During the last decades the specific manipulation of matter on the (sub-) nanometer scale, also known as nanoscience, became possible by technologies such as the scanning tunneling microscope. Nanocatalysts, i.e. catalytic active structures of up to a few nanometers in size, belong to this rather new class of materials. Unlike ordinary ’macroscopic’ catalytic materials, the performance of nanocatalysts does not simply scale, for instance, with the surface to volume ratio of the active material. In this Thesis model nanocatalysts are investigated by means of ab-initio density functional theory calculations. In paper I, we explain the experimentally observed catalytic characteristics of small gold clusters, Au1-4, on a regular magnesium oxide terrace towards the oxidation of carbon monoxide by thoroughly studying the adsorption of CO and O2 on these clusters. In the subsequent paper II, we study the feasibility of a catalytic water-mediated CO oxidation reaction on Au1-4/MgO and find that this reaction mechanism is not assessable for Au2,4/MgO and unlikely for Au1,3/MgO. Papers III and IV concentrate on the reactivity of clusters in the gas phase. Particularly, we focus on the relative stability of Au13 isomers and its potential for O2 dissociation (paper III). We find the lowest energy isomers, which contain a triangular prism at their center surrounded by a ring of the remaining seven atoms, to be generally stable upon O2 adsorption. The dissociation of O2 at certain sites of Au13 is found to be exothermic. In paper IV we performed scans of the Born-Oppenheimer potential energy surfaces of neutral and charged Cu3, Ag3, and Au3 to explore the thermally excited vibrations of these trimers. While the Born-Oppenheimer surface of Cu3 exhibits one fairly deep energy minimum, it is comparatively flat with two shallow minima in the case of Ag3. Hence for Ag3 there exist many thermally accessible geometries in a wide range of angles and bond lengths. For Au3, two distinct energy minima appear, being well-separated by a barrier of 180 meV. Already at room temperature, we find bond lengths changes of up to 5% for the studied trimers. Choosing Au3 as a case study for the changed reactivity of thermally excited modes, we find CO to bind up to 150 meV stronger to the excited cluster. Gold deposited on graphene and graphite was observed to form larger aggregates. In paper V, we study the electronic structures, high mobility, and substrate-mediated clustering processes of Au1-4 on graphene. Already in the 1970s is was speculated that dispersion forces, i.e. van der Waals forces, significantly contribute to the adsorption energies of gold atoms on graphite. We accounted for van der Waals interactions in our density functional theory calculations (paper VI) and investigated the influence of these dispersion forces on the binding of copper, silver, and gold adatoms on graphene. While copper and gold show a mixed adsorption mechanism, i.e. chemical binding plus attraction due to the van der Waals forces, silver is purely physisorbed on graphene. / Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 719

