Single and few-layer graphene (SLG and FLG) have stimulated great scientific interest because of their distinctive properties and potential for novel applications. In this dissertation, we investigate the mechanical, electronic and vibrational properties of these remarkable materials by various techniques, including atomic-force microscopy (AFM) and Raman, infrared (IR), and ultrafast optical spectroscopy. With respect to its mechanical properties, SLG is known to be capable of undergoing significant mechanical deformation. We have applied AFM to investigate how the morphology of SLG is influenced by the substrate on which it is deposited. We have found that SLG is strongly affected by the morphology of the underlying supporting surface. In particular, SLG deposited on atomically flat surfaces of mica substrates exhibits an ultraflat morphology, with height variation essentially indistinguishable from that observed for the surface of cleaved graphite. One of the most distinctive aspects of SLG is its spectrum of electronic excitations, with its characteristic linear energy-momentum dispersion relation. We have examined the dynamics of the corresponding Dirac fermions by optical emission spectroscopy. By analyzing the spectra of light emission induced in the spectral visible range by 30-femtosecond laser pulses, we find that the charge carriers in graphene cool by the emission of strongly coupled optical phonons in a few 10's of femtoseconds and thermalize among themselves even more rapidly. The charge carriers and the strongly coupled optical phonons are thus essentially in thermal equilibrium with one another on the picosecond time scale, but can be driven strongly out of equilibrium with the other phonons in the system. Temperatures exceeding 3000 K are achieved for the subsystem of the charge carriers and optical phonons under femtosecond laser excitation. While SLG exhibits remarkable physical properties, its few-layer counterparts are also of great interest. In particular, FLG can exist in various crystallographic stacking sequences, which strongly influence the material's electronic properties. We have developed an accurate and convenient method of characterizing stacking order in FLG using the lineshape of the Raman 2D-mode. Raman imaging allows us to visualize directly the spatial distribution of Bernal (ABA) and rhombohedral (ABC) stacking in trilayer and tetralayer graphene. We find that 15% of exfoliated graphene trilayers and tetralayers are comprised of micrometer-sized domains of rhombohedral stacking, rather than of usual Bernal stacking. The accurate identification of stacking domains in FLG allows us to investigate the influence of stacking order on the material's electronic properties. In particular, we have studied by means of IR spectroscopy the possibility of opening a band gap by the application of a strong perpendicular electric field in trilayer graphene. We observe an electrically tunable band gap exceeding 100 meV in ABC trilayers, while no band gap is found for ABA trilayers. We have also studied the influence of layer thickness and stacking order on the Raman response of the out-of-plane vibrations in FLG. We observe a Raman combination mode that involves the layer-breathing vibrations in FLG. This Raman mode is absent in SLG and exhibits a lineshape that depends sensitively on both the material's layer thickness and stacking sequence.

