Introduction An atom or ion in a solid is associated with a given lattice site. Translational motion can however occur in solids and such diffusion processes can be studied by nuclear magnetic resonance, tracer diffusion and other methods. In ionic compounds the diffusion is also a mechanism for charge transport and hence there is an associated ionic conductivity. [continued in text ...] NOTE: The Abstract contains many indistinct letters in mathematical formulas and it is impracticable to reproduce it here.

The production of three gauge bosons in high-energy collisions - in particular in view of a next-linear collider with center of mass energies in the TeV range - offers an unique opportunity to probe the Standard Model (SM) of today's particle physics. In this thesis we pay particular attention to the electroweak sector of the theory. We investigate the gauge structure {i. e. possible deviations from the SM predictions of gauge boson self-interactions manifest e. g. in anomalous quartic gauge boson couplings and Radiation zeros) as well as electroweak radiative corrections in order to improve theoretical predictions for SM processes. Quartic gauge boson couplings can be regarded as a direct window on the sector of electroweak symmetry breaking. We have studied the impact of three such anomalous couplings on the processes e+e(^-) → WWγ, ZZγ and Zγγ at LEP2 and a future linear collider. In certain high-energy scattering processes involving charged particles and the emission of one or more photons, the scattering amplitude vanishes for particular configurations of the final state particles. The fact that gauge symmetry is a vital ingredient for the cancellation to occur means that radiation zeros can be used to probe physics beyond the standard model. For example anomalous electroweak gauge boson couplings destroy the delicate cancellation necessary for the zero to occur. We have studied the process qq → WWγ. To match the expected experimental precision at future linear colliders, improved theoretical predictions beyond next-to-leading order are required. By choosing an appropriate gauge, we have developed a formalism to calculate such corrections for arbitrary electroweak processes. As an example we consider here the processes e(^+)e → f f and e(^+)e(^-) → W(^+)(_T)W(^-)(_T), W(^+)(_L)W(^-)(_L) and study the perturbative structure of the electroweak Sudakov logarithms by means of an explicit two-loop calculation. In this way we investigate how the Standard Model, with its mass gap between the photon and Z boson in the neutral sector, compares to unbroken theories like QED and QCD. We observe that the two-loop corrections are consistent with an exponentiation of the one-loop corrections. In this sense the Standard Model behaves like an unbroken theory at high energies.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 142-151).

Mott insulators are a family of materials in which strong electron-electron interactions induce an unconventional insulating state in the system that would otherwise behave as an electrical conductor according to the non-interacting band theory. In particular, the nature of the Mott metal-insulator transition (MIT) has been the subject of intense research interest because it can involve a complicated interplay between magnetic and electronic properties. In some Mott systems, Mott transitions occur in the one-step process, from an antiferromagnetic insulator (AFI) to a paramagnetic metal phase (PMM), while in other Mott systems a two-step transition with an intermediate antiferromagnetic metal (AFM) phase can be observed. Since 2015, the muon spin relaxation (𝜇SR) group at Columbia University started systematic 𝜇SR studies on a series of Mott systems, including one-step transition Mott systems 𝑅𝐸NiO₃ and V₂O₃, as well as two-step transition Mott systems Ba(Co, Ni)S₂, Ni(S, Se)₂ and (La, Sr)VO₃. This dissertation first introduces the comprehensive 𝜇SR research on multiple families of Mott systems conducted by our 𝜇SR group, including 𝑅𝐸NiO₃, V₂O₃, and BaCoS₂. Then the 𝜇SR experimental findings on the Mott system NiS₂₋ₓSeₓ will be presented, which is the most extensively studied material in this thesis. The NiS₂₋ₓSeₓ system is of particular interest because there is a large region of intermediate AFM state emerging between AFI and PMM states with Se doping, making it an ideal platform to provide information on static magnetism in the AFM state and thus can help us better understand the evolution of magnetic NiS₂₋ₓSeₓ, with our key findings being: (1) The AFM state of the NiS₂₋ₓSeₓ system shows significantly random spin correlations, and the magnetic order is suppressed by a gradual reduction of the ordered moment size, with a nearly full ordered volume fraction until very close to the AFM-PMM boundary. (2) No signature of dynamic critical behavior was observed in the thermal phase transition, indicating a first-order thermal phase transition. The next part of this dissertation presents our computational simulations on the NiS₂₋ₓSeₓ system. Dipolar field simulations have shown that only the combination of easy axis randomization and Ni moment dilution in NiS₂ can lead to the internal field distribution corresponding to the observed 𝜇SR spectrum in the AFM region. Also, this picture could qualitatively explain the neutron and muon results consistently, thus reconciling the seemingly contradicting experimental results by 𝜇SR and the previous neutron scattering studies shown in the AFM region. Furthermore, we propose a percolation model that can capture both the charge and spin connections of the interpenetrating percolating spin and charge networks in the NiS₂₋ₓSeₓsystem, which raises the possibility of "compromising metallicity and magnetic order" in the two-step Mott transition evolving AFI to AFM to PMM states in NiS₂₋ₓSeₓ.

