No presente estudo, amostras policristalinas ricas em Ta e com estequiometrias Ta1-xZrx; x < 0.15; foram preparadas através da mistura apropriada dos elementos metálicos, os quais foram fundidos em forno a arco elétrico sobre uma placa de cobre refrigerada a água e sob atmosfera de argônio de alta pureza. Os padrões de difração de raios-X das ligas, como fundidas (as cast) e tratadas termicamente a 850 °C por 24 h, revelaram a ocorrência de uma estrutura cristalina cúbica de corpo centrada bcc, tipo W, e parâmetros de rede que aumentam suavemente com o aumento do teor de Zr nas ligas. Medidas de susceptibilidade magnética dc, conduzidas nas condições de resfriamento da amostra em campo zero (ZFC) e do resfriamento com o campo magnético aplicado (FC), indicaram que supercondutividade volumétrica é observada abaixo de ~ 5.8, 6.9, 7.0 K em amostras com x = 0.05, 0.08, e 0.10, respectivamente. Essas temperaturas críticas supercondutoras são bastante superiores àquela observada no Ta elementar ~ 4.45 K. Medidas de resistividade elétrica na presença de campos magnéticos aplicados de até 9 T confirmaram a temperatura crítica supercondutora das amostras estudadas. O campo crítico superior Hc2 e o comprimento de coerência E foram estimados a partir dos dados de magnetorresistência. Os valores estimados de Hc2 foram de ~ 0.46, 1.78, 3.85 e 3.97 T, resultando em valores de E ~ 26.0, 13.6, 9.2 e 9.1 nm para as ligas as cast com x = 0.00, 0.05, 0.08 e 0.10, respectivamente. A partir dos dados experimentais do calor específico Cp das ligas, magnitudes estimadas do salto em Cp nas vizinhanças das transições supercondutoras indicaram valores maiores que o previsto pela teoria BCS. Utilizando as equações analíticas derivadas da teoria do acoplamento forte da supercondutividade foi então proposto que o aumento da temperatura de transição supercondutora nas ligas devido a substituição parcial do Ta por Zr está intimamente relacionado ao aumento do acoplamento elétron-fônon, visto que a densidade de estados eletrônicos no nível de Fermi foi estimada ser essencialmente constante através da série Ta1-xZrx com x < 0.10. / In the present study, polycrystalline samples of Ta-rich binary alloys with stoichiometry Ta1-xZrx; x < 0.15; were prepared by mixing appropriate amounts of the metallic elements which were arc-melted on a water-cooled hearth under high-purity argon atmosphere. The X-ray diffraction patterns of the as cast alloys and heat treated ones at 850 °C by 24 h revealed the occurrence of the body-centered cubic crystal structure bcc, type W, and lattice parameters that increase slightly with increasing Zr content. Magnetic susceptibility measurements dc, performed in zero-field cooling ZFC and field cooling FC processes, indicated that bulk superconductivity is observed below ~ 5.8, 6.9, and 7.0 K, in samples with x = 0.05, 0.08, and 0.10, respectively. These superconducting critical temperatures are higher than that of ~ 4.45 K found in elemental Ta. Electrical resistivity measurements under applied magnetic fields to 9 T corroborated the superconducting critical temperatures for the samples studied. The thermodynamic upper critical field Hc2 and the coherence length E were estimated from the magnetoresistance data. The estimated values of Hc2 were 0.46, 1.78, 3.85, and 3.97 T, leading to E 26.0, 13.6, 9.2, and 9.1 nm for the as cast alloys with x = 0.00, 0.05, 0.08, and 0.10, respectively. In addition to this, from the results of heat capacity Cp data, jumps in the vicinity of the superconducting transition were estimated and found to be larger than the one expected from the BCS theory. By using analytic equations derived from the strong coupling theory of superconductivity we argued that the enhancement of Tc in alloying Ta with Zr is due to the increase of the electron-phonon coupling, provided that the density of states in the Fermi level was found to be essentially constant in the series Ta1-xZrx; x < 0.10.

