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.

Recent experimental investigations into charge transfer during ion/semiconductor surface collisions indicate dependence of the scattered ion's neutralization probability upon the target surface's local electronic environment along the scattered ion trajectory. This work presents qualitative modeling of these experiments demonstrating how the target surface's local electrostatic potential and charge density modify the scattered ion's neutralization rates. These models have been applied to Ne+ scattering and S- recoil from CdS {0001} and {0001¯} surfaces as well as Ne + scattering from intrinsic, n- and p-doped Si(100)-(2x1) surfaces. Correlation between electrostatic surface potential and ion neutralization probability has been shown for ion scattering from the CdS surfaces. Ne + neutralization during scattering from the Si(100)-(2x1) surface correlates to local surface charge density along the ion trajectory. Variations in ion neutralization rate for the intrinsic, n- and p-doped surfaces have been correlated to band bending at the Si surface.

Wavelength-dependent, near-infrared pump-probe study of micelle-suspended Single-Walled Carbon Nanotubes (SWCNTs) whose linear absorption spectra show chirality-assigned peaks is presented. Two distinct relaxation regimes were observed: fast (0.3--1.2 ps) and slow (5--20 ps). The slow component, which has previously been unobserved in pump-probe measurements of bundled tubes, was resonantly enhanced whenever the pump photon energy matched with an interband absorption peak, and it is attributed to interband carrier recombination. It represents the lower limit of the intrinsic radiative recombination time of photoexcited carriers in SWCNTs since the exact value of this parameter depends on the presence of possible nonradiative recombination channels. The slow decay component was highly dependent on the pH of the solution, suggesting that the surrounding H+ ions strongly affect electronic states in nanotubes through the Burnstein-Moss effect. The effect was bandgap energy dependent, affecting the smaller bandgap tubes more significantly. To elucidate carrier dynamics in more detail, nondegenerate pump-probe experiments with wide and continuum probing throughout the lowest and second lowest energy transition ranges of SWCNTs were used. Complex signals were revealed with photoinduced absorption and bleaching, both of which were strongly wavelength dependent. Due to the high optical quality of unbundled SWCNT samples, clear signs of band filling and broadening of the exciton absorption peaks were found to be the main nonlinear mechanisms. The identification of these nonlinear mechanisms presents a novel explanation of the observed nonlinear behavior of nanotubes in general and helps clarify the controversial issues presented in previously published work. This explanation is also consistent with the previously observed pump-probe signals in bundled nanotube samples. Another novel and important conclusion drawn from the nondegenerate pump-probe experiments is that the position of the exciton absorption peaks is unchanged in the presence of high density electron-hole pairs, even when their density is comparable to the Mott density. The stability of the excitons observed for the first time in nanotubes is similar to what has been seen in the studies on the emission properties of GaAs-based semiconductor quantum wires. Although binding energies of these two 1D material systems are very different, the exciton stability seems to be a mark of their unique 1D nature.

Recent ultrafast pump-probe experiments studying the relaxation rate of an optically excited hot electron distribution on Au/Au2S gold nanoshells indicate that this relaxation rate can be modified by the chemical environment surrounding the shell. This work will begin a theoretical investigation of the effect of chemical adsorbates---solvents and impurities---upon nanoshell hot electron dynamics. The effects of water, polyvinyl alcohol (PVA), sulfur, p-aminobenzoic acid, p-mercaptobenzoic acid and propylamine adsorbates are examined for their electronic interaction with a noble metal surface. p-Aminobenzoic acid is found to have a very large dipole moment when adsorbed to the metal surface, in contrast to p-mercaptobenzoic acid, propylamine and water. This correlates well to the experimentally observed results where nanoshells dispersed in an aqueous soulution with p-aminobenzoic acid display a faster relaxation rate compared to nanoshells dispersed in a pure water, aqueous propylamine or aqueous p-mercaptobenzoic acid environments. This thesis will also introduce a non-equilibrium Green's function approach, based on the formalism developed by Baym and Kadanoff, to model the dynamics of a hot electron distribution. The model will be discussed in terms of a simple potential scattering mechanism, which may in later work be expanded to include more complex electron-electron and electron-phonon interactions. Lastly acoustic oscillation modes are calculated for solid gold spheres and gold-silicon nanoshells. These modes describe an effect of electron-phonon coupling between the hot electron distribution and the nanoshell lattice, whereby the electronic energy is converted into mechanical energy.