We develop a transport formalism for interacting electrons in the presence of quenched disorder. Quantum effects on transport, due both to quantum interference and interaction effects, are incorporated through non-analytic terms in the irreducible interactions and appropriate contributions to the electron self-energy. Perturbatively, our approach recovers the standard results on quantum corrections to the Drude conductivity. We argue the strong coupling fixed point is a magnetic metal beyond perturbation theory. Extensions of the theory are outlined.

Using the RPA, we calculate the plasmon frequencies of an electron gas on a two-dimensional spherical surface in the presence of a weak magnetic field. We show that the magnetic field results in a coupling between electronic states with different angular momentum numbers. This coupling results in a blueshift of the dipolar plasmon resonance with increasing magnetic field. We also investigate how the plasmon energies vary as a function of the number of electrons and radius of the sphere.

The effect of spin injection into d-wave, p-wave, and s-wave superconductors is studied here. A theory is developed which treats the interplay between the bulk and boundary spin transport, as well as the interplay between pair and single-particle transport at the boundary. This theory is used to study the relationship between Andreev reflection and the linear-response spin-injection characteristics. Among the quantities of interest are, the amount of injected magnetization (m), the induced spin-dependent current (I s), and the induced boundary voltage (Vs). In general, Andreev reflection makes each of these three quantities depend on a different combination of the boundary and bulk contributions. The conditions are identified under which some of these quantities that depend solely on the bulk properties can be isolated. A correlation between the Andreev bound states and the spin-injection characteristics is established, which implies a strong directional dependence of spin injection into high-temperature superconductors and in p-wave superconductors.

This thesis will be divided into two parts. In the first part, theory and results of a novel system in which a superconducting single-electron transistor (S-SET) coupled to a two-dimensional electron gas (2DEG) serving as a tunable electromagnetic environment for the S-SET will be discussed, including effects of dissipation, resonant tunneling with photon emission, and photon-assisted tunneling. In the second part, we discuss the techniques for which the SET is incorporated in an RF resonant circuit, resulting in an ultra high charge sensitivity and bandwidth. After the 2DEG is confined into a quantum dot, random telegraph signals (RTS) caused by individual electrons tunneling on and off the dot have been observed. In the equilibrium configuration, the occupational probabilities of the charge states of the dot can be directly measured from the RTS and were found to follow a Fermi distribution. In the non-equilibrium configuration, the RTS correctly detected the onset of the current through the dot.

In the fast collision approximation, the scattering amplitude operator of the quasi-elastic scattering is expressed as the summation of multipole moment operators $M\sp{(k)}(l\sb{i},s\sb{i})$ of the valence shell involved in the resonance$\sp1$ with distinct polarization factors. Each multipole moment operator is expressed as the sum of an orbital moment operator and two spin-orbital moment operators with unique coefficients. The explicit form of these coefficients is obtained and the numerical values are calculated. For the transitions to continuous bands, the explicit forms of $M\sp{(k)}(l\sb{i},s\sb{i})$ are extended from electric dipole transitions to any electric multipole transitions. Within the manifolds of good total L and good total S, the $k\sp{\rm th}$ rank multipole moment operator $M\sp{(k)}(l\sb{i},s\sb{i})$ can be expressed in terms of the $k\sp{\rm th}$ rank spin-orbital moments $M\sp{(k)}({\bf L,S})$ of the total L- and total ${\bf S}$-operators of the valence shell involved in the resonance. Furthermore, within the manifolds of good total J, $M\sp{(k)}(l\sb{i},s\sb{i})$ can be further simplified in terms of the spherical tensor operators of the total J of the resonance valence shell. For Hund's rule ground states, the corresponding proportionality coefficients for both cases were obtained. For rare earths, we obtained the thermal expectation value of $M\sp{(k)}(l\sb{i},s\sb{i})$ at T = 0 for coherent elastic scattering. These results are inconsistent with Hamrick's single electron method$\sp2$ for the second half of the rare earth series. For the first half of the rare earth series, we showed that the single electron method is an approximation of our theory. In spiral antiferromagnets, such as holmium, the magnetic sensitivity results in a series of magnetic satellites distributed at each side of Bragg peak. This behavior can be understood on the basis of the XRES electric multipole transition theory we developed. As temperature increases, the higher order harmonics decrease more rapidly than the lower order harmonics, which can be qualitatively explained by mean-field theory. Just above the Neel temperature, there is weak magnetic scattering which can be understood as the short range moment-moment correlations of different spin-orbital multipole moment operators. ftn $\sp1$J. Luo, J. P. Hannon, G. T. Trammell, Phys. Rev. Lett., 71 287 (1993). $\sp2$M. Hamrick, M.A. Thesis, Physics Department, Rice University, 1991.

