This thesis presents experimental results on strongly interacting γ-Fe2O3 magnetic nanoparticles and their collective properties. The main findings are that very dense randomly packed (≈60%) γ-Fe2O3 nanoparticles form a replica of a spin glass. The magnetic properties of the nanoparticle system are in most regards the same as those of an atomic spin glass. The system is therefore proposed as a model superspin glass. In superspin glasses the interacting building blocks that form the collective state are single domain nanoparticles, superspins with a magnetic moment of about 10000 μB, which can be compared to the atomic magnetic moment in spin glasses of approximately 1 μB.  It was found that the relaxation time of the individual nanoparticles impacts the collective properties and governs the superspin dimensionality. Several dense compacts, each prepared with nanoparticles of a specific size, with diameters 6, 8, 9 and 11.5 nm, were studied. All the studied compacts were found to form a superspin glass state. Non-interacting reference samples, consisting of the same particles but coated with a silica shell, were synthesized to determine the single particle magnetic properties.  It was also found that the effects of the nanoparticle size distribution, which lead to a variation of the magnetic properties, can be mitigated by having strong enough interparticle interactions. The majority of the work was carried out using SQUID magnetometry.

An exact quantum Monte Carlo algorithm for interacting particles in the spatial continuum is extended to exploit the massive parallelism offered by graphics processing units. Its efficacy is tested on the Calogero-Sutherland model describing a system of bosons interacting in one spatial dimension via an inverse square law. Due to the long range nature of the interactions, this model has proved difficult to simulate via conventional path integral Monte Carlo methods running on conventional processors. Using Graphics Processing Units, optimal speedup factors of up to 640 times are obtained for N = 126 particles. The known results for the ground state energy are confirmed and, for the first time, the effects of thermal fluctuations at finite temperature are explored.

Amorphous transition metal oxides [aTMOs], have emerged as innovative functional materials for wide-ranging electronic, optical and energy-related applications. However, no systematic and broadly applicable method exists to assess their atomic-scale correlations, and since the optical and electronic processes are local structure-dependent, still there are not well-stablished mechanisms that suitably explain the physical properties of aTMOs. This thesis presents experimental and theoretical studies of the atomic short-range order, optical and electronic properties, and state-defects induced by Li+-ion-intercalation and oxygen-vacancies in amorphous titanium aTiO2 and tungsten aWO3 thin-film oxides. Those properties play a key role for application in high energy-density Li+-ion batteries and in switchable dynamical modulation of solar-irradiation transmittance for energy efficient "smart windows", where the disorder-dependent Li+-ion-intercalation and oxygen-vacancy-induced defect-states influence charge-carrier transfer mechanisms. After introducing the scope of this thesis, the fundamental theoretical concepts describing the experimental findings on amorphous solids are reviewed. Thereafter, a comprehensive analysis on the optical absorption phenomena experimentally observed in oxygen-deficient and Li+-ion-intercalated aLixTiO2−y and aLixWO3−y thin-films and a discussion on the electrochromic properties are presented. The optical absorption is described in the framework of the small polaron absorption model. Finally, a state-of-the-art systematic procedure involving theory and experiment in a self-consistent computational framework is implemented to unveil the atomic-scale structure of aTiO2 and aWO3, and its role for the electronic properties. The procedure is based in Reverse Monte Carlo [RMC] and Finite Difference Method [FDM] simulations of X-ray-Absorption spectra to construct a disordered theoretical model having the same bonding and coordination distribution as the experimental system. Ab-initio molecular dynamics simulations and density functional theory are then used to assess defect-states induced by Li+-ion-intercalation and oxygen-vacancies in aTiO2 and aWO3 oxides. The schemes introduced in this study offer a consistent route to experimentally and theoretically assess the role of the atomic-scale structure on the optical and electronic properties of aTiO2 and aWO3 and could be extended to the study of other aTMOs. The final results provide crucial insight towards the understanding of optical and electronic mechanisms where disorder-dependent ion-intercalation and oxygen-vacancy-induced localized defect-states influence charge transfer mechanisms of crucial importance for wide ranging optical and energy-related application of aTiO2 and aWO3 oxides.

