In this thesis, we report on our studies of the transport properties, optical response and slow dynamical nature of novel room temperature ionic liquids. Using computer simulations we have demonstrated that the diffusive dynamics of these systems is in many ways analogous to that of other glassy or supercooled liquids. These solvents show non-Gaussian rotational and translational diffusion which have a temporal extent on the order of nanoseconds at room temperature. Our study of their response upon application of an external mechanical perturbation shows that even for systems with a box length as large as 0.03 microns the viscosities computed from perturbation wavenumbers compatible with this box size have not yet reached the hydrodynamic limit. We found these systems to behave in a non-Newtonian fashion and we also observe a clear break down of linear response theory on the nano- or sub-micrometer scale. Upon photoexcitation of an organic probe with lifetime shorter than the reorganization timescale in these ionic liquids, (which is quite long on the order of several nanoseconds at least), the emission spectrum is absorption wavelength dependent.Our computer simulations rationalized this observation in terms of local solvent environment around individual subensemble probe members. Excitation of different solute molecules in the liquid gives rise to site-specic optical responses. We revealed that the origin of this excitation wavelength dependence is the existence of persistent excited-state environments that do not get solvent averaged on a time scale relevant to fluorescence. The computed time resolved fluorescence spectra show that the full loss of correlation between absorption and emission frequencies for probes in room temperature ionic liquids occur on a time scale of nanoseconds. One of the most interesting features of ionic liquids is their uncommonly large range of dynamical time scales which in turn makes some of their properties to be quite different from that of most other conventional solvents. We hope that our understanding of these phenomena will be useful in the future in the development of tools to harness their potential to control the outcome of chemical and photo-chemical reactions.

Thermoelectric materials play an important role in energy conversion as they represent environmentally safe and solid state devices with a great potential towards enhancing their efficiency. The ability to generate electric power in a reliable way without using non-renewable resources motivates many experimentalists as well as computational physicists to search and design new thermoelectric materials. Several classes of materials have been identified as good candidates for high efficient thermoelectrics because of their inherently low thermal conductivity. The complex study of the crystal and electronic structures of such materials helps to reveal hidden properties and give fundamental understanding, necessary for the development of a new generation of thermoelectrics. In the current thesis, ab-initio computational methods along with experimental observations are applied to investigate several material classes suitable for thermoelectric applications. One example are Bi-Sb bismuth rich alloys, for which it is shown how structural anomalies affect the electronic structure and how inclusion of the Spin-Orbit coupling is necessary for this type of materials. Another example are bournonite materials whose low thermal conductivity is attributed to distortions and interactions associated with lone-electron s^2 pair distributions. In addition, it is shown how doping with similar atoms can affects electronic structure of these materials leading to changes in their transport properties. Clathrate materials from the less studied type II Sn class are also investigated with a detailed analysis for their structural stability, electronic properties and phonons. These systems are considered with partially substituted atoms on the framework and different guests inside. The effect upon insertion of Noble gases into the cage network is also investigated. In addition, the newly synthesized As based cationic material is also studied finding novel structure-property relations. Another class of materials, quaternary chalcogenides, have also been studied. Because of their inherently low thermal conductivity and semiconducting nature their transport properties may be optimized in a favorable way for thermoelectricity. The present work provides an in-depth study of structural and electronic properties of several classes of materials, which can be used by experimentalists for input and guidance in the laboratory.

Amorphous and nanocrystalline transition metal magnetic alloys (TMMAs) have been the subjects of fundamental and applied study due to their unique structure. The lack of long-range order in these materials sets the stage for their soft magnetic properties to be tuned for a variety of technological applications, such as sensitive magnetic field sensors, high frequency transformers, and stress sensors. Fundamental investigation of the magnetic and structural properties of these materials is also motivated by their unique amorphous or nanocrystalline-embedded amorphous matrix morphology, which has consequences on both the magnetism seen from both the atomic and macro-scale. The surfaces of these materials become important to their high frequency applications, where the skin depth of the excitation field is distributed near the surface. In conjunction with high frequency magnetoimpedance measurements, surface sensitive probes of magnetism and structure must be employed to provide a complete picture of the relationship between the surface and dynamic magnetism. This dissertation focuses on the surface impact of chemical composition, annealing conditions, and coatings on TMMAs on their magnetoimpedance response through multiple surface sensitive techniques such as atomic/magnetic force microscopy, magneto-optical Kerr effect, and scanning/transmission electron microscopy. These tools provide a view into the relationship between the nanostructure, microstructure and soft magnetic properties that make these materials highly desired for fundamental study and technological application.

