With a multitude of different phases and quantum critical points, heavy fermion materials should reign supreme as the prototype for competing order, a major contemporary theme in condensed matter physics. One key feature that differentiates the types of magnetic phases and critical points is the presence or absence of Kondo screening. This singlet formation is dramatically manifested in the Fermi surface, which may or may not include atomic f-orbital electron states. To provide a theoretical basis for the different types of magnetism, we have carried out asymptotically exact studies of the Kondo lattice model inside both the antiferromagnetic and ferromagnetic phases. A fundamental aspect of the approach is to map the magnetic Hamiltonian for the f-orbitals onto a quantum nonlinear sigma model (QNLsigmaM). The Kondo interaction results in an effective coupling between the QNLsigmaM fields and the conduction electrons. Renormalization group analyses show that the Fermi surface in the corresponding ordered states is small (not incorporating the f-orbitals) for both the ferromagnetic and antiferromagnetic cases. These results are of relevance to a number of materials, including YbRh2Si2 and CeRu2Ge2, where experimental measurements of magnetotransport and de Haas van Alphen effects have supplied evidence for small Fermi surface phases. The implications of our results for heavy fermion quantum critical points will also be discussed.

Two-dimensional electron (2DES) and hole (2DHS) systems have attracted intense research attentions in past decades. A 2DES or 2DHS modulated by one-dimensional or two-dimensional spatially periodic potential shows particular importance because the existence of modulation provides a tunable parameter for exploring interaction between electrons and scattering centers presenting on the two-dimensional systems. This thesis documents a systematic experimental study, in collaboration with Bell Labs, of electronic transport in very-high mobility 2DES and 2DHS in GaAs/AlGaAs quantum structures. Fabrication of triangular antidot lattice in 2DES, as well as low-temperature transport and photoconductivity properties in spatially modulated 2DES, has been studied. Strong Geometric resonance (GR), up to seven peaks resolved, is observed in the longitudinal magnetoresistance because of high mobility of 2DES after fabrication of antidot lattice. Photoresistance shows clear millimeterwave-induced resistance oscillations (MIRO) but with heavily damping amplitudes, and magnetoplasmon resonance (MPR) is also observed as well. GR, MIRO and MPR are decoupled from each other in our modulated 2DES. These experimental findings pave the way for studies of nonlinear transport in modulated 2DES. Magnetotransport measurements on a new material, the Carbon delta-doped 2DHG in GaAs/AlGaAs quantum well, indicate that the 2DHG has a transport scattering time compatible with those in very-high mobility 2DES. However, photoresistance measurement shows much weaker MIRO in the 2DHS than that in 2DES with compatible transport scattering time. Low-temperature transport measurements on Landau, Zeeman, and spin-orbital parameters imply that the C-doped 2DHS has small zero field spin splitting and large effective g-factor. As part of the thesis work, the thesis also presents a development of low-temperature/high magnetic field (300mK/12T) scanning Hall probe microscope (SHPM) technique for measuring small local magnetic fields at low temperature and an algorithm for calculating the current density from measured magnetic fields based on Fourier transformation technique. Integration of SHPM and the algorithm provides a practical tool for imaging the current distribution and a powerful method to explore electronic transport properties of 2DES and 2DHS.

Carbon allotropes such as nanotubes, graphene, and buckyball all preserve the same lattice structure. However, their electronic properties are very different depending on their dimensionality. These nanostructures can be functionalized with other chemical groups or can be used to form complicated molecular structures. By using scanning tunneling microscopy and Raman spectroscopy, the functionalization of carbon nanotubes with fluorine was studied as a potential route to tailoring the electrical and chemical properties of carbon nanotubes, and functionalization and exfoliation techniques of graphite without inducing basal plane defects were investigated. Also, building upon our previous research on nanocars, nanodragsters combining buckyball and p-carborane wheels were studied with scanning tunneling microscopy. Unlike its predecessors, a nanodragster can show interesting motions even at room temperature as well as at elevated temperatures.

Through polarization-dependent magneto-optical absorption spectroscopy, the magnetic susceptibility anisotropy for metallic single-walled carbon nanotubes has been extracted and found to be up to 4x greater than values for semiconducting single-walled carbon nanotubes. Consistent with theoretical predictions, this is the first experimental evidence of the paramagnetic nature arising from the Aharonov-Bohm-phase-induced gap opening in metallic nanotubes. We also compare our values with previous work for semiconducting nanotubes, which confirm a break from the prediction that the magnetic susceptibility anisotropy increases linearly with the diameter.