This thesis reports the study of single photon sources that emit one infrared wavelength photon at a time, creating cavity quantum electrodynamical effects for applications such as quantum information processing. This work considers two major single photon sources: a) InAs single quantum dots and b) single carbon nanotubes, which both emit in the infrared range. Photonic crystal slabs and photonic crystal waveguides are served as distinctive passive devices with manipulated photonic band-gaps to control the propagating light. A simulation of leaky modes of two-dimensional photonic crystal slabs is introduced to constrain model parameters in the device design. Fullerenes are used as fluorescent material to achieve resonance of a leaky mode with excitation 1492 nm and emission at 1519 nm and to see enhancement of the PL. We include novel characterization techniques and PL measurements to show sharp emission peaks from single quantum dots and successfully couple them to micro-cavities. The strong coupling effect is observed and is amongst the best examples of cavity-dot structures achieved to date. Single-walled carbon nanotubes have shown anti-bunched light emission, thus we systematically study them as another possible candidate of single photon sources. PLE spectra show clear evidence of the existence of excited states, and time evolution measurements reveal the disorder induced diffusion, which separate the tubes into a series of quantum dots. These strongly confined states are concluded as the origin of the possibility that single-walled carbon nanotubes are single photon sources.

The highly parallel nature of the fundamental principles of quantum mechanics means that certain key resource-intensive tasks --- including searching, code decryption and medical, chemical and material simulations --- can be computed polynomially or even exponentially faster with a quantum computer. In spite of its remarkably fast development, the field of quantum computing is still young, and a large-scale prototype using any one of the candidate quantum bits (or 'qubits') under investigation has yet to be developed. Spin-based qubits in condensed matter systems are excellent candidates. Spins controlled using magnetic resonance have provided the first, most advanced, and highest fidelity experimental demonstrations of quantum algorithms to date. Despite having highly promising control characteristics, most physical ensembles investigated using magnetic resonance are unable to produce entanglement, a critical missing ingredient for a pure-state quantum computer. Quantum objects are said to be entangled if they cannot be described individually: they remain fundamentally linked regardless of their physical separation. Such highly non-classical states can be exploited for a host of quantum technologies including teleportation, metrology, and quantum computation. Here I describe how to experimentally create, control and characterise entangled quantum ensembles using magnetic resonance. I first explore the relationship between entanglement and quantum metrology and demonstrate a sensitivity enhancement over classical resources using molecular sensors controlled with liquid-state nuclear magnetic resonance. I then examine the computational potential of irreversible relaxation processes in combination with traditional reversible magnetic resonance control techniques. I show how irreversible processes can polarise both nuclear and electronic spins, which improves the quality of qubit initialisation. I discuss the process of quantum state tomography, where an arbitrary quantum state can be accurately measured and characterised, including components which go undetected using traditional magnetic resonance techniques. Lastly, I combine the above findings to initialise, create and characterise entanglement between an ensemble of electron and nuclear spin defects in silicon. I further this by generating pseudo-entanglement between an ensemble of nuclear spins mediated by a transient electron spin in a molecular system. These findings help pave the way towards a particular architecture for a scalable, spin-based quantum computer.

This thesis is concerned with furthering our understanding of the basis of visible region photocatalytic activity exhibited by doped TiO2-based materials. A range of experimental techniques including high resolution X-ray photoemission spectroscopy and diffuse reflectance spectroscopy are used to investigate electronic structure and an attempt is made to link these results to the observed photocatalytic activity. Both anionic (N) and cationic (Rh and Sn) dopants are investigated. [See pdf file for full abstract].

This thesis is concerned with the collective dynamics in different spin chains and spin ensembles in solid-state materials. The focus is on the manipulation of electron spins, through spin-spin and spin-photon couplings controlled by voltage potentials or electromagnetic fields. A brief review of various systems is provided to describe the possible physical implementation of the ideas, and also outlines the basis of the adopted effective interaction models. The first two ideas presented explore the collective behaviour of non-interacting spin chains with external couplings. One focuses on mapping the identical state of spin-singlet pairs in two currents onto two distant, static spins downstream, creating distributed entanglement that may be accessed. The other studies a quantum memory consisting of an array of non-interacting, static spins, which may encode and decode multiple flying spins. Both chains could effectively `enhance' weak couplings in a cumulative fashion, and neither scheme requires active quantum control. Moreover, the distributed entanglement generated can offer larger separation between the qubits than more conventional protocols that only exploit the tunnelling effects between quantum dots. The quantum memory can also `smooth' the statistical fluctuations in the effects of local errors when the stored information is spread. Next, an interacting chain of static spins with nearest-neighbour interactions is introduced to connect distant end spins. Previously, it has been shown that this approach provides a cubic speed-up when compared with the direct coupling between the target spins. The practicality of this scheme is investigated by analysing realistic error effects via numerical simulations, and from that perspective relaxation of the nearest-neighbour assumption is proposed. Finally, a non-interacting electron spin ensemble is reviewed as a quantum memory to store single photons from an on-chip stripline cavity. It is then promoted to a full quantum processor, with major error effects analysed.