Lo Loc Ping = 多體量子系統問題 / 盧樂平. / Thesis submitted in: October 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 168-171). / Text in English; abstracts in English and Chinese. / Lo Loc Ping = Duo ti liang zi xi tong wen ti / Lu Leping. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgment --- p.iii / Chapter I --- Computational Quantum Mechanics and Its Applications 電算量子力學及其應用 --- p.1 / Chapter 1 --- An Overview of Quantum Mechanics and Some Important Tools of Theory --- p.2 / Chapter 1.1 --- The Schrodinger Equation --- p.2 / Chapter 1.2 --- The Variational Method --- p.4 / Chapter 1.2.1 --- Rayleigh-Ritz Approach --- p.4 / Chapter 1.2.2 --- Linear Variation --- p.5 / Chapter 2 --- Theoretical Methodology of Electronic Structures: Ab Initio Molecular Orbital Theory --- p.7 / Chapter 2.1 --- The Molecular Hamiltonian --- p.7 / Chapter 2.2 --- Hartree Description and Linear Combination of Atomic Orbitals Expan- sion --- p.8 / Chapter 2.3 --- Slater Determinant and the Pauli Exclusion Principle --- p.9 / Chapter 2.4 --- The Expansion of E in Terms of Integrals over MOs --- p.11 / Chapter 2.5 --- Derivation of the Hartree´ؤFock Equations --- p.15 / Chapter 2.6 --- The Self-Consistent Field Calculation --- p.18 / Chapter 2.7 --- Koopmans' Theorem --- p.19 / Chapter 2.8 --- Orbital and the Total SCF Electronic Energy --- p.20 / Chapter 2.9 --- AO Basic Sets --- p.21 / Chapter 2.9.1 --- Slater-Type Orbitals --- p.21 / Chapter 2.9.2 --- Gaussian Functions --- p.22 / Chapter 2.10 --- The Hartree-Fock Limit --- p.23 / Chapter 2.11 --- Electron Correlation --- p.23 / Chapter 2.11.1 --- Weakness in the Single Determinant Model --- p.23 / Chapter 2.11.2 --- Configuration Interaction --- p.24 / Chapter 2.11.3 --- The Coupled-Cluster Method --- p.25 / Chapter 2.11.4 --- Density Functional Theory --- p.26 / Chapter 2.12 --- Frontier Orbitals --- p.31 / Chapter 3 --- Theoretical Investigation of the Interaction between Metal and Tris(8- hydroxyquinoline) aluminum in Organic Light Emitting Diodes --- p.32 / Chapter 3.1 --- Organic Light Emitting Diodes and Tris(8-hydro-xyquinoline) aluminum --- p.32 / Chapter 3.2 --- Computational Methodology --- p.33 / Chapter 3.3 --- Alq3 --- p.34 / Chapter 3.3.1 --- Molecular Structure --- p.34 / Chapter 3.3.2 --- Electronic Structure --- p.36 / Chapter 3.3.3 --- Transition and Relaxation Energies --- p.44 / Chapter 3.3.4 --- Interactions with Metals --- p.45 / Chapter 3.4 --- "Li-Alq3, Na-Alq3 and K-Alq3 Complexes" --- p.46 / Chapter 3.4.1 --- Molecular Structure --- p.46 / Chapter 3.4.2 --- Ground-State Electronic Structure --- p.55 / Chapter 3.4.3 --- Transition and Relaxation Energies --- p.67 / Chapter 3.5 --- "Be-Alq3, Mg´ؤAlq3 and Ca´ؤAlq3 Complexes" --- p.68 / Chapter 3.5.1 --- Molecular Structure --- p.68 / Chapter 3.5.2 --- Ground-State Electronic Structure --- p.76 / Chapter 3.5.3 --- Transition and Relaxation Energies --- p.87 / Chapter 3.6 --- "B-Alq3, Al-Alq3 and Ga-Alq3 Complexes" --- p.87 / Chapter 3.6.1 --- Molecular Structure --- p.87 / Chapter 3.6.2 --- Ground-State Electronic Structure --- p.95 / Chapter 3.6.3 --- Transition and Relaxation Energies --- p.106 / Chapter II --- Analytical Studies of Polarons and the Electron-Phonon Interaction 極子與電子一聲子相互作用的 解析研究 --- p.107 / Chapter 4 --- Optimal Coupled-Cluster Approximation of the Ground-State Energy of the E× (α1 + α1) Jahn-Teller System --- p.108 / Chapter 4.1 --- The Jahn-Teller Effect --- p.108 / Chapter 4.2 --- Approximation in the Coupled-Cluster Method and the Jahn-Teller Hamiltonian --- p.110 / Chapter 4.3 --- Variational Coupled-Cluster Approximation --- p.112 / Chapter 4.3.1 --- The Zeroth Level --- p.113 / Chapter 4.3.2 --- The First Level --- p.113 / Chapter 4.3.3 --- The Second and the Third Levels --- p.114 / Chapter 4.4 --- An 'Optimal' Hamiltonian --- p.115 / Chapter 4.5 --- Treatment for the k> 1 Case --- p.117 / Chapter 4.6 --- Energies and Other Physical Phenomena --- p.118 / Chapter 5 --- Small-to-Large Ground-State Polaron Crossover in One-Dimension Extended E×e Jahn-Teller System Using Variational Coupled-Cluster Approximation --- p.134 / Chapter 5.1 --- Polaron Formation --- p.134 / Chapter 5.2 --- Model Hamiltonian and the MLF Transformation --- p.135 / Chapter 5.3 --- Variatonal Coupled-Cluster Approximation --- p.137 / Chapter 5.3.1 --- Zeorth Level --- p.139 / Chapter 5.3.2 --- First Level --- p.139 / Chapter 5.3.3 --- Second Level --- p.142 / Chapter 5.4 --- Energies and Static Correlation Functions --- p.142 / Chapter 5.5 --- Approximate Form of the MLF Transformation for K = 0 --- p.153 / Chapter 5.5.1 --- Zeroth Level --- p.154 / Chapter 5.5.2 --- First Level --- p.155 / Chapter 5.5.3 --- Second Level --- p.156 / Chapter 5.5.4 --- Energies and Static Correlation Functions --- p.157 / Chapter 5.6 --- Synopsis --- p.167 / Bibliography --- p.171

Yeung Man Yi = 多體量子系統問題 / 楊曼儀. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves [247-249]). / Text in English; abstracts in English and Chinese. / Yeung Man Yi = Duo ti liang zi xi tong wen ti / Yang Manyi. / Abstract --- p.i / Acknowledgment --- p.iii / Chapter I --- Computational Quantum Mechanics and Its Applications / 電算量子力學及其應用 --- p.1 / Chapter 1 --- Theoretical Methodology of Electronic Structures: Ab Initio Molecular Orbital Theory --- p.2 / Chapter 1.1 --- Molecular Hamiltonian --- p.2 / Chapter 1.2 --- Hartree Products --- p.5 / Chapter 1.3 --- Slater Determinants and Pauli Exclusion Principle --- p.6 / Chapter 1.4 --- Expansion of Total Electronic Energy in terms of Integrals over MOs --- p.8 / Chapter 1.5 --- Derivation of the Hartree-Fock Equations --- p.11 / Chapter 1.6 --- Orbital Energies and the Koopmans' Theorem --- p.14 / Chapter 1.7 --- AO Basic Sets --- p.17 / Chapter 1.7.1 --- Slater-Type Orbitals --- p.18 / Chapter 1.7.2 --- Gaussian Functions --- p.18 / Chapter 1.8 --- Self-Consistent Field Calculation --- p.19 / Chapter 1.9 --- Hartree-Fock Limit --- p.20 / Chapter 1.10 --- Electron Correlation --- p.20 / Chapter 1.10.1 --- Configuration Interaction --- p.20 / Chapter 1.10.2 --- Density Functional Theory --- p.21 / Chapter 2 --- Theoretical Investigation of Organic Light Emitting Molecules --- p.29 / Chapter 2.1 --- Introduction --- p.29 / Chapter 2.2 --- Methodology --- p.31 / Chapter 2.2.1 --- Theoretical Methodology --- p.31 / Chapter 2.2.2 --- Computational Methodology --- p.35 / Chapter 2.3 --- ADN series --- p.35 / Chapter 2.3.1 --- Molecular Structure --- p.36 / Chapter 2.3.2 --- Electronic Structure --- p.49 / Chapter 2.3.3 --- Absorption and Emission Energy --- p.55 / Chapter 2.3.4 --- Reorganization Energy --- p.56 / Chapter 2.3.5 --- Mobility --- p.57 / Chapter 2.3.6 --- Summary on ADN series --- p.66 / Chapter 2.4 --- XOT series --- p.67 / Chapter 2.4.1 --- Molecular Structure --- p.68 / Chapter 2.4.2 --- Electronic Structure --- p.89 / Chapter 2.4.3 --- Absorption and