Super growth of single-walled carbon nanotubes (SWNTs) has emerged as a unique method for synthesizing self-assembled, pristine, aligned SWNT materials composed of ultra-long (millimeter-long) nanotubes. This thesis focuses on novel routes of synthesizing such self-assembled SWNTs and the challenges that arise in integrating this material into next-generation applications. First of all, this work provides unique insight into growth termination of aligned SWNTs, emphasizing the mechanism that inhibits the growth of infinitely long nanotubes. Exhaustive real-time growth studies, combined with ex-situ and in-situ TEM characterization emphasizes that Ostwald ripening and subsurface diffusion of catalyst particles play a key role in growth termination. As a result, rational steps to solving this problem can enhance growth, and may ultimately lead to the meter or kilometer-long SWNTs that are necessary for a number of applications. In addition, other novel synthesis routes are discussed, such as the ability to form macroscopic fibrils of SWNTs, called "flying carpets" from 40 nm thick substrates, and the ability to achieve supergrowth of SWNTs that are controllably doped with nitrogen. In the latter case, molecular heterojunctions of doped and undoped sections in a single strand of ultralong SWNTs are demonstrated Secondly, as supergrowth is conducted on alumina coated SiO2 substrates, any applications will require that one can transfer the SWNTs to host surfaces with minimal processing. This work demonstrates a unique contact transfer route by which both patterned arrays of SWNTs, or homogenous SWNT carpets, can be transferred to any host surface. In the first case, the SWNTs are grown vertically aligned, and transferred in patterns of horizontally aligned SWNT. This transfer process relies on simple water-vapor etching of amorphous carbons at the catalyst following growth, and strong van der Waals adhesion of the high surface-area SWNT to host surfaces (gecko effect). Next, as the SWNTs produced in supergrowth are notably large in diameter (2-5 nm), this work provides the first characterization of these SWNTs using combined microscopy and infrared polarized absorption studies. Perfectly aligned SWNTs are transferred to infrared optical windows and mounted in a rotatable vacuum cell in which polarization dependent characterization is carried out. By modeling features observed in absorption to expected optical excitonic transition energies, diameter distributions are rapidly extracted. In addition, other concepts of optical characterization in ultra-long aligned SWNTs are explored. For example, the concept of using polarized near-IR characterization for such SWNT samples is inadequate to characterize the bulk alignment due to the mismatch of the excitation wavelength and the SWNT length. Therefore, comparing anisotropy in polarized near-IR Raman or absorption gives substantially different results than anisotropic electrical transport measurements. In addition to optical characterization, this work uniquely finds that the electrical transport properties of SWNTs is ultimately limited by SWNT-SWNT junctions. This is evident in temperature-dependent DC and AC conductivity measurements that emphasize localization-induced transport characteristics. A number of non-classical electrical transport features are observed that can simply be related to the sensitivity of electrical transport to SWNT-SWNT junctions. This means that despite the incredible electrical properties of individual SWNTs, it is necessary to focus on the growth and processing of ultra-long SWNTs in order to realistically make nanotube-based materials comparable in transport characteristics to conventional materials. Finally, this work concludes by demonstrating progress on the fabrication of new SWNT-based applications. First of all, a new type of solid-state supercapacitor material is fabricated where vertically aligned SWNT are coated with metal-oxide dielectric and counterelectrode layers to form efficient supercapacitors. This design benefits from the ultra-high surface area available in SWNT arrays, the intrinsic ultra-high current carrying capacity of ultra-long SWNT (1000 times copper), the high breakdown voltages one can achieve using solid dielectric layers, and the lightweight and temperature insensitive design of this capacitor. As a result, performance comparable to current electric-double layer capacitor devices is reported, and energy densities significant larger are predicted by material optimization. In addition, progress on other applications are discussed, including devices utilizing self-assembled molecular heterojunction arrays, and terahertz polarizers made from perfectly aligned transferred SWNT films. This work demonstrates a bottom-up route toward the synthesis of new materials for novel characterization and applications.

We present a comprehensive study of low temperature quantum transport in double gated InAs/GaSb composite quantum wells. Recently, it has been proposed that this system in inverted regime should exhibit the topologically insulating (TI) phase, characterized by an energy gap in the bulk and gapless edge modes, protected from backscattering by time reversal symmetry. We sweep the Fermi level through the bulk mini-gap, observing resistance peaks and finding strong evidence for the existence of the mini-gap; however, the mini-gap does not show insulating behavior, with a residual bulk conductivity which is a few times larger then the expected contribution from the edge. Our data indicate, that bulk conductivity is not an issue of "dirt", which can be improved by simply reducing the amount of disorder, but a fundamental property of strongly coupled electron-hole systems in realistic materials, which must be considered in studies of proposed TI edge modes.