In recent years there has been significant work aimed at understanding what effect the variation of electronic doping has on material properties. In the high transition-temperature (high-T$_c$) cuprate superconductors hole doping has an impact on the superconducting transition temperature. In the underdoped regime, the cuprates exhibit anomalous properties due to a pseudogap which forms and is thought to be related to Mott insulating physics. While there is no general consensus as to the mechanism underlying high temperature superconductivity, the resonating valence bond (RVB) theory proposed by Anderson in 1987 with a Gutzwiller projected d-wave BCS wave function could give a first picture of the high-T$_c$ cuprates. We have calculated properties of the cuprates using the assumption that the pseudogap state acts as a normal state to an otherwise standard BCS mean field theory. We find that the phenomenological RVB spin liquid model proposed by Yang, Rice and Zhang (YRZ) is highly successful at describing the doping dependent features of the cuprates. Through application of the YRZ model and the tools of many-body theory we present results on anomalous properties observed in: electronic specific heat; Raman and angle-resolved photoemission spectroscopy (ARPES) data; effective mass renormalization; and thermal broadening seen in ARPES. We verify that the YRZ ansatz qualitatively describes these anomalies along with their doping dependent variations. We conclude from this work that the physics underlying the pseudogap, while distinct in origin from superconductivity, is likely to arise from an RVB wavefunction that is closely related to the BCS state. In graphene, variation in doping modifies the polarization function which describes a screened electron-electron interaction. This leads to additional features in the spectral function which are due to electron-plasmon coupling. In this work, we calculated the electronic density of states including this interaction along with its doping dependence with and without an electron-phonon interaction. We find clear features of electron-electron interactions in the density of states. These features are related to the energies of plasmaron bands in the spectral function and can be modified through doping so as to be distinct from the phonon energy scales.

Le présent travail se concentre sur l'étude des niveaux d'énergie et des processus de recombinaison de complexes excitoniques larges - jusqu'à quatre paires électron-trou - considérés au niveau d'une boîte quantique unique remplie optiquement. Les boîtes étudiées dans ces expériences, formées à partir d'une matrice de Ga(Al)As, représentent un système à zéro dimension avec un confinement relativement fort et peuvent en effet avoir plusieurs couches électroniques s, p, comme dans le cas d'atomes. Les boîtes peuvent être facilement sélectionnées à l'état individuel du fait de la très faible densité de surface des structures considérées. Les techniques expérimentales utilisée dans ce travail comprennent : les méthodes de spectroscopie sur boîtes uniques, la détection optique résolue en polarisation, l'utilisation de champs magnétiques intenses et des mesures de corrélation de photons. En ce qui concerne les expériences de photoluminescence, nous avons distingué les excitations en dessous de la barrière de celles se produisant en dessus. Finalement, des expériences de spectroscopie d'excitation de la photoluminescence ont aussi été réalisées en champ magnétique.En fonction des conditions d'excitation, les boîtes étudiées présentent une multitude de raies relativement étroites, chaque boîte révélant un schéma caractéristique de raies groupées en amas distincts, similaires à une série de couches électroniques pour un atome. La présente étude s'est concentrée sur l'intervalle spectral correspondant aux couches électroniques s et p. L'identification des raies spectrales s'est principalement basé sur les résultats obtenus lors d'observations résolues en polarisation ou bien lors de mesures de corrélation de photons. Ces expériences révèlent trois familles distinctes de raies d'émission, chacune étant respectivement reliée à un complexe électron-trou (excitonique) neutre, chargé positivement, ou bien négativement. Une attention particulière a été portée aux raies d'émission observées dans une cascade en quatre étapes partant d'un complexe à quatre excitons, jusqu'au niveau de la recombinaison d'un exciton neutre, ainsi que celles observées dans une cascade en deux étapes partant d'un bi-exciton chargé positivement, jusqu'à la recombinaison d'un état singulet ou triplet d'un exciton chargé positivement. La structure fine induite par les interactions d'échange - et préalablement observée lors des mesures résolues en polarisation à champ magnétique nul - a été étudiée pour différentes raies d'émission. L'évolution de ce dédoublement de raies a été examiné en fonction du champ magnétique. Les résultats sont interprétés en terme d'anisotropie de