Vad karaktäriserar en kristall? Svaret på denna till synes enkla fråga blir kanske att det är en anordning av atomer uppradade i periodiska mönster. Så ordnade strukturer kan studeras genom att det uppträder så kallade Braggtoppar i röntgendiffraktionsmönstret. Om frågan gäller elektrontäthetsfördelningen, kanske svaret blir att denna är periodisk och grundar sig på elektronvågor som genomtränger hela kristallen. I och med att nya typer av ordnade system, så kallade kvasikristaller, upptäcks och framställs på artificiell väg blir svaren på dessa frågor mer intrikata. En kristall behöver inte bestå av enheter upprepade periodiskt i rummet, och den klassiska metoden att karaktärisera strukturer via röntgendiffraktionsmönstret kanske inte alls är den allena saliggörande. I denna avhandling visas att ett ordnat gitter vars röntgendiffraktionsmönster saknar inre struktur, dvs är av samma diffusa typ som vad ett oordnat material uppvisar, fortfarande kan ha elektronerna utsträckta över hela strukturen. Detta implicerar att det inte finns något enkelt samband mellan diffraktionsmönstret från gittret och dess fysikaliska egenskaper såsom t ex lokalisering av vågfunktionerna. Man talar om lokalisering när en vågfunktion är begränsad inom en del av materialet och inte utsträckt över hela dess längd, vilket är av betydelse när man vill avgöra huruvida ett material är en isolator, halvledare eller ledare. Det vittnar samtidigt om behovet av att söka efter andra karakteristika när man försöker beskriva skillnaden mellan ett ordnat och ett oordnat material, där den senare kategorin kan uppvisa lokalisering. Resultaten utgör en klassificering av det svåröverskådliga området aperiodiska gitter i en dimension. Det leder till hypotesen att ideala kvasikristaller, genererade med bestämda regler, har kontinuerligt energispektrum av fraktal natur. I reella material spelar korrelation en viktig roll. Vid icke-linjär återkoppling till gittret kan man erhålla intrinsiskt lokaliserade vågor, som i många avseenden beter sig som partiklar, solitoner, vilka har visat sig ha viktiga tillämpningar inom bl a optisk telekommunikation. Sådana vågors roll for lagring och transport av energi har undersökts i teoretiska modeller for optiska vågledare och kristaller där ljuset har en förmåga att manipulera sig självt. / Spectral and dynamical properties of electrons, phonons, electromagnetic waves, and nonlinear coherent excitations in one-dimensional modulated structures with long-range correlations are investigated from a theoretical point of view. First a proof of singular continuous electron spectrum for the tight-binding Schrödinger equation with an on-site potential, which, in analogy with a random potential, has an absolutely continuous correlation measure, is given. The critical behavior of such a localization phenomenon manifests in anomalous diffusion for the time-evolution of electronic wave packets. Spectral characterization of elastic vibrations in aperiodically ordered diatomic chains in the harmonic approximation is achieved through a dynamical system induced by the trace maps of renormalized transfer matrices. These results suggest that the zero Lebesgue measure Cantor-set spectrum (without eigenvalues) of the Fibonacci model for a quasicrystal is generic for deterministic aperiodic superlattices, for which the modulations take values via substitution rules on finite sets, independent of the correlation measure. Secondly, a method to synthesize and analyze discrete systems with prescribed long-range correlated disorder based on the conditional probability function of an additive Markov chain is effectively implemented. Complex gratings (artificial solids) that simultaneously display given characteristics of quasiperiodic crystals and amorphous solids on the Fraunhofer diffraction are designated. A mobility edge within second order perturbation theory of the tight-binding Schrödinger equation with a correlated disorder in the dichotomic potential realizes the success of the method in designing window filters with specific spectral components. The phenomenon of self-localization in lattice dynamical systems is a subject of interest in various physical disciplines. Lattice solitons are studied using the discrete nonlinear Schrödinger equation with on-site potential, modeling coherent structures in, for example, photonic crystals. The instability-induced dynamics of the localized gap soliton is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsic localized modes from the extended out-gap soliton reveals a phase transition of the solution.

<p>Strong coupling between light and matter has been demonstrated both in classical</p><p>cavity quantum electrodynamics (QED) systems and in more recent circuit-QED</p><p>experiments. This enables the generation of strong nonlinear photon-photon interactions</p><p>at the single-photon level, which is of great interest for the observation</p><p>of quantum nonlinear optical phenomena, the control of light quanta in quantum</p><p>information protocols such as quantum networking, as well as the study of</p><p>strongly correlated quantum many-body systems using light. Recently, strong</p><p>coupling has also been realized in a variety of one-dimensional (1D) waveguide-</p><p>QED experimental systems, which in turn makes them promising candidates for</p><p>quantum information processing. Compared to cavity-QED systems, there are</p><p>two new features in waveguide-QED: the existence of a continuum of states and</p><p>the restricted 1D phase space, which together bring in new physical effects, such</p><p>as the bound-state effects. This thesis consists of two parts: 1) understanding the</p><p>fundamental interaction between local quantum objects, such as two-level systems</p><p>and four-level systems, and photons confined in the waveguide; 2) exploring</p><p>its implications in quantum information processing, in particular photonic</p><p>quantum computation and quantum key distribution.</p><p>First, we demonstrate that by coupling a two-level system (TLS) or three/fourlevel</p><p>system to a 1D continuum, strongly-correlated photons can be generated</p><p>inside the waveguide. Photon-photon bound states, which decay exponentially as a function of the relative coordinates of photons, appear in multiphoton scattering</p><p>processes. As a result, photon bunching and antibunching can be observed</p><p>in the photon-photon correlation function, and nonclassical light source can be</p><p>generated on demand. In the case of an N-type four-level system, we show</p><p>that the effective photon-photon interaction mediated by the four-level system,</p><p>gives rise to a variety of nonlinear optical phenomena, including photon blockade,</p><p>photon-induced tunneling, and creation of single-photon states and photon</p><p>pairs with a high degree of spectral entanglement, all in the absence of a cavity.</p><p>However, to enable greater quantum networking potential using waveguide-</p><p>QED, it is important to study systems having more than just one TLS/qubit.</p><p>We develop a numerical Green function method to study cooperative effects in</p><p>a system of two qubits coupled to a 1D waveguide. Quantum beats emerge in</p><p>photon-photon correlations, and persist to much longer time scales because of</p><p>non-Markovian processes. In addition, this system can be used to generate a</p><p>high-degree of long-distance entanglement when one of the two qubits is driven</p><p>by an on-resonance laser, further paving the way toward waveguide-QED-based</p><p>quantum networks.</p><p>Furthermore, based on our study of light-matter interactions in waveguide-</p><p>QED, we investigate its implications in quantum information processing. First,</p><p>we study quantum key distribution using the sub-Possonian single photon source</p><p>obtained by scattering a coherent state off a two-level system. The rate for key</p><p>generation is found to be twice as large as for other sources. Second, we propose</p><p>a new scheme for scalable quantum computation using flying qubits--propagating</p><p>photons in a one-dimensional waveguide--interacting with matter qubits. Photonphoton</p><p>interactions are mediated by the coupling to a three- or four-level system,</p><p>based on which photon-photon -phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is</p><p>possible given recent dramatic experimental progress in superconducting circuits</p><p>and photonic-crystal waveguides. The proposed system can be an important</p><p>building block for future on-chip quantum networks.</p> / Dissertation