Emission Energy --- p.96 / Chapter 2.4.4 --- Reorganization Energy and Mobility --- p.98 / Chapter 2.4.5 --- Summary on XOT series --- p.100 / Chapter 2.5 --- KPA series --- p.102 / Chapter 2.5.1 --- Molecular Structure --- p.102 / Chapter 2.5.2 --- Electronic Structure --- p.123 / Chapter 2.5.3 --- Absorption and Emission Energy --- p.131 / Chapter 2.5.4 --- Reorganization Energy and Mobility --- p.131 / Chapter 2.5.5 --- Summary on KPA series --- p.133 / Chapter 2.6 --- NPA series --- p.136 / Chapter 2.6.1 --- Molecular Structure --- p.136 / Chapter 2.6.2 --- Electronic Structure --- p.160 / Chapter 2.6.3 --- Absorption and Emission Energy --- p.166 / Chapter 2.6.4 --- Reorganization Energy and Mobility --- p.167 / Chapter 2.6.5 --- Summary on NPA series --- p.169 / Chapter II --- Analytical Studies of Polarons and the Electron-Phonon Interaction / 極子與電子一聲子相互作用的解析研究 --- p.172 / Chapter 3 --- Study on Holstein Model Using Variational Approximation --- p.173 / Chapter 3.1 --- Holstein Hamiltonian --- p.173 / Chapter 3.2 --- Variational Transformation --- p.175 / Chapter 3.2.1 --- Lang-Firsov Transformation --- p.175 / Chapter 3.2.2 --- Squeezing Transformation --- p.177 / Chapter 3.3 --- Energy and Static Correlation Functions --- p.179 / Chapter 4 --- Study on Holstein Model Using Coupled-Cluster Method --- p.193 / Chapter 4.1 --- Approximation in the Coupled-Cluster Method --- p.193 / Chapter 4.2 --- Approach 1 --- p.195 / Chapter 4.2.1 --- The Zeroth and the First Levels --- p.195 / Chapter 4.2.2 --- Energies and Static Correlation Functions --- p.196 / Chapter 4.3 --- Approach 2 --- p.206 / Chapter 4.3.1 --- The Zeroth and the First Levels --- p.206 / Chapter 4.3.2 --- Energies and Static Correlation Functions --- p.210 / Chapter 4.4 --- Approach 3 --- p.225 / Chapter 4.4.1 --- The Zeroth and the First Levels --- p.226 / Chapter 4.4.2 --- Energies and Static Correlation Functions --- p.228 / Chapter 4.5 --- Comparison with the Variational Method --- p.243

The following dissertation presents a comprehensive study of the interaction between Dirac fermion quasiparticles (DFQs) and surface phonons on the surfaces of the topological insulators Bi2Se3 and Bi2Te3. Inelastic helium atom surface scattering (HASS) spectroscopy and time of flight (TOF) techniques were used to measure the surface phonon dispersion of these materials along the two high-symmetry directions of the surface Brillouin zone (SBZ). Two anomalies common to both materials are exhibited in the experimental data. First, there is an absence of Rayleigh acoustic waves on the surface of these materials, pointing to weak coupling between the surface charge density and the surface acoustic phonon modes and potential applications for soundproofing technologies. Secondly, both materials exhibit an out-of-plane polarized optical phonon mode beginning at the SBZ center and dispersing to lower energy with increasing wave vector along both high-symmetry directions of the SBZ. This trend terminates in a V-shaped minimum at a wave vector corresponding to 2kF for each material, after which the dispersion resumes its upward trend. This phenomenon constitutes a strong Kohn anomaly and can be attributed to the interaction between the surface phonons and DFQs. To quantify the coupling between the optical phonons experiencing strong renormalization and the DFQs at the surface, a phenomenological model was constructed based within the random phase