Two-dimensional electronic systems have long attracted interest in the physics and material science communities due to the exotic physics that arises from low-dimensional confinement. Studying the electronic behavior of 2D systems can provide insight into a variety of phenomena that are important to condensed-matter physics, including epitaxial growth, two-dimensional electron scattering and many-body physics. Correlation effects are strongly influenced by dimensionality, which determines the many-body excitations available to a system. In this dissertation, I examine the electronic structure of two very dierent types of two-dimensional systems: valence band electrons in single layer graphene and electronic states created at the vacuum interface of single crystal copper surfaces.The characteristics of both electronic systems depend intimately on the morphology of the surfaces they inhabit. Thus, in addition to discussing the respective band structures of these systems, a significant portion of this dissertation will be devoted to measurements of the surface morphology of these systems. Free-standing exfoliated monolayer graphene is an ultra-thin flexible membrane and, as such, is known to exhibit large out-of-plane deformation due to substrate and adsorbate interaction as well as thermal vibrations and, possibly, intrinsic buckling. Such crystal deformation is known to limit mobility and increase local chemical reactivity. Additionally, deformations present a measurement challenge to researchers wishing to determine the band structure by angle-resolved photoemission since they limit electron coherence in such measurements. In this dissertation, I present low energy electron microscopy and microprobe diffraction measurements, which are used to image and characterize corrugation in SiO2-supported and suspended exfoliated graphene at nanometer length scales. Diffraction line-shape analysis reveals quantitative differences in surface roughness on length scales below 20 nm which depend on film thickness and interaction with the substrate. Corrugation decreases with increasing film thickness, reflecting the increased stiffness of multilayer films. Specifically, single-layer graphene shows a markedly larger short range roughness than multilayer graphene. Due to the absence of interactions with the substrate, suspended graphene displays a smoother morphology and texture than supported graphene. A specific feature of suspended single-layer films is the dependence of corrugation on both adsorbate load and temperature, which is manifested by variations in the diffraction lineshape. The effects of both intrinsic and extrinsic corrugation factors will be discussed. Through a carefully coordinated study I show how these surface morphology measurements can be combined with angle resolved photoemission measurements to understand the role of surface corrugation in the ARPES measurement process. The measurements described here rely on the development of an analytical formulation for relating the crystal corrugation to the photoemission linewidth. I present ARPES measurements that show that, despite signicant deviation from planarity of the crystal, the electronic structure of exfoliated suspended graphene is nearly that of ideal, undoped graphene; the Dirac point is measured to be within 25 meV of EF . Further, I show that suspended graphene behaves as a marginal Fermi-liquid, with a quasiparticle lifetime which scales as (E - EF)-1; comparison with other graphene and graphite data is discussed. Image and surface states formed at the vacuum interface of a single crystal provide another example of a two dimensional electronic system. As with graphene, the surface quality and morphology strongly inuence the physics in this 2D electronic system. However, in contrast to graphene, which must be treated as a flexible membrane with continuous height variation, roughness in clean single crystal surfaces arises from lattice dislocations, which introduce discrete height variations. Such height variations can be exploited to generate a self assembled nano-structured surface. In particular, by making a vicinal cut on a single crystal surface, a nanoscale step array can be formed. A model system for such nanoscale self assembly is Cu(111). Cu(775) is formed by making an 8.5° viscinal cut of Cu(111) along the [11 -2] axis. The electronic states formed on the surface of this system, with a nanoscale step array of 14 Å terraces, shows markedly different behavior those formed on Cu(111). In this dissertation, I show that the tunability of a femtosecond optical parametric oscillator, combined with its high-repetition rate and short pulse length, provides a powerful tool for resonant band mapping of the sp surface and image states on flat and vicinal Cu(111)- Cu (775) surfaces, over the photon energy range from 3.9 to 5 eV. Since the time scale for excitation of the metal image state from the Cu surface state is comparable with the electron-electron equilibration time scale, sharp features are measured due to resonant excitation in the photoelectron energy distribution curves. In addition, I explore the range of photon energies and optical intensities which may be used for this approach and show that, despite the relatively high pump intensity, the 250 kHz repetition rate of this laser ameliorates the space-charge broadening and electron-energy shifting even for photon energies close to the vacuum edge. The strong excitation conditions generated by a femtosecond laser pulse applied to a Cu surface also allow the excitation and observation of a recently measured bulk state. In this dissertation I show that angle-resolved, tunable, two-photon photoemission (2PPE) can be used to map a bulk unoccupied band, viz. the Cu sp band 0 to 1 eV below the vacuum level, in the vicinity of the L point. This short-lived bulk band can be accessed using our setup due to the strong optical pump rate. I describe how photoemission from this state can be distinguished from photoemission from 2D states which is also present in the data. In particular, the variation of the initial-state energy with photon energy has a measured slope of ~ 1.64 in contrast with values of 1 or 2 observed for 2PPE from two-dimensional (2D) states. This unique variation illustrates the significant role of the perpendicular momentum of initial and final states in interpreting 2PPE data.