The two-dimensional phase of carbon known as graphene is actively being pursued as a primary material in future electronic devices. The goals of this thesis are to investigate the growth and electronic properties of epitaxial graphene on SiC, with a particular focus on nanostructured graphene. The first part of this thesis examines the kinetics of graphene growth on SiC(0001) and SiC(0001 ̅) by high-temperature sublimation of the substrate using a custom-built, ultra-high vacuum induction furnace. A first-principles kinetic theory of silicon sublimation and mass-transfer is developed to describe the functional dependence of the graphene growth rate on the furnace temperature and pressure. This theory can be used to calibrate other graphene growth furnaces which employ confinement controlled sublimation. The final chapter in this thesis involves a careful study of self-organized epitaxial graphene nanoribbons (GNRs) on SiC(0001). Scanning tunneling microscopy of the sidewall GNRs confirms that these self-organized nanostructures are susceptible to overgrowth onto nearby SiC terraces. Atomic-scale imaging of the overgrown sidewall GNRs detected local strained regions in the nanoribbon crystal lattice, with strain coefficients as high as 15%. Scanning tunneling spectroscopy (STS) of these strained regions demonstrate that the graphene electronic local density of states is strongly affected by distortions in the crystal lattice. Room temperature STS in regions with a large strain gradient found local energy gaps as high as 400 meV. Controllable, strain-induced quantum states in epitaxial graphene on SiC could be utilized in new electronic devices. / Per request of the author and the advisor, and with the approval of the graduate office, the Acknowledgements page was replaced with an errata.

We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics. Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient numerical methods to integrate the NLSE have to be developed in order to perform the extensive number of required simulations. To facilitate this, compact high-order numerical schemes for the spatial derivatives are developed which include a new semi-compact modulus-squared Dirichlet boundary condition. The schemes are combined with a fourth-order Runge-Kutta time-stepping scheme in order to keep the overall method fully explicit. To ensure efficient use of the schemes, a stability analysis is performed to find bounds on the largest usable time step-size as a function of the spatial step-size. The numerical methods are implemented into codes which are run on NVIDIA graphic processing unit (GPU) parallel architectures. The codes running on the GPU are shown to be many times faster than their serial counterparts. The codes are developed with future usability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with a MEX-compiler interface. Reproducibility of results is achieved by combining the codes into a code package called NLSEmagic which is freely distributed on a dedicated website.