forme des boîtes et d'une interaction avec les effets spin-orbite, caractéristiques des différents processus de recombinaison. Une partie importante de ce travail a été dévolue à la comparaison entre le spectre d'émission mesuré pour des puissances d'excitations relativement importantes avec les spectres d'excitation de la photoluminescence. De telles expériences ont aussi été conduites sous champ magnétique. Comme attendu, les spectres d'émission des complexes excitoniques d'ordres élevés sont particulièrement affectés par les interactions coulombiennes entre porteurs, et sont par conséquent très différents des spectres d'excitation de la photoluminescence (quasi-absorption) des excitons neutre et chargés. Deux types d'évolution en champ magnétique de raies d'absorption observées (résonance) - reliées aux couches s et p - ont été mesurés. Les résonances de type s sont attribuées à la transition entre un niveau excité de trou de la bande de valence et l'état fondamental de la couche s dans la bande de conduction. Une raie d'émission, observée dans le groupement de la couche p, coïncide cependant avec la raie d'absorption. Nous concluons que cette résonance vient d'un état excitonique excité qui se recombine de manière radiative dû à un blocage efficace de sa relaxation vers l'état fondamental. / The studies of energy levels and of recombination processes of single quantum dots, optically filled with up to four electron-hole pairs are the subject of this work. The dots used in the present experiments, formed out of the Ga(Al)As matrix, represent relatively strongly confined zero-dimensional systems, and display several, atomic-like s-, p-,. . . shells. Single dots can be easily selected in our structures as they exhibit an extremely low surface density. Experimental techniques applied in this work include the methods of single dot spectroscopy, polarization resolved techniques, application of magnetic fields and photon correlation measurements. Distinct, below- and above-dot-barrier laser excitation has been used for photoluminescence experiments. Importantly, the photoluminescence excitations experiments (in magnetic fields) have been carried out, as well.Depending on excitation conditions (power and wavelength of laser), the investigated dots show a multitude of relatively sharp lines, each dot displaying the same, characteristic pattern of lines, grouped into distinct clusters corresponding to subsequent atomic-like shells. Spectral range covering the s- and p-shells region has been explored in the present studies. The assignment of spectral lines has been at large provided by the results of polarization resolved micro-photoluminescence and photon correlation experiments. Those experiments depict three distinct families of emission lines, each related to recombination of, correspondingly, neutral, positively charged and negatively charged electron-hole (excitonic) complexes. The emission lines observed within a four step cascade of a neutral quadexciton down to the recombination of a neutral exciton and two step cascades of positively charged biexcitons down to the recombination of a singlet and triplet state of positively charged excitons have been studied in details. The fine structure, induced by exchange interactions and preliminarily seen in (linear) polarization resolved emission experiment at zero magnetic field, has been studied for various emission lines (related to s- and p- shells). The evolution of this splitting has been then investigated as a function of the magnetic field. The results are interpreted in terms of the shape anisotropy of dots and an interplay between spin- and orbital-mediated effects, characteristic of different recombination processes. A significant portion of this work has aimed to compare the emission spectra measured at a relatively high excitation power (which include the recombination processes of up to quadexciton complexes) with photoluminescence excitation spectra (which probe the excited states of a single exciton). Such experiments have been also carried out as a function of the magnetic field. As expected the emission spectra of high order excitonic complexes are indeed greatly affected by Coulomb interactions between carriers and in consequence are in general very different from the photoluminescence excitation spectra (quasi absorption) of a neutral and charged exciton. Two types of the magnetic field evolution of detected absorption lines (resonant peaks), the s- and p-shell related, have been measured. The s-shell like resonant peaks were attributed to the transition between the excited hole levels in the valence band and the ground s-shell level in the conduction band. Nevertheless, there exists an emission line which is observed within the p-shell cluster, and which coincides with the absorption line. That "coinciding resonance" is concluded to be an excited excitonic state which recombines radiatively due to efficient blocking of its relaxation towards the ground state.

