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.
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