approximates structural properties of solids accurately but does not calculate energies as well. It was also found that using a pseudopotential model resulted in a 1% difference from the all electron calculations. / Density functional theory -- Molecular data -- Solids -- Second order GGA -- Discussions and conclusions. / Department of Physics and Astronomy

Thesis (M.S.)--Texas State University-San Marcos, 2008. / Vita. Appendices: leaves 132 -234. Includes bibliographical references (leaves 235-236). Also available on microfilm.

Thesis (Ph. D.)--University of Nevada, Reno, 2008. / "May 2008." Includes bibliographical references (leaves 66-76). Online version available on the World Wide Web.

This thesis deals with electron correlation effects within low-dimensional, mesoscopic systems. We study phenomena within two different types of system in which correlations play an important role. The first involves the spectra and spin structure of small symmetric quantum dots, or &quoteartificial atoms&quote. The second is the &quote0.7 structure&quote, a well-known but mysterious anomalous conductance plateau which occurs in the conductance profile of a quantum point contact. Artificial atoms are manufactured mesoscopic devices: quantum dots which resemble real atoms in that their symmetry gives them a &quoteshell structure&quote. We examine two-dimensional circular artificial atoms numerically, using restricted and unrestricted Hartree-Fock simulation. We go beyond the mean-field approximation by direct calculation of second-order correlation terms; a method which works well for real atoms but to our knowledge has not been used before for quantum dots. We examine the spectra and spin structure of such dots and find, contrary to previous theoretical mean-field studies, that Hund's rule is not followed. We also find, in agreement with previous numerical studies, that the shell structure is fragile with respect to a simple elliptical deformation. The 0.7 structure appears in the conductance of a quantum point contact. The conductance through a ballistic quantum point contact is quantised in units of 2e^2/h. On the lowest conductance step, an anomalous narrow conductance plateau at about G = 0.7 x 2e^2/h is known to exist, which cannot be explained in the non-interacting picture. Based on suggestive numerical results, we model conductance through the lowest channel of a quantum point contact analytically. The model is based on the screening of the electron-electron interaction outside the QPC, and our observation that the wavefunctions at the Fermi level are peaked within the QPC. We use a kinetic equation approach, with perturbative account of electron-electron backscattering, to demonstrate that these simple features lead to the existence of a 0.7-like structure in the conductance. The behaviour of this structure reproduces experimentally observed features of the 0.7 structure, including the temperature dependence and the behaviour under applied in-plane magnetic fields.

[Truncated abstract] This work investigated electron correlation and spin-dependent effects in electron scattering from zinc for incident electron energies from the lowest excitation threshold at 4.003 eV to 50 eV. Experiments were performed using a crossed-beams electron impact spectrometer, which included an unpolarised electron gun, and also a spin-polarised electron gun. The apparatus was tested, and shown to be operating well, by repeating past studies of electron scattering from helium and argon. Emission cross sections for the 4s4p 3P1, 4s4p 1P1, 4s5s 3S1, 4s4d; 5d; 6d 3D1;2;3 and 4s4d; 5d 1D2 states were measured from the respective thresholds to 50 eV. These were compared with Convergent Close-Coupling (CCC) and B-spline R-matrix (BSRM) calculations of the 4s4p 3P1, 4s4p 1P1, 4s5s 3S1, 4s4d 1D2 and 4s4d 3D1;2;3 emission cross sections. There are serious discrepancies between the theories, and between the theories and experiment, which indicates strong continuum coupling and innershell excitation effects in the electron excitation of zinc. The differential elastic scattering signal at scattering angles of 30 , 54 , 90 and 110 was measured for incident electron energies from just below the lowest excitation threshold at 4.003 eV, to the ionisation threshold at 9.394 eV. Some assignments given by Sullivan et al [1] and Zatsarinny and Bartschat [2] were confirmed by the present experiment. An area of disagreement in the literature concerning the nature of a feature observed at the 4s4p 1P1 threshold at 5.796 eV was resolved in favour of Zatsarinny and Bartschat, who assign the feature as a cusp. ... Below the ionisation threshold, the 4s4p 3P1 photon excitation function supports the assignment of the near-4s4p 1P1 threshold feature as a cusp. Some of the overlapping negative-ion resonances which were observed near 7.5 eV in the 4s4p 3P1, 4s4p 1P1 and 4s5s 3S1 photon excitation functions were assigned with the assistance of the BSRM calculations of Zatsarinny and Bartschat. However, continuum coupling effects above 8 eV seem to cause the theoretical negative-ion resonance predictions to break down. Above the ionisation threshold, the near-11 eV negative-ion resonance effects depend on the configuration n, L and S of the neutral state excitation observed. This may be due to the properties of the mixed negative ion component states. Postcollision interaction (PCI) effects the 4s5s 3S1, 4s4d; 5d; 6d 3D1;2;3 and 4s4d; 5d 1D2 photon excitation functions. The PCI mechanism can populate the 4s4d; 5d; 6d 3D1;2;3 and 4s4d; 5d 1D2 states because the scattered and ejected electrons have a similar energy, and can thus exchange a large amount of orbital angular momentum. The present work demonstrates that electron correlation effects, especially those associated with innershell excitation, are very significant in electron scattering from zinc. Existing theoretical models of electron scattering from zinc inadequately treat electron correlations, and as a result of this are inaccurate, as shown here. The studies presented here should guide the development of models that accurately describe the innershell excitation effects, which are important for zinc and a great many other atoms.