approximation. Fitting the theoretical model to the experimental data allowed for the extraction of the matrix elements of the coupling Hamiltonian and the modifications to the surface phonon propagator encoded in the phonon self energy. This allowed, for the first time, calculation of phonon mode-specific quasiparticle-phonon coupling λⱱ(q) from experimental data. Additionally, an averaged coupling parameter was determined for both materials yielding ¯λ^Te ≈ 2 and ¯λ^Se ≈ 0.7. These values are significantly higher than those of typical metals, underscoring the strong coupling between optical surface phonons and DFQs in topological insulators. In an effort to connect experimental results obtained from phonon and photoemission spectroscopies, a computational process for taking coupling information from the phonon perspective and translating it to the DFQ perspective was derived. The procedure involves using information obtained from HASS measurements (namely the coupling matrix elements and optical phonon dispersion) as input to a Matsubara Green function formalism, from which one can obtain the real and imaginary parts of the DFQ self energy. With these at hand it is possible to calculate the DFQ spectral function and density of states, allowing for comparison with photoemission and scanning tunneling spectroscopies. The results set the necessary energy resolution and extraction methodology for calculating ¯λ from the DFQ perspective. Additionally, determining ¯λ from the calculated spectral functions yields results identical to those obtained from HASS, proving the self-consistency of the approach.

Un nanotube de carbone est une molécule tubulaire dont les propriétés électroniques et quantiques sont tout à fait remarquables. Lorsqu'il est utilisé en tant que canal de conduction d'un transistor à effet de champ, il est possible de détecter électriquement la présence de charges stockées à proximité de celui-ci, permettant ainsi la création d'une mémoire non-volatile ultime. Dans cette thèse, nous présentons les travaux réalisés sur des transistors à nanotubes (CNTFETs) utilisés pour la détection de charges, le tout imagé par microscopie à force de Kelvin (KFM). Le calibrage de la sonde KFM sur des CNTFETs y est egalement présenté. Les mesures de transport sont ainsi couplées à la cartographie des potentiels de surface du nanodispositif. Les charges électriques sont injectées à proximité d'un nanotube de carbone à l'aide d'une pointe métalisée d'un microscope à force atomique (AFM) et directement stockées dans la surface de SiO2. Les mesures électriques du CNTFET montrent un effet de grille inverse à celui attendu par le signe des charges injectées. L'explication est donnée par la détection KFM qui permet l'observation de charges stockées dans l'environnement du nanotube et de signe opposé à celles injectées. Dans une dernière partie, une étude phénoménologique est effectuée sur l'apparition de résonances périodiques dans les caractéristiques de transfert des nanotubes. Par la connaissance du bras de levier du CNTFET déterminé par le KFM, ces résonances sont quantitativement évaluées à l'énergie des phonons optiques longitudinaux des nanotubes de carbone et du SiO2. Une statistique de type Franck Condon en considérant la présence de N sites diffuseurs est appliquée sur ces résonances et permettent, dans une première approximation, d'évaluer l'intéraction électron-phonon de notre dispositif.