Quantum critical properties of strongly correlated metals in heavy fermion systems are investigated. Based on an extended dynamic mean field theory of the Kondo lattice model, two types of quantum phase transitions are found to exist in these materials: the conventional spin density wave transition and a novel locally critical quantum phase transition where the local dynamics is also critical. The associated quantum impurity model, the Bose-Fermi Kondo model, is extensively studied with an epsilon-expansion renormalization group analysis and a large N method. A local quantum critical point is identified in all these approaches, when the bosonic bath has a sub-ohmic spectrum; the results guarantee that a self-consistent solution of the locally critical type is a robust solution to the Kondo lattice model. Quantum critical properties such as thermodynamics are also theoretically investigated for both pictures. A universally diverging Gruneisen ratio is discovered at any quantum critical point, which can be used to characterize different classes of quantum phase transitions.

Intersubband resonances in InAs/AlSb are an ideal tool for optically pumped terahertz (THz) generation because of their enormous tunability and their strength at room temperature. We have carried out a systematic temperature-dependent study of intersubband absorption in InAs/AlSb quantum wells from S to 10 nm well width. The resonance energy redshifts with increasing temperature from 10 to 300 K, and the amount of redshift increases with decreasing well width. We have also observed intersubband absorption in wells as narrow as 3 nm, investigated the carrier distribution in the wells and its influence on intersubband absorption, and performed temperature-dependent cyclotron resonance using a THz quantum cascade laser. We have observed multiple intersubband resonances in coupled quantum well structures designed for THz difference frequency generation. We have modeled the resonances using eight-band k·p theory combined with semiconductor Bloch equations, including the main many-body effects. Temperature is incorporated via band filling and nonparabolicity.

This paper discusses the investigation and manipulation by scanning tunneling microscopy of new fullerene derivative molecules synthesized specifically to achieve nanoscale motion. Two, three, and four-fullerene molecules with connecting oligo (phenylene-ethynylene) structures have been studied statically, and manipulated dynamically to ascertain the type of motion they undergo under direct tip-manipulation and thermal excitation. The dimer molecules were found to have a low surface-diffusion barrier on a Au(111) surface, and were seen to pivot around a single fullerene between scans. Trimer molecules were heated to temperatures where pivoting motion was observed over time spans of minutes, but did not illustrate significant translational motion. Quadrimers, or nanocars, were both directly tip-manipulated and thermally annealed to examine their surface-mechanics, and were found to prefer motion along an axis perpendicular to the oligo (phenylene ethynylene) axle structure, suggesting a coordinated rolling of the fullerenes.

In this thesis, we develop a dynamical mean field approach to strongly correlated electron systems. Our approach is based on the standard limit of infinite dimensions but goes beyond that by treating inter-unit-cell interactions on an equal footing with inter-unit-cell ones. We apply this approach to several systems, including the Kondo lattice model and the extended Hubbard model. For the extended Hubbard model, we find that certain non-Fermi liquid states survive in the presence of intra-unit-cell interactions. Our results provide the first step towards establishing the relevance of these states to physical systems in finite dimensions. For the Kondo lattice model, we identify a novel quantum critical point where the local Kondo dynamics is also critical. This novel critical point appears to describe what happens in certain heavy fermion metals close to a magnetic phase transition.

A technique for positioning single-walled carbon nanotubes (SWNT) at a specific location on a substrate has been developed. Self-assembled monolayers were used in conjunction with electron-beam lithography to produce patterned regions of --NH2 terminated organosilanes. SWNTs adhere to the --NH2 terminated patterns, allowing these positioned tubes to be electrically contacted with macroscopic gold leads. I-V Characteristics were measured for both annealed and nonannealed SWNTs contacted in this fashion. The lithographic technique works extremely well with nonannealed nanotubes; however, such tubes exhibit highly insulating electrical characteristics. Conversely SWNTs annealed at 1100°C for 30 minutes have electrical characteristics in agreement with predictions, but are not attracted to the --NH 2 terminated patterns.