L'effet Hall quantique, qui apparaît dans les gaz d'électrons bidimensionnels soumis à un champ magnétique perpendiculaire et à basses températures, a été un sujet de recherche intense pendant les derniers trente ans, en particulier, à cause des manifestations spectaculaires de la mécanique quantique dans les propriétés de transport à l'échelle macroscopique. Dans cette thèse, on étend l'horizon de la recherche au niveau théorique sur ce sujet en considérant les effets du couplage spin-orbite et l'interaction électron-électron de façon analytique dans ce régime.Dans la première partie de ce manuscrit, on considère l'effet simultané du couplage spin-orbite de type Rashba et l'interaction Zeeman dans le régime de l'effet Hall quantique entier. Pour cela, on étend un formalisme de fonctions de Green basé sur des états de vortex cohérents avec l'objectif d'inclure le couplage entre les degrés de liberté orbitaux et de spin dans les états de dérive électroniques. Puis, comme première application, on montre comment obtenir analytiquement, nonperturbativement et de manière contrôlée des fonctionnelles quantiques (spectre et densité d'états locale) pour des potentiels électrostatiques arbitraires et localement plats. Les fonctionnelles sont ensuite analysées dans différents régimes de températures et comparées aux données expérimentales obtenues à partir des sondes de spectroscopie locales. Comme seconde mise en pratique du formalisme, on étudie en profondeur les propriétés de transport de charge et de spin dans un régime hydrodynamique d'équilibre local (ou quasi-équilibre) et dérive des expressions analytiques qui incorporent les caractères non-relativiste et relativiste des gaz d'électrons avec couplage spin-orbite de type Rashba.Dans la deuxième partie de cette thèse, on s'occupe du problème de traiter analytiquement les fortes interactions électron-électron dans le régime de l'effet Hall quantique fractionnaire. A cette fin, on étudie un problème à deux corps généralisé avec du désordre et des corrélations électroniques, en utilisant une nouvelle représentation d'états de vortex cohérents. Des corrélations à longue portée entre les particules sont incorporées de manière topologique à travers la présence d'une métrique non-Euclidienne. Subséquemment, on montre que ces états de vortex forment bien une base d'un espace de Hilbert élargi, puis on dérive l'équation du mouvement pour la fonction de Green. Enfin, on vérifie la consistance de notre théorie pour tout niveau de Landau de paire et on discute la nécessité d'aller au-delà de la limite semiclassique (à champ magnétique infinie) pour obtenir des gaps dans chaque niveau de énergie. / The quantum Hall effect, appearing in disordered two-dimensional electron gases under strong perpendicular magnetic fields and low temperatures, has been a subject of intense research during the last thirty years due to its very spectacular macroscopic quantum transport properties. In this thesis, we expand the theoretical horizon by analytically considering the effects of spin-orbit coupling and strong electron-electron interaction in these systems.In the first part of the manuscript, we examine the simultaneous effect of Rashba spin-orbit and Zeeman interaction in the integer quantum Hall regime. Under these conditions, we extend a coherent-state vortex Green's function formalism to take into account the coupling between orbital and spin degrees of freedom within the electronic drift states. As a first application of this framework, we analytically compute controlled microscopic nonperturbative quantum functionals, such as the energy spectrum and the local density of states, in arbitrary locally flat electrostatic potential landscapes, which are then analyzed in detail in different temperature regimes and compared to scanning tunnelling experimental data. As a second application, we thoroughly study local equilibrium charge and spin transport properties and derive analytical useful formulas which incorporate the mixed non-relativistic and relativistic character of Rashba-coupled electron gases.In the second part of this thesis, we deal with the problem of analytically incorporating strong electron-electron interactions in the fractional quantum Hall regime. To this purpose, we consider a generalized two-body problem where both disorder and correlations are combined and introduce a new vortex coherent-state representation of the two-body states that naturally include long-range correlations between the electrons. The novelty of this theory is that correlations are topologically built in through the non-Euclidean metric of the Hilbert space. Next, we show that this kind of vortex states form a basis of an enlarged Hilbert space and derive the equation of motion for the Green's function in this representation. Finally, we check the consistency of our approach for any Landau level of the pair and discuss the necessity of going beyond the semiclassical (infinite magnetic field) approximation to obtain energy gaps within each energy level.