Quantum mechanics has a long history of helping computer science. For a long time, it provided help only at the hardware level by giving a better understanding of the properties of matter and thus allowing the design of ever smaller and ever more efficient components. For the last few decades, much research has been dedicated to finding whether one can change computer science even more radically by using the principles of quantum mechanics at both the hardware and algorithm levels. This field of research called Quantum Information Processing (QIP) has rapidly seen interesting theoretical developments: it was in particular shown that using superposition of states leads to computers that could outperform classical ones. The experimental side of QIP however lags far behind as it requires an unprecedented amount of control and understanding of quantum systems. Much effort is spent on finding which particular systems would provide the best physical implementation of QIP concepts. Because of their nearly endless versatility and the high degree of control over their synthesis, organic materials deserve to be assessed as a possible route to quantum computers. This thesis studies the QIP potential of spin degrees of freedom in several such organic compounds. Firstly, a study on low-spin antiferromagnetic rings is presented. It is shown that in this class of molecular nanomagnets the relaxation times are much longer than previously expected and are in particular long enough for up to a few hundred quantum operations to be performed. A detailed study of the relaxation mechanisms is presented and, with it, routes to increasing the phase coherence time further by choosing the suitable temperature, isotopic and chemical substitution or solvent. A study of higher-spin systems is also presented and it is shown that the relaxation mechanisms are essentially the same as in low-spin compounds. The route to multi-qubit system is also investigated: the magnetic properties of several supermolecular assemblies, in particular dimers, are investigated. Coupling between neighbouring nanomagnets is demonstrated and experimental issues are raised concerning the study of the coherent dynamics of dimers. Finally a study of the purely organic compound phenanthrene is reported. In this molecule the magnetic moment does not result from the interactions between several transition metal ions as in molecular nanomagnets but from the photoexcitation of an otherwise diamagnetic molecule. The interest of such a system in terms of QIP is presented and relaxation times and coupling to relevant nuclei are identified.

This thesis focuses on two problems lying within the field of soft condensed matter: the viscous fingering or Saffman-Taylor instability and nematic liquid crystals in confinement. Whenever a low viscosity fluid displaces a high viscosity fluid in a porous medium, for example water pushing oil out of oil reservoirs, the interface between the two fluids is rendered unstable. Viscous fingers develop, grow and compete until a single finger spans all the way from inlet to outlet. Here, using a free energy lattice Boltzmann algorithm, we examine the Saffman-Taylor instability for two different wetting situations: (a) when neither of the two fluids wet the walls of the channel and (b) when the displacing fluids completely wets the walls. We demonstrate that curvature effects in the third dimension, which arise because of the wetting boundary conditions, can lead to a novel suppression of the instability. Recent experiments in microchannels using colloid-polymer mixtures support our findings. In the second part of the thesis we examine nematic liquid crystals confined in wedge-structured geometries. In these systems the final stable configuration of the liquid crystal system is controlled by the complex interplay between confinement, elasticity and surface anchoring. Varying the wedge opening angle this competition leads to a splay to bend transition mediated by a defect in the bulk of the wedge. Using a hybrid lattice Boltzmann algorithm we study the splay-bend transition and compare to recent experiments on {em fd} virus particles in microchannels. Our numerical results, in quantitative agreement with the experiments, enable us to predict the position of the defect as a function of opening angle, and elucidate its role in the change of director structure. This has relevance to novel energy saving, liquid crystal devices which rely on defect motion and pinning to create bistable director configurations.