The two dimensional charge carriers in mono- and bilayer graphene are described by massless and massive chiral Dirac Hamiltonians, respectively. This thesis describes low temperature transport experiments designed to probe the consequences of this basic fact. The first part concerns the effect of the lattice pseudospin, an analog of a relativistic electron spin, on the scattering properties of mono- and bilayer graphene. We fabricate graphene devices with an extremely narrow local gates, and study ballistic carrier transport through the resulting barrier. By analyzing the interference of quasiparticles confined to the region beneath the gate, we are able to determine that charge carriers normally incident to the barrier are transmitted perfectly, a solid state analog of the Klein tunneling of relativistic quantum mechanics. The second part of the work describes the development of hexagonal boron nitride (hBN), an insulating isomorph of graphite, as a substrate and gate dielectric for graphene electronics. We use the enhanced mobility of electrons in h-BN supported graphene to investigate the effect of electronic interactions. We find interactions drive spontaneous breaking of the emergent SU(4) symmetry of the graphene Landau levels, leading to a variety of quantum Hall isospin ferromagnetic (QHIFM) states, which we study using tilted field magnetotransport. At yet higher fields, we observe fractional quantum Hall states which show signatures of the unique symmetries and anisotropies of the graphene QHIFM. The final part of the thesis details a proposal and preliminary experiments to probe isospin ordering in bilayer graphene using capacitance measurements.

In this thesis we use the recently developed dynamical mean-field approximation to study problems in strongly correlated electron systems, including high-Tc cuprate superconductors as well as a few quantum chemical reference systems. We start with an introduction to the background of the interacting electron systems, followed by a brief description on the current understanding of the physics of high-Tc cuprate superconductors. The approximate models that enter the theoretical framework will be discussed afterwards. Some quantum chemical methods for many-body quantum systems are included for review. Next we present the numerical methods employed in our study. The formalism of the dynamical mean-field approximation will be introduced including the single-site and cluster versions, followed by the Exact Diagonalization impurity solver for the solution of the quantum impurity model. Maximum Entropy analytic continuation method is also discussed, which is useful to obtain the physically relevant response functions. Then we apply dynamical mean-field approximation to high-Tc cuprate superconductors. The two-particle response functions, such as Raman scattering intensity and optical conductivity, are computed for the two dimensional Hubbard model. The calculations include the vertex corrections which are essential to obtain physically reasonable results in interacting electron systems. We also study the physics of the pseudogap in cuprates. The suppression of density of states near Fermi surface is present in our calculations, which is in qualitative agreement with the experimental data. Finally we discuss the application of dynamical mean-field theory to quantum chemistry. We extend the formalism of dynamical mean-field approximation to finite systems, and compare its performance in hydrogen clusters with different spatial configurations to other leading quantum chemical approaches. Dynamical mean-field theory involves mapping onto a quantum impurity model. We further examine the quantum impurity model representation of the transition metal dioxide molecules. The conceptual and technical difficulties will be discussed.

A one-dimensional quantum mechanical system is experimentally synthesized and investigated for physical phenomena that it may inherit due to quantum confinement and electron correlations. The experimentally realized system is a self-assembled array of monatomic cobalt wires that are grown under ultra-high vacuum conditions on a vicinal copper (111) substrate using a recipe developed specifically for this work. This work experimentally demonstrates that this 1-D system undergoes a charge density wave instability, which is a first for such a 1-D phenomenon on a metallic substrate. It is determined experimentally that this 1-D system undergoes an electronic phase transition at a temperature of about 85K, in which the higher temperature electronic phase is itinerant rather than localized. Using ab initio density functional theory, the cause of the measured charge density wave instability is assigned to erromagnetic interactions along the chain. Specifically, it is deduced that the instability is driven by spin -minority pin-exchange interactions predominately in the cobalt dxz/dyz orbitals. Beyond, shedding light on electron correlations in a physically realized quantum mechanical 1-D system, this work demonstrates that this particular system is a new test-case example for advanced theoretical techniques in predicting the correct structural ground phase.