Understanding how electrons and phonons relax in energy and momentum is one of the current goals in carbon nanotube spectroscopy as well as an important step toward developing novel electronic and optoelectronic devices based on carbon nanotubes. Here, we investigate the polarization anisotropy of coherent phonon (CP) dynamics of radial breathing mode (REM) phonons in highly-aligned single-walled carbon nanotubes (SWNTs). Using CP spectroscopy, we measure REM CPs as a function of angle for two different geometries and in both cases, we observe quenching of the RBM when polarization is perpendicular to the nanotubes. We also make progress in understanding the role of dark excitons in SWNTs at ultralow temperatures. Measuring the magnetic field dependence to 5 T, we obtained an unexpected zero-field photoluminescence (PL) and PL brightening at 50 mK. To explain this contradiction with current theory, we introduced a non-thermal distribution of excitons into current theory.

This Master of Science Thesis is concerned with electronic transport in the higher Landau levels (LL) in a two-dimensional electron system, where novel many-body electronic phases have been observed. Particular attention is paid to the even-denominator fractional quantum Hall states at LL filling factors 5/2 and 7/2, and the anisotropic states at 9/2 and 11/2. In a high electron density (n = 6.3 x 10 11cm-2), high mobility (mu = 1 x 107cm2/Vs) modulation-doped GaAs/Al0.24Ga 0.76As quantum well, we observed the nu = 5/2 quantum Hall plateau at a high magnetic field B = 10 T. In contrast to previous findings in a lower density system, electronic transport at nu = 9/2 and nu = 11/2 is essentially isotropic. Anisotropic transport at 9/2 and 11/2 can be induced by an in-plane magnetic field, B//. Depending on the B// direction, the nu = 5/2 diagonal resistances in a high B// either remain isotropic or become strongly anisotropic. Our data suggest a new regime for electronic transport in higher LLs.

Two types of novel ferromagnetic materials, (Ga,Mn)As and Fei/4TaS2, were studied in this dissertation. Interest in (Ga,Mn)As is stimulated by the emerging field of spintronics, which has a potential of bringing a technology revolution in information processing, information storage, and quantum computing. The latter, Feu1/4TaS2, belongs to the family of intercalated transition-metal dichalcogenides (TMDC) with highly anisotropie layered structures. At cryogenic temperatures, ferromagnetic order appears in both materials through the interaction of localized spins and itinerant carriers. In order to investigate these underlying exchange interactions and spin-split band structures, we developed a magneto-optical Kerr effect (MOKE) spectrometer with the full capabilities of magnetic field, temperature, and photon energy scanning. We observed novel and unusual MOKE data as a function of these three continuously tunable parameters. Remanent Kerr angles of (Ga,Mn)As samples showed strong dependence on the photon energy, exhibiting a large positive peak at ∼ 1.7 eV. This peak increased in intensity and blue-shifted with Mn doping and further blue-shifted with annealing. We attribute these changes to the increased hole density and effective Mn content. Our data agree very well with theoretical calculations using a 30-band k · p model with antiferromagnetic p-d exchange interaction without any ad hoc introduction of impurity transitions. The agreement between the data and the model led us to conclude that above-bandgap magneto-optical Kerr rotation in ferromagnetic (Ga,Mn)As is determined by interband transitions. Fe1/4TaS2 exhibited abnormal Kerr hysteresis behavior with a strong sensitivity to the probing photon energy. The abnormal shapes can be fitted with the sum of two error functions, and we provide a tentative physical description based on domain wall physics. However, a few open questions remains, and its microscopic origin is still under investigation. The Kerr spectra were explained by the difference of joint-density-of-state (JDOS) of spin-up and spin-down bands in a simplified model, adopting literature DOS values of Fe1/3TaS2. Accurate simulations require future calculations of the band structure.

<p>This doctoral thesis presents density functionalcalculations applied in several domains of interest in solidstate physics and materials science. Non-collinear magnetismhas been studied both in an artificial multi-layer structure,which could have technological relevance as a magnetic sensordevice, and as excitations in 3d ferromagnets. The intricatebulk crystal structure of γ-alumina has been investigated.An improved embedded cluster method is developed and applied tostudy the geometric and electronic structures and opticalabsorption energies of neutral and positively charged oxygenvacancies in α-quartz. Ab initio total energycalculations, based on the EMTO theory, have been used todetermine the elastic properties of Al_1-xLi_xrandom alloys in the face-centered cubiccrystallographic phase. The obtained overall good agreementwith experiment demonstrates the applicability of the quantummechanics formulated within the framework of the DensityFunctional Theory for mapping the structural and mechanicalproperties of random alloys against chemical composition.</p>