This thesis deals with electron correlation effects within low-dimensional, mesoscopic systems. We study phenomena within two different types of system in which correlations play an important role. The first involves the spectra and spin structure of small symmetric quantum dots, or &quoteartificial atoms&quote. The second is the &quote0.7 structure&quote, a well-known but mysterious anomalous conductance plateau which occurs in the conductance profile of a quantum point contact. Artificial atoms are manufactured mesoscopic devices: quantum dots which resemble real atoms in that their symmetry gives them a &quoteshell structure&quote. We examine two-dimensional circular artificial atoms numerically, using restricted and unrestricted Hartree-Fock simulation. We go beyond the mean-field approximation by direct calculation of second-order correlation terms; a method which works well for real atoms but to our knowledge has not been used before for quantum dots. We examine the spectra and spin structure of such dots and find, contrary to previous theoretical mean-field studies, that Hund's rule is not followed. We also find, in agreement with previous numerical studies, that the shell structure is fragile with respect to a simple elliptical deformation. The 0.7 structure appears in the conductance of a quantum point contact. The conductance through a ballistic quantum point contact is quantised in units of 2e^2/h. On the lowest conductance step, an anomalous narrow conductance plateau at about G = 0.7 x 2e^2/h is known to exist, which cannot be explained in the non-interacting picture. Based on suggestive numerical results, we model conductance through the lowest channel of a quantum point contact analytically. The model is based on the screening of the electron-electron interaction outside the QPC, and our observation that the wavefunctions at the Fermi level are peaked within the QPC. We use a kinetic equation approach, with perturbative account of electron-electron backscattering, to demonstrate that these simple features lead to the existence of a 0.7-like structure in the conductance. The behaviour of this structure reproduces experimentally observed features of the 0.7 structure, including the temperature dependence and the behaviour under applied in-plane magnetic fields.

Thesis (Ph.D.) -- McMaster University, 1999. / Disk in pocket. Includes bibliographical references (leaves 232-237). Also available via World Wide Web.

This research studied the Anderson localization of electrons in two-channel wires with correlated disorder and in DNA molecules. It involved an analytical calculation part where the formula for the inverse localization length for electron states in a two-channel wire is derived. It also involved a computational part where the localization length is calculated for some DNA molecules. Electron localization in two-channel wires with correlated disorder was studied using a single-electron tight-binding model. Calculations were within second-order Born-approximation to second-order in disorder parameters. An analytical expression for localization length as a functional of correlations in potentials was found. Anderson localization in DNA molecules were studied in single-channel wire and two-channel models for electron transport in DNA. In both of the models, some DNA sequences exhibited delocalized electron states in their energy spectrum. Studies with two-channel wire model for DNA yielded important link between electron localization properties and genetic information.