Atomically thin two-dimensional crystals form a distinct and growing class of new materials. The electromagnetic response of a two-dimensional crystal provides direct access to its electronic properties. This thesis presents a series of experimental studies of the electromagnetic response of model two-dimensional crystals as probed by optical spectroscopy. Our aim is to obtain understanding of their intrinsic linear and nonlinear response and the many-body interactions in these materials, as well as to explore the potential to use the two-dimensional materials for sensing applications. In the two studies of graphene, we either removed contaminations from the environment to reveal the intrinsic response or intentionally applied adsorbates to investigate how the electrons interact with the extrinsic molecules. In the first study, we obtained ultra-clean graphene using hexagonal boron nitride as the substrate, which allowed us to probe using Raman spectroscopy the intrinsic electron-phonon and electron-electron interactions free from substrate induced sample inhomogeneity. In a second study, we demonstrate a strong near-field electromagnetic interaction of graphene plasmons with the vibrations of adsorbed molecules. Our results reveal the potential of graphene for molecular sensing. In our investigations of the monolayer transition metal dichalcogenides, we performed measurements of the linear and the second-order nonlinear dielectric response. From the linear dielectric response, we demonstrate strong light-matter interactions even for a single layer of these materials. Several trends in the excitonic properties of this group of materials were obtained from the measured dielectric function. In the nonlinear optical study, we observed a large enhancement of the second-harmonic signal from monolayers as compared to the bulk sample, a consequence of the breaking of the inversion symmetry present in the bulk. In addition to the results for monolayers, we describe the behavior of few-layer materials, where the symmetry properties change layer by layer. For monolayers (and samples of odd layer thickness with broken inversion symmetry), the strong and anisotropic second-harmonic response provides a simple optical probe of crystallographic orientation. In the magneto-optic study of transition metal dichalcogenide monolayers, we demonstrate the induction of valley splitting and polarization by the application of an external magnetic field. The interaction of the valleys with the magnetic field reflects their non-zero magnetic moments, which are compared to theoretical models. We further clarify the electronic configuration of the charged excitons and important many-body corrections to the trion binding energy through the control of valley polarization achieved by the external magnetic field.

In this thesis we theoretically study new aspects of charge density waves in transition metal materials recently revealed by scanning tunneling microscopy measurements. The two important problems that we have investigated are the effects of orbital degeneracy on the formation of the charge-density waves in cobalt nanowires, and the effects of dilute but strongly pinning impurities on the charge-density wave in niobium diselenide. We first present an overview on charge-density waves, and then introduce a general theoretical model describing charge-density waves. We also explain several known results about disorder effects on charge-density waves. We briefly touch on the principle of scanning tunneling microscopy and its advantages compared to other experimental tools. Second, we discuss the physics of one-dimensional cobalt nanowires along with experimental results. We propose a theoretical model that is relevant to cobalt nanowires, and then analyze the model by two theoretical tools: mean-field theory and bosonization. Our results show that the multi-orbitals allow a spin-triplet interaction among electrons leading to different phase diagrams from the ones considered previously for similar models. Numerical results obtained by first-principles calculations are also briefly explained. Third, we consider the effects of dilute strong impurities on the charge-density wave in niobium diselenide, a transition metal dichalcogenide. We first explain the material and properties of its charge-density wave phase. Then, detailed analysis of a scanning tunneling microscopy measurement is presented. Next, we analytically and numerically study a phenomenological model relevant to the experiment. We show that the dilute strong impurities have little effects at large length scales compared to the average inter-impurity distance, leading to a topologically ordered phase with a (quasi-)long-range autocorrelation; this result is quite different from conventional pictures predicting short-range order with the proliferation of topological defects.