Orientadores: Peter A. B. Schulz, John T. Chalker / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-06T19:00:22Z (GMT). No. of bitstreams: 1 Pereira_AnaLuizaCardoso_D.pdf: 2880300 bytes, checksum: ffd133973b4bc6e23c91694bc47d8794 (MD5) Previous issue date: 2005 / Resumo: Esse trabalho é dedicado ao estudo de dois problemas de interesse atual em sistemas quânticos de baixa dimensionalidade. Ambos são relacionados ao processo de localização eletrônica no regime Hall quântico. O primeiro problema diz respeito ao destino dos estados estendidos no limite de baixos campos magnéticos ou forte desordem, onde ocorre a transição de líquido de Hall para o isolante de Hall. O problema é abordado através de simulações numéricas, com um modelo de rede bidimensional tratado por um Hamiltoniano tight-binding, considerando-se tanto desordem tipo ruído branco quanto desordem correlacionada com perfil Gaussiano. Nós observamos que à medida que o campo magnético tende a zero ou a desordem é suficientemente aumentada no sistema, os estados estendidos sofrem um deslocamento em relação ao centro das bandas de Landau, indo em direção às mais altas energias e, eventualmente, ultrapassando a energia de Fermi. Esse mecanismo é chamado na literatura de levitação de estados estendidos. Nossos resultados permitem uma análise quantitativa. Identificamos os seguintes parâmetros como sendo os relevantes para mapear a levitação: (i) a razão entre escalas de energia ¿ entre a energia de separação dos níveis de Landau e o alargamento do nível devido à desordem; e (ii) a razão entre escalas de comprimento ¿ entre o comprimento magnético e o comprimento de correlação da desordem. Analisando uma vasta gama de parâmetros, uma expressão de escala descrevendo a levitação de estados estendidos é estabelecida neste trabalho. O segundo problema abordado nesta tese é relacionado ao processo de blindagem do potencial de desordem e ao mecanismo de formação dos estados localizados em sistemas Hall quânticos. O trabalho analítico apresentado aqui é motivado por recentes resultados experimentais, que mostram imagens de microscopia com medidas locais do potencial eletrostático e da compressibilidade desses sistemas, evidenciando como se dá o processo de carga de estados localizados por cargas inteiras ou fracionárias (quase-partículas). Em um regime onde o comportamento é dominado por interações Coulombianas, estabelecemos um modelo eletrostático que descreve o estado localizado como sendo uma região compressível (quantum dot ou antidot) envolta por um plano incompressível, usando a aproximação de Thomas-Fermi para tratar as interações. O potencial eletrostático nas vizinhanças da região compressível é calculado, fornecendo o tamanho dos saltos que ocorrem no potencial à medida que cada carga é adicionada ou removida do estado localizado. Além de mostrar como estes saltos se tornam menores com o aumento do índice de Landau, nossos resultados mostram a dependência deles com a altura de observação do potencial (ou seja, a altura da ponta de prova em relação ao gás de elétrons). O modelo apresentado pode ser usado para tratar estados localizados observados nos platôs do efeito Hall quântico inteiro ou fracionário / Abstract: This work is devoted to the study of two problems of current interest in low dimensional quantum systems. Both are related to the process of electron localization in the quantum Hall regime. The first problem refers to the fate of extended states in the limit of low magnetic fields or strong disorder, where the transition from quantum Hall liquid to Hall insulator takes place. A numerical approach to the problem is used, with a 2D lattice model treated in a tight-binding framework, considering both white-noise and Gaussian correlated disorder. We observe that as the magnetic field vanishes or the disorder is sufficiently increased in the system, the extended states are shifted from the Landau band centers, going to higher energies and, eventually, rising above the Fermi energy. This mechanism is referred in the literature as levitation of extended states. Our results allow a quantitative analysis. We identify the following parameters as the relevant ones to map the levitation: (i) the energy scales ratio - between the energy separation of consecutive Landau levels and the level broadening due to disorder; and (ii) the length scales ratio - between the magnetic length and the disorder correlation length. Analyzing a wide range of parameters, a scaling expression describing the levitation of extended states is established. The second problem considered in this thesis is related to the screening of the disorder potential and to the mechanism of formation of localized states in quantum Hall systems. The analytical work we present here is motivated by recent imaging experiments, which probe locally the electrostatic potential and the compressibility of these systems, showing the charging of individual localized states by integer or fractional charges (quasiparticles). For a regime where the behavior is dominated by Coulomb interactions, we set out an electrostatic model describing the localized state as a compressible region (quantum dot or antidot) embebed in an incompressible background, using the Thomas-Fermi approximation to treat the interactions. The electrostatic potential in the vicinity of the compressible region is calculated, providing the size of potential steps as each charge is added or removed from the localized state. Besides from showing how the potential steps get smaller for higher Landau levels, our results show the dependence of these steps with the height of observation (i.e., the distance from the scanning probe to the electron gas). The proposed model can be used to treat localized states observed on integer or fractional quantum Hall plateaus / Doutorado / Física da Matéria Condensada / Doutor em Ciências