MISE EN EVIDENCE, EN REGIME DE FORTE EXCITATION, DU DEGRE DE FRAGILITE DU SYSTEME QUASI-PARTICULES<->CONDENSAT DE PAIRES. LES MATERIAUX DE GRANDE DIFFUSIVITE ELECTRONIQUE ONT CANTONNE L'ETUDE A DES SITUATIONS DE QUASI-HOMOGENEITE. EN CE QUI CONCERNE LES PHONONS BALISTIQUES, DES RESULTATS PRECIS ONT ETE OBTENUS: L'ETAT SUPRACONDUCTEUR A T=0 AGIT COMME UN FILTRE PARFAIT DES FREQUENCES JUSQU'A LA CASSURE DES PAIRES DONT LE SEUIL ET L'ANISOTROPIE SONT AINSI MESURABLES; EN FRANCHANT THERMIQUEMENT L'INTERACTION AVEC LES QUASI-PARTICULES, LES DUREES DE VIES LIMITEES PAR LES ELECTRONS ONT ETE OBTENUES MODE PAR MODE. DES MESURES SUR LE NIOBIUM ONT PERMIS DE DONNER UNE VALEUR MOYENNE DU POTENTIEL DE DEFORMATION. APPROCHE SYNTHETIQUE DES MODES POSSIBLES DE LA CONDUCTIVITE ELECTRONIQUE PAR UNE METHODE D'EQUATIONS DE TRANSPORT COUPLEES. CONCLUSION

The structural, electronic, and superconducting properties of one dimensional materials are calculated from first principles, using the density functional theory. Nanotubes and nanowires are important building blocks in nanotechnology, in particular for nanoelectronics. In this manuscript, the growth of carbon nanotubes is studied through the interaction between carbon and the transition metal atoms used as growth catalysts. The accepted model for a new phase of nanotube-like molybdenum disulfide is critically examined using comparisons of energetic stability and types of chemical bonding in different candidate structures which have similar compositions. The epitaxial growth of diamond carbon on (100) iridium is exceptionally favorable. The differences between various substrates used experimentally are studied, and the specificity of Ir is shown. Finally, the characteristics of the electron-phonon interaction in aluminium nanowires are determined. The structural instabilities and the differences in the electron-phonon coupling are calculated for straight monoatomic wires, zigzag wires, and thicker straight wires. The constrained geometry of the wires generates a coupling which can be very strong or almost vanish, depending on the structural details, but which is concentrated in the longitudinal high-frequency phonons.

The structural, electronic, and superconducting properties of one dimensional materials are calculated from first principles, using the density functional theory. Nanotubes and nanowires are important building blocks in nanotechnology, in particular for nanoelectronics. In this manuscript, the growth of carbon nanotubes is studied through the interaction between carbon and the transition metal atoms used as growth catalysts. The accepted model for a new phase of nanotube-like molybdenum disulfide is critically examined using comparisons of energetic stability and types of chemical bonding in different candidate structures which have similar compositions. The epitaxial growth of diamond carbon on (100) iridium is exceptionally favorable. The differences between various substrates used experimentally are studied, and the specificity of Ir is shown. Finally, the characteristics of the electron-phonon interaction in aluminium nanowires are determined. The structural instabilities and the differences in the electron-phonon coupling are calculated for straight monoatomic wires, zigzag wires, and thicker straight wires. The constrained geometry of the wires generates a coupling which can be very strong or almost vanish, depending on the structural details, but which is concentrated in the longitudinal high-frequency phonons.

Since the advent of nanoscale material based electronic devices, there has been a considerable interest in exploring carbon nanotubes from fundamental science and technological perspectives. In carbon nanotubes, the atoms form a cylindrical structure with a diameter of the order 1nm. The length of the nanotubes can extend up to several hundred micrometers. Carbon nanotubes exhibit a variety of intriguing electronic properties such as semiconducting and metallic behaviour, due to the quantum confinement of the electrons in the circumferential direction. Much of the study dedicated to describe the behaviour of carbon nanotube-based devices assumes for simplicity the nanotube to be a ballistic material. However, in reality the phonon scattering mechanism exists also in nanotubes, of course, and can generally not be neglected, except in very short nanotubes. In this work, we focus attention on exploring the steady-state electron transport properties of semiconducting single-walled carbon nanotubes, including both phonon scattering and defect (vacancy) scattering, using the semi-classical bulk single electron Monte Carlo method.   The electron energy dispersion relations are obtained by applying the zone folding technique to the dispersion relations of graphene, which are calculated using the tight-binding description. The vibrational modes in the carbon nanotubes are studied using a fourth nearest-neighbour force constant model. Both the electron-phonon and the electron-defect interactions are formulated within the tight-binding framework, and their corresponding scattering rates are computed and analyzed. In particular, the dependence of the phonon scattering rate and the defect scattering rate on the diameter of the nanotube, on temperature and on electron energy is studied. It is shown that the differences observed in the scattering rate between different nanotubes mainly stem from the differences in their band structure.   