Scanning Tunneling Microscopy is a very powerful technique to study electronic properties of condensed matter systems at the nanoscale. Part I of this thesis describes my work on Charge Density Waves (CDW) in NbSe₂. NbSe₂ is a layered dichalcogenide that has a CDW phase below 33K. We describe our study of the phase transition from the normal phase to the CDW phase at atomic scales. This is more relevant in light of recent discoveries of charge order in cuprates. Brand new research has shed some light about the relationship between the pseudogap phase, charge order and superconductivity in cuprates. The behavior of the CDW phase in NbSe₂ described in chapter 3 is strongly reminiscent of this physics of cuprates. NbSe₂ is an excellent test bed for the study of the effect of impurities in correlated phases. In chapter 4 we revisit the cause of CDW formation in NbSe₂. By including a very dilute concentration of impurities, we obtain information of the electronic bands of the material in the CDW phase. Based on this information, we are able to discuss the relationship between nesting, electron-phonon coupling and CDW in NbSe₂. We demonstrate that by combining quasiparticle interference data with additional knowledge of the quasiparticle band structure from angle resolved photoemission measurements, one can extract the wavevector and energy dependence of the important electronic scattering processes. Part II focuses on Muon Spin Rotation and its application to the study of high-Tc superconductors. We describe our muSR studies on Nickel doped BaFe₂As₂. By analyzing several doping concentrations, we explore the phase diagram in the antiferromagnetic and in the superconducting phases. This discussion also includes a detailed discussion of a doping concentration which falls in-between the AF and the SC phase.

Despite almost a century of exploration, we continue to discover new systems where quantum mechanics, strong interactions and disorder combine in novel ways. These systems test the capabilities of our strongest theoretical tools. In this thesis I discuss work on three of these systems: bilayer graphene, disordered conductors and cold atom systems. In bilayer graphene I show that the large number of degenerate bands leads to a plethora of possible spontaneous symmetry breaking ground state. In disordered conductors I discuss how quantum interference can lead to arbitrarily long lived responses, so called memory eects. I also consider whether a novel spontaneous symmetry breaking state can be created in cold atomic gasses using nonequilibrium perturbations.

<p>Dopant diffusion in semiconductors is an interestingphenomenon from both technological and scientific points ofview. Firstly, dopant diffusion is taking place during most ofthe steps in electronic device fabrication and, secondly,diffusion is related to fundamental properties of thesemiconductor, often controlled by intrinsic point defects:self-interstitials and vacancies. This thesis investigates thediffusion of P, B and Sb in Si as well as in strained andrelaxed SiGe. Most of the measurements have been performedusing secondary ion mass spectrometry on high purityepitaxially grown samples, having in-situ incorporated dopantprofiles, fabricated by reduced pressure chemical vapordeposition or molecular beam epitaxy. The samples have beenheat treated both under close-to-equilibrium conditions (i. e.,long time annealings in an inert ambient) and conditions whichresulted in non-equilibrium diffusion (i. e., vacuum annealing,oxidation, short annealing duration, and protonirradiation).</p><p>Equilibrium P and B diffusion coefficients in Si asdetermined in this thesis differ from a substantial part ofpreviously reported values. This deviation may be attributed toslow transients before equilibrium concentrations of pointdefects are established, which have normally not been takeninto account previously. Also an influence of extrinsic dopingconditions may account for the scattering of the diffusivityvalues reported in literature. B and Sb diffusion in Si underproton irradiation at elevated temperatures was found to obeythe so-called intermittent model. Parameters describing themicroscopic diffusion process were derived in terms of theintermittent diffusion mechanism, and it was found also thatthe presence of Sb strongly affected the B diffusion and viceversa.</p><p>In relaxed Si_1-xGe_x-alloys, which has the same lattice structure as Sibut a larger lattice constant, P diffusion is found to increasewith increasing Ge content (<i>x</i>≤ 0.2). In Si/SiGe/Si heterostructures, wherethe SiGe layer is biaxially strained in order to comply withthe smaller lattice parameter of Si, P diffusion in thestrained layer is retarded as compared with relaxed materialhaving the same Ge content. In addition, P is found tosegregate into the Si layer via the Si/SiGe interface and thesegregation coefficient increases with increasing Ge content inthe SiGe layer.</p>