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.

We prepared nanoscopically flat open-ended SWNT substrates from SWNT spun fibers by using the microtome cutting technique or the focused ion beam cutting technique followed by various etching and cleaning schemes or alternatively from vertically aligned SWNT film by flipping-over. Deposited catalyst was docked to the open ends of SWNTs, and carbon feedstocks were catalyzed into continued single-walled carbon nanotube growth resembling 1D molecular epitaxy. The data obtained from Raman spectroscopy indicates that the (n, m) structure of the newly grown SWNT was cloned from that of the pre-existing SWNT substrate. Such results lead us to believe that this method will provide us with a means of chirality-controlled SWNTs growth on a macroscopic scale using a fairy general and scalable setup in the future.

This work reports the successful production of neat macroscopic membranes of aligned single-walled carbon nanotubes (SWNTs) via filtration in intense magnetic fields of 25 Tesla and 7 Tesla. These membranes comprise a novel material that allows an unprecedented capability to characterize and manipulate aligned SWNTs, providing access to the more remarkable properties of SWNTs. Surface areas in excess of 100 cm 2 and thickness in excess of seven microns were produced. A density within a factor of two of close packing was achieved. These assemblies exhibit anisotropy in Raman resonance, electrical transport, thermal transport, and reflection of polarized light. These samples provide a macroscopic window to exploring the properties of SWNTs and pave the way for many potential applications. The successful extension of this process to 7 Tesla provides a more pragmatic path towards aligned assemblies of carbon nanotubes. Variations in the properties of the materials made under different magnetic field intensities were observed.* *This dissertation includes a CD that is compound (contains both a paper copy and a CD as part of the dissertation). The CD requires the following application: Notepad.

This thesis will discuss the principles, techniques and applications of the Radio Frequency Single Electron Transistor (RF-SET). In the first part, the operating principles of Single Electron Transistors (SETS) in the normal and superconducting states will be introduced. The general techniques of fabricating and calibrating SETs will also be introduced. In the second part, two of our recent experiments are reviewed. One is related to the sensitivity and linearity of superconducting RF-SETs. We found that the RF-SET achieves the best balance of charge sensitivity and linearity in the subgap regime, as opposed to the usual preferred working point in the above-gap regime. The second experiment relates to the real-time counting of single electrons. We demonstrated that the RF-SET can be used as a fast and ultra-sensitive electrometer which can even detect tunneling of a single electron inside a tunable quantum dot (QD) formed in a two dimensional electron gas (2DEG).

We have developed a coherent time-domain THz magneto-spectroscopy system. It can be used for measuring the refractive index, complex conductivities, and cyclotron resonance of different semiconductor structures as well as for investigating fundamental physical phenomena. As a first application, we have carried out time-domain cyclotron resonance studies of an ultrahigh-mobility two-dimensional electron gas at low temperatures. We observed coherent cyclotron resonance oscillations that persist as long as ∼ 50 ps. We show that the basic physics of these oscillations can be described as the free induction decay of a coherent superposition between the lowest unfilled Landau level and the highest filled Landau level prepared by an incident THz pulse. Using the 0 Tesla data as a reference, we successfully extracted the real and imaginary conductivities for different magnetic fields in the frequency domain. Finally, I will discuss a few future experiments that will be performed with this novel system.

Bose-Einstein condensation (BEC) in ultra-cold magnetically-trapped $\sp7$Li vapor was experimentally observed and quantitative measurements of condensate number were made. Compared to other BEC experiments, lithium is unique due to its negative s-wave scattering length, corresponding to effectively attractive interactions. Due to this attraction, condensates are expected to undergo mechanical collapse if the condensate number exceeds a critical value. In this experiment, an upper limit of about 1000 condensate atoms is found, in agreement with theoretical predictions. In the experiment, the atoms are confined by a set of six permanent magnets in the Ioffe configuration. Optical forces are used to slow and guide atoms from a thermal atomic beam into the magnetic trap. With about $10\sp8$ atoms loaded into the trap, the vapor is laser-cooled to near 200 $\mu$K and then evaporatively cooled by application of a resonantly-tuned microwave field. Evaporative cooling produces a million-fold increase in phase-space density, reaching quantum-degenerate conditions with about 10$\sp5$ atoms at temperatures near 300 $\mu$K. After cooling, the trapped atom distribution is observed by in situ imaging via an optical probe. Calculated atom distributions are fit to the image data. In initial data, the imaging resolution was insufficient to see the spatially-narrow condensate peak, but as phase-space densities approached the expected phase transition, the images suddenly became distorted. Initial fits to the data suggested as many as 10$\sp5$ condensate atoms, in strong disagreement with theoretical predictions. An imaging model, accounting for imperfections in the imaging optics, shows that the sudden appearance of the distortions is a consequence of BEC, and that these distortions led to the initial over-estimation of cloud phase-space density and condensate number. Improved imaging was obtained using large probe detunings, a Phase-Contrast Polarization Imaging (PCPI) technique, and near-diffraction-limited imaging optics. The PCPI method exploits the birefringence of the trapped atoms. From the resulting images, quantitative estimates of condensate number are obtained and compared with theory.