A bulk single electron Monte Carlo simulator was developed to study the electron transport in semiconducting zigzag carbon nanotubes. As a first step, we included only electron-phonon scattering, neglecting all other possible scattering mechanisms. With this scattering mechanism, the steady-state drift velocity and the mobility for the nanotubes (8,0), (10,0), (11,0), (13,0) and (25,0) were calculated as functions of the electric-field strength and lattice temperature, and the results are presented and analysed here. The dependence of the mobility on the lattice temperature can be clearly seen at low electric-field strengths. At such electric-field strengths, the scattering is almost entirely due to acoustic phonons, whereas at high electric-field strengths optical phonon emission processes dominate. It is shown that the saturation of the steady-state drift velocity at high electric-field strengths is due to the emission of high-energy optical phonons. The results indicate the presence of Negative differential resistance for some of the nanotubes considered in this work. The discrepancy found in the literature concerning the physical reason for the appearance of negative differential resistance is clarified, and a new explanation is proposed. It is also observed that the backward scattering is dominant over the forward scattering at high electric-field strengths.                                                                                   We then included also defect scattering, actually electron-vacancy scattering, for the nanotubes (10,0) and (13,0). The steady-state drift velocities for these nanotubes are calculated as functions of the density of vacancies, electric-field strength and the lattice temperature, using three different vacancy concentrations. The results indicate the presence of Negative differential resistance at very low concentration of defects, and how this feature may depend on the concentration of defects. The dependence of the steady-state drift velocity on the concentration of defect and the lattice temperature is discussed. The electron distribution functions for different temperatures and electric field strengths are also calculated and investigated for all the semiconducting nanotubes considered here. In particular, a steep barrier found in the electron distribution function is attributed to the emission of high energy optical phonons.

Over the past 20 years a great deal of progress has been made towards understanding the physics of the high-temperature (high-Tc) cuprate superconductors. Much of the low- energy physics of these materials appears to be captured by two-dimensional Hubbard or t-J models which have provided significant insight into a number of properties such as the pseudogap, antiferromagnetism and superconductivity itself. However, intrinsically planar models are unable to account for the large variations in Tc observed across materials nor do they capture the electron-phonon (el-ph) interaction, the importance of which a number of experimental probes now indicate. This thesis examines the el-ph interaction in cuprates using a combination of analytical and numerical techniques. Starting from the microscopic mechanism for coupling to in-plane and c-axis polarized oxygen phonons, the theory of el-ph coupling is presented. The el-ph self-energy is derived in the context of Migdal-Eliashberg theory and then applied to understanding the detailed temperature and doping dependence of the renormalizations observed by Angle-resolved photoemission spectroscopy. The qualitative signatures of el- boson coupling in the density of states of a d-wave superconductor are also examined on general grounds and a model calculation is presented for el-ph coupling signatures in the density of states. Following this, the theory is extended to include the effects of screening and the consequences of this theory are explored. Due to the quasi-2D nature of the cuprates, screening is found to anomalously enhance the el-ph contribution to d-wave pairing. This result is then considered in light of the material and doping dependence of Tc and a framework for understanding the materials variations in Tc is presented. From these studies, a detailed picture of the role of the el-ph interaction in the doped cuprates emerges where the interaction, working in conjunction with a dominant pairing interaction, provides much of the materials variations in Tc observed across the cuprate families. Turning towards numerical techniques, small cluster calculations are presented which examine the effects of a local oxygen dopant in an otherwise ideal Bi2Sr2CaCu2O8+δ crystal. Here, it is demonstrated that the dopant locally enhances electronic properties such as the antiferromagnetic exchange energy J via local el-ph coupling to planar local oxygen vibrations. Finally, in an effort to extend the scope of this work to the underdoped region of the phase diagram, an examination of the properties of the single-band Hubbard and Hubbard-Holstein model is carried out using Determinant Quantum Monte Carlo. Here focus is placed on the spectral properties of the model as well as the competition between the the antiferromagnetic and charge-density-wave orders. As with the small cluster calculations, a strong interplay between the magnetic and lattice properties is observed.