Molecular electronics is envisioned as a possible next step in device miniaturization. It is usually taken to mean the design and manufacturing of electronic devices and applications where organic molecules work as the fundamental functioning unit. It involves the measurement and manipulation of electronic response and transport in molecules attached to conducting leads. Organic molecules have the advantages over conventional solid state electronics of inherent small sizes, endless chemical diversity and ambient temperature low cost manufacturing. In this thesis we investigate the switching and conducting properties of photoswitching dithienylethene derivatives. Such molecules change their conformation in solution when acted upon by light. Photochromic molecules are attractive candidates for use in molecular electronics because of the switching between different states with different conducting properties. The possibility of optically controlling the conductance of the molecule attached to conducting leads may lead to new device implementations. The switching reaction is investigated with potential energy calculations for different values of the reaction coordinate between the closed and the open isomer. The electronic and atomic structure calculations are performed with Density Functional Theory (DFT). The potential energy barrier separating the open and closed isomer is investigated, as well as the nature of the excited states involved in the switching. The conducting properties of the molecule inserted between gold, silver and nickel leads is calculated within the Non Equilibrium Green Function theory (NEGF). The molecule is found to be a good conductor in both conformations, with the low-bias current for the closed one being about 20 times larger than that of the open in the case of gold contacts, and over 30 times larger in the case of silver contacts. For the Ni leads the current for the closed isomer is almost 40 times larger than that of the open. Importantly, the current-voltage characteristics away from the linear response is largely determined by molecular orbital re-hybridization in an electric field, in close analogy to what happens for Mn12 molecules. However in the case of dithienylethene attached to Au and Ag such a mechanism is effective also in conditions of strong electronic coupling to the electrodes. In reality these molecules are in constant motion, and the dynamical properties has to be considered. In this thesis such a line of work is initiated. In order to facilitate efficient and stable dynamical simulations of molecular systems the extended Lagrangian formulation of Born-Oppenheimer molecular dynamics have been implemented in two different codes. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. In the density functional theory code FreeON, different symplectic integrators up to the 6th order have been adapted and optimized. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular for the case of very high accuracy requirements. Geometric integration schemes, including a weak dissipation to remove numerical noise, are developed and implemented in the self-consistent tight-binding code LATTE. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. The modification of the integration breakes symplecticity and introduces a global energy drift. The systematic driftin energy and the broken symplecticity can be kept arbitrarily small without significant perturbations of the molecular trajectories. / QC 20101202

doctoral thesis, Ph.D, University of California, Berkeley, Berkeley, CA. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--55855" Gedik, Nuh. USDOE Director. Office of Science. Office of Basic Energy Sciences 05/20/2004. Report is also available in paper and microfiche from NTIS.

Thesis (Ph.D.); Submitted to the University of California, Berkeley, CA (US); 24 Nov 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56751" McGuire, John Andrew. USDOE Director. Office of Science. Office of Basic Energy Sciences. Materials Science and Engineering Division (US) 11/24/2004. Report is also available in paper and microfiche from NTIS.

Thesis (Ph.D.); Submitted to Iowa State Univ., Ames, IA (US); 12 Dec 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "IS-T 2028" Haibo Cao. 12/12/2003. Report is also available in paper and microfiche from NTIS.

Nuclear magnetic resonance (NMR) is a powerful experimental technique for probing the local environment of nuclei in materials. However, it can be difficult to separate the large number of interactions that are recorded in the resulting spectra. First-principles calculations based on quantum mechanics therefore provide much-needed support for interpreting experimental spectra. In this way, the underlying mechanisms recorded in experimental spectra can be investigated on an atomic level, and trends can be noted with which to guide the direction of future experiments. This thesis presents two cases in which first-principles calculations do just that. The first is an investigation of the perovskite structures of NaNbO₃, KNbO₃, LiNbO₃ and the related solid solutions of Na_xK_1-xNbO₃, K_xNa_1-xNbO₃ and Li_xNa_1-xNbO₃ in order to study how structural disorder affects their NMR parameters. The second investigation involves the calculation of the Knight shift in platinum, palladium and rhodium---in their elemental bulk forms and in a set of surface structures. The Knight shift is a systematic shift in the NMR frequencies of metallic systems. It arises from the hyperfine interaction between the nuclear spins and the spins of the unpaired conduction electrons. When calculating the Knight shift, it is found that the Brillouin zone must be very finely sampled. A discussion of core polarisation is also presented. This is the polarisation of core electrons as a result of their interaction with valence electrons. In the case of Curie paramagnets, core polarisation can have a significant effect on the calculation of hyperfine parameters.