Since its isolation in 2004, that resulted in the Nobel Prize award in 2010, graphene has been the object of an intense interest, due to its novel physics and possible applications in electronic devices. Graphene has many properties that differ it from usual semiconductors, for example its low-energy electrons behave like massless particles. To exploit the full potential of this material, one first needs to investigate its fundamental properties that depend on shape, number of layers, defects and interaction. The goal of this thesis is to perform such an investigation. In paper I, we study electronic transport in monolayer and bilayer graphene nanoribbons with single and many short-range defects, focusing on the role of the edge termination (zigzag vs armchair). Within the discrete tight-binding model, we perform an-alytical analysis of the scattering on a single defect and combine it with the numerical calculations based on the Recursive Green's Function technique for many defects. We find that conductivity of zigzag nanoribbons is practically insensitive to defects situated close to the edges. In contrast, armchair nanoribbons are strongly affected by such defects, even in small concentration. When the concentration of the defects increases, the difference between different edge terminations disappears. This behaviour is related to the effective boundary condition at the edges, which respectively does not and does couple valleys for zigzag and armchair ribbons. We also study the Fano resonances. In the second paper we consider electron-electron interaction in graphene quantum dots defined by external electrostatic potential and a high magnetic field. The interaction is introduced on the semi-classical level within the Thomas Fermi approximation and results in compressible strips, visible in the potential profile. We numerically solve the Dirac equation for our quantum dot and demonstrate that compressible strips lead to the appearance of plateaus in the electron energies as a function of the magnetic field. This analysis is complemented by the last paper (VI) covering a general error estimation of eigenvalues for unbounded linear operators, which can be used for the energy spectrum of the quantum dot considered in paper II. We show that an error estimate for the approximate eigenvalues can be obtained by evaluating the residual for an approximate eigenpair. The interpolation scheme is selected in such a way that the residual can be evaluated analytically. In the papers III, IV and V, we focus on the scattering on ultra-low long-range potentials in graphene nanoribbons. Within the continuous Dirac model, we perform analytical analysis and show that, considering scattering of not only the propagating modes but also a few extended modes, we can predict the appearance of the trapped mode with an energy eigenvalue close to one of the thresholds in the continuous spectrum. We prove that trapped modes do not appear outside the threshold, provided the potential is sufficiently small. The approach to the problem is different for zigzag vs armchair nanoribbons as the related systems are non-elliptic and elliptic respectively; however the resulting condition for the existence of the trapped mode is analogous in both cases. / Sedan isoleringen av grafen 2004, vilket belönades med Nobelpriset 2010, har intresset för grafen varit väldigt stort på grund av dess nya fysikaliska egenskaper med möjliga tillämpningar i elektronisk apparatur. Grafen har många egenskaper som skiljer sig från vanliga halvledare, exempelvis dess lågenergi-elektroner som beter sig som masslösa partiklar. För att kunna utnyttja dess fulla potential måste vi först undersöka vissa grundläggande egenskaper vilka beror på dess form, antal lager, defekter och interaktion. Målet med denna avhandling är att genomföra sådana undersökningar. I den första artikeln studerar vi elektrontransporter i monolager- och multilagergrafennanoband med en eller flera kortdistansdefekter, och fokuserar på inverkan av randstrukturen (zigzag vs armchair), härefter kallade zigzag-nanomband respektive armchair-nanoband. Vi upptäcker att ledningsförmågan hos zigzag-nanoband är praktiskt taget okänslig för defekter som ligger nära kanten, i skarp kontrast till armchairnanoband som påverkas starkt av sådana defekter även i små koncentrationer. När defektkoncentrationen ökar så försvinner skillnaden mellan de två randstrukturerna. Vi studerar också Fanoresonanser. I den andra artikeln betraktar vi elektron-elektron interaktion i grafen-kvantprickar som definieras genom en extern elektrostatisk potential med ett starkt magnetfält. Interaktionen visar sig i kompressibla band (compressible strips) i potentialfunktionens profil. Vi visar att kompressibla band manifesteras i uppkomsten av platåer i elektronenergierna som en funktion av det magnetiska fältet. Denna analys kompletteras i den sista artikeln (VI), vilken presenterar en allmän feluppskattning för egenvärden till linjära operatorer, och kan användas för energispektrumav kvantprickar betraktade i artikel II. I artiklarna III, IV och V fokuserar vi på spridning på ultra-låg långdistanspotential i grafennanoband. Vi utför en teoretisk analys av spridningsproblemet och betraktar de framåtskridande vågor, och dessutom några utökade vågor. Vi visar att analysen låter oss förutsäga förekomsten av fångade tillstånd inom ett specifikt energiintervall förutsatt att potentialen är tillräckligt liten.