Throughout the last half century of materials science, significant motivations came from, and still do, the industrial applications of these materials. Whether it is electronic, thermal, tribological or chemical in nature, the study of metals, semiconductors and insulators eventually reveals that the surface plays a significant part in the properties of these materials. Understanding metal terminations reveals often that an oxide is the stable state of the metallic surface in an ambient atmosphere and the ability to predict and control these oxides has led to significant strides forward in not just the metallic bulk but the oxide as well. Here we add to the understanding of the class of materials known as transition metal oxides by focusing on the structural and chemical nature of their surfaces. Vanadia, chromia and a new mixed metal oxide, VTiO3, all of which form the corundum structure and have physical properties that need further study. Specifically, Cr2O3 has been at the center of much debate over how oxygen chemical potential influences surface terminations and top layer relaxation. Chromia is a wide band gap (~3.4eV) insulator with substantial ligand field interaction and measurements of the 3d states reveal these states split to t2g and eg– consistent with the distorted octahedral. V2O3 is known to be a Mott insulator and paramagnetic, properties that can be modified through dopants, stoichiometry and strain. In this work, solid solutions of V2O3 and Ti2O3 are studied. VTiO3, has been synthesized in a corundum – like structure by epitaxial growth on an isostructural α-Al2O3 substrate. Section I offers a review of corundum like transition metal oxides and their surface properties and motivations of continued research. In section II we describe in detail, the critical components of PLD thin film growth and in the next section a review of the pertinent characterization techniques utilized in the process. Finally, the results are presented of the study of two transition metal oxide structures namely: 1) Novel VTiO3 in a corundum structure has been grown via Pulsed Laser Deposition – Molecular Beam Epitaxy on a single crystal Al2O3(0001) substrate. The sapphire substrate with modest lattice mismatch was utilized in an effort to compel heteroepitaxial growth of the VTiO3 film. Confirmation of the films structure & chemical state were performed by X-Ray diffraction, Transmission Electron Microscopy (HR), X-Ray Photo-electron Diffraction, Ultra-Violet Photo-Electron Diffraction and Reflection High Energy Electron expected that the metal ions exist in a 3+ charge state. While XPS clearly points to a V3+ charge state and this suggests that Ti should as well, however there is also a strong Ti4+ component present. EELS spectra support the existence of a mixed state Ti3+ & 4+. Broadening of the valance band edge as revealed by UPS spectra indicate that the 3d orbitals are occupied and that the a1g molecular states are occupied. The conflict in diffraction data supporting corundum and PES/EELS data suggesting a mixed state implies that additional final state effects are present and/or an oxygen rich structure. 2) Additionally, corundum like Chromium(III) Oxide is formed on a Cr(110) surface and characterized with X-Ray Photoelectron Diffraction, Low Energy Electron Diffraction and XPS for the purpose of characterizing surface termination and terminating layer relaxation. Comparison of the XPD diffraction data with known and previously discussed terminations reveal the as grown film does not conform. Consequently, we propose a new, stoichiometric termination with oxygen termination and 1st layer chromium interstitials. Atop this structure was grown an ultra-thin film of V2O3 by vanadium e-beam evaporation in background oxygen. This final structure supports the previously proposed vanadyl structured surface

<p>Entanglement are the non-local correlations permitted by quantum theory, believed to play a fundamental role in a quantum computer. We have investigated these correlations in a number of theoretical models for condensed matter systems. Such systems are likely candidates for quantum computing, and experimentally feasible for instance as superconducting qubits. At quantum critical points the ground state of these systems is very complicated, and the entanglement is usually larger than at non-critical points. This entanglement can be used to identify the critical points through what we denote the entanglement signature, even for very small systems. From another perspective, it seems that the entanglement is an essential tool to find an unknown ground state, since this gives rise to a simple decomposition of the state.</p>

<p>A complex system is a system for which the statement "the whole is greater than the sum of its parts" holds. A network can be viewed as a backbone of a complex system. Combining the knowledge about the entities constituting the complex system with the properties of the interaction patterns we can get a better understanding of why the whole is greater than the sum. One of the purposes of network studies, is to relate the particular structural and dynamical properties of the network to the function it is designed to perform. In the present work I am briefly presenting some of the advances that have been achieved in the field of the complex networks together with the contributions which I have been involved in.</p>