We present the development of a novel, UHV-compatible device fabrication strategy for the realisation of nano- and atomic-scale devices in silicon by harnessing the atomic-resolution capability of a scanning tunnelling microscope (STM). We develop etched registration markers in the silicon substrate in combination with a custom-designed STM/ molecular beam epitaxy system (MBE) to solve one of the key problems in STM device fabrication ??? connecting devices, fabricated in UHV, to the outside world. Using hydrogen-based STM lithography in combination with phosphine, as a dopant source, and silicon MBE, we then go on to fabricate several planar Si:P devices on one chip, including control devices that demonstrate the efficiency of each stage of the fabrication process. We demonstrate that we can perform four terminal magnetoconductance measurements at cryogenic temperatures after ex-situ alignment of metal contacts to the buried device. Using this process, we demonstrate the lateral confinement of P dopants in a delta-doped plane to a line of width 90nm; and observe the cross-over from 2D to 1D magnetotransport. These measurements enable us to extract the wire width which is in excellent agreement with STM images of the patterned wire. We then create STM-patterned Si:P wires with widths from 90nm to 8nm that show ohmic conduction and low resistivities of 1 to 20 micro Ohm-cm respectively ??? some of the highest conductivity wires reported in silicon. We study the dominant scattering mechanisms in the wires and find that temperature-dependent magnetoconductance can be described by a combination of both 1D weak localisation and 1D electron-electron interaction theories with a potential crossover to strong localisation at lower temperatures. We present results from STM-patterned tunnel junctions with gap sizes of 50nm and 17nm exhibiting clean, non-linear characteristics. We also present preliminary conductance results from a 70nm long and 90nm wide dot between source-drain leads which show evidence of Coulomb blockade behaviour. The thesis demonstrates the viability of using STM lithography to make devices in silicon down to atomic-scale dimensions. In particular, we show the enormous potential of this technology to directly correlate images of the doped regions with ex-situ electrical device characteristics.

We present the development of a novel, UHV-compatible device fabrication strategy for the realisation of nano- and atomic-scale devices in silicon by harnessing the atomic-resolution capability of a scanning tunnelling microscope (STM). We develop etched registration markers in the silicon substrate in combination with a custom-designed STM/ molecular beam epitaxy system (MBE) to solve one of the key problems in STM device fabrication ??? connecting devices, fabricated in UHV, to the outside world. Using hydrogen-based STM lithography in combination with phosphine, as a dopant source, and silicon MBE, we then go on to fabricate several planar Si:P devices on one chip, including control devices that demonstrate the efficiency of each stage of the fabrication process. We demonstrate that we can perform four terminal magnetoconductance measurements at cryogenic temperatures after ex-situ alignment of metal contacts to the buried device. Using this process, we demonstrate the lateral confinement of P dopants in a delta-doped plane to a line of width 90nm; and observe the cross-over from 2D to 1D magnetotransport. These measurements enable us to extract the wire width which is in excellent agreement with STM images of the patterned wire. We then create STM-patterned Si:P wires with widths from 90nm to 8nm that show ohmic conduction and low resistivities of 1 to 20 micro Ohm-cm respectively ??? some of the highest conductivity wires reported in silicon. We study the dominant scattering mechanisms in the wires and find that temperature-dependent magnetoconductance can be described by a combination of both 1D weak localisation and 1D electron-electron interaction theories with a potential crossover to strong localisation at lower temperatures. We present results from STM-patterned tunnel junctions with gap sizes of 50nm and 17nm exhibiting clean, non-linear characteristics. We also present preliminary conductance results from a 70nm long and 90nm wide dot between source-drain leads which show evidence of Coulomb blockade behaviour. The thesis demonstrates the viability of using STM lithography to make devices in silicon down to atomic-scale dimensions. In particular, we show the enormous potential of this technology to directly correlate images of the doped regions with ex-situ electrical device characteristics.