We carried out systematic neutron scattering experiments to investigate the magnetic properties and their relationship to the high-$T_c$ superconductivity, when the materials are tuned from their antiferromagnetic (AF) parent compounds to the superconducting regime. We observed resonance mode in the electron doped cuprate Nd$_{1.85}$Ce$_{0.15}$CuO$_4$, demonstrating that the resonance is a general phenomenon in cuprate superconductors regardless of hole- or electron-doping. In Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$, the local susceptibility displays two distinct energy scales that are broadly consistent with the bosonic modes revealed by scanning tunneling microscopy experiments. These results indicate the presence of very strong electron spin excitations couplings in electron doped cuprates. Shortly after the discovery of high-$T_c$ superconductivity in the Fe pnictides, we discovered that the magnetic phase diagram of CeFeAsO$_{1-x}$F$_x$ is remarkably similar to that of the cuprates. Besides CeFeAsO, similar magnetic and lattice structures are also observed in PrFeAsO and SrFe$_2$As$_2$ systems. Neutron scattering measurements show that in SrFe$_2$As$_2$, the spectrum of magnetic excitations consists of a Bragg peak at the elastic position, a spin gap, and sharp spin-wave excitations at higher energies. Based on the observed dispersion relation, we estimated the effective magnetic exchange coupling using a Heisenberg model. In order to study the nature of the exchange interactions in the parent compound of Fe pnictides, we studied the high energy spin-wave excitations in CaFe$_2$As$_2$. Although the spin waves in the entire Brillouin zone can be described by an effective three-dimensional anisotropic Heisenberg Hamiltonian, the magnetism in this system is neither purely local nor purely itinerant; rather it is a complicated mix of the two. When the Fe pnictide is tuned into superconducting regime with doping, the low energy spin fluctuation is dominated by a resonance mode. In the optimally electron doped BaFe$_{1.9}$Ni$_{0.1}$As$_2$, application of a magnetic field that suppresses the superconductivity and superconducting gap energy also reduces the intensity and energy of the resonance. These results suggest that the energy of the resonance is proportional to the electron pairing energy, and thus indicate that spin fluctuations are intimately related to the mechanism of high $T_c$ superconductivity.

The recent discovery of the iron-pnictide superconductors has generated tremendous excitement, in part because there are many tantalizing similarities to the cuprate superconductors. As with the cuprates, it is strongly suspected that the spins contribute to superconductivity. There seems to be a strong relationship between the lattice and magnetism in this system. Several authors have discussed the possibility of spin-phonon coupling, but direct experimental evidence has remained elusive. This work discusses the relationship between the spins and the lattice in the $BaFe_{2}As_{2}$ family. We demonstrate the presence of negative thermal expansion in these materials, which is a strong indicator of spin-lattice interaction. In addition, we have conducted inelastic neutron scattering experiments to examine the dynamical relationship between the spins and the lattice. In particular, we make use of the phenomenon known as magnetovibrational scattering to search for evidence of spin-phonon coupling. We believe that this is the first work to use magnetovibrational scattering in an antiferromagnetic system as a tool to study the spin-phonon interaction. Our results provide direct experimental evidence for the existence of spin-phonon coupling, with possible implications about the role of phonons in the superconductivity of iron pnictides.

We performed ab initio studies of the electronic excitation spectra of the ferro- magnetic, Mott-insulator YTiO3 using density functional theory (DFT) and time- dependent density functional theory (TDDFT). In the ground state description, we included a Hubbard U to account for the strong correlations present within the d states on the cation. The excitation spectra was calculated using TDDFT linear response formalism in both the optical limit and the limit of large wavevector transfer. In order to identify the local d-d transitions in the response, we also computed the density response of YTiO3 using a novel technique where the basis included Wannier functions generated for the Ti and Y sites. Also, we describe the first implementation of the all-electron Kohn-Sham density functional equations in a periodic system using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n- e-s-s). This implementation is highlighted by the real space lattice sums involved in the application of the Coulomb and bound state Helmlholtz integral operators.

Tb6FeSb2 and Tb6FeBi2 are novel rare earth compounds with little prior research. These compounds show high and variable curie temperatures for rare-earth compounds. This has lead to a literature review which includes the discussion of: elasticity, resonance, and magnetism. This review is used to discuss the theory and methodology which can relate these various properties to each other. Furthermore, synthesis, x-ray analysis, and RUS sample preparation of Tb6FeSb2 and Tb6FeBi2 were completed. Resonant Ultrasound Spectroscopy (RUS) elastic studies were taken for Tb6FeSb2 and Tb6FeBi2 as a function temperature from 5-300K, in various magnetic fields ranging from 0-9T. Tb6FeSb2’s and Tb6FeBi2’s elastic moduli are related to their magnetic properties. Magnetization data, primarily M v. H, provides another measure the magnetic properties are used to help correlate the data to elasticity. Tb6FeSb2 and Tb6FeBi2 Curie temperatures are 253(3)K and 246(5)K respectively. The low temperature magnetic transition of Tb6FeSb2 is 65-90K and Tb6FeBi2 is 55-75K. RUS suggests that this low temperature transition is somehow related to a structural transition but this transition does not occur in these two compounds. Co-substitution of Tb6FeSb2 and Tb6FeBi2 seem to greatly affect this lower temperature transition in RUS. It does not greatly effect the curie temperature. Low temperature XRD shows that Co-substitution also creates a structural transition in this family of compounds.