Sarah Burke

Electrical conduction becomes non-local when an inhomogeneous electronic distribution is induced with a spatial variation shorter than the mean free path (MFP) between momentum-relaxing scattering processes. Two important methods of inducing such a distribution are via the size and skin effects. In the size effect, one or more dimensions of a medium are reduced below the MFP. The scattering of electrons from the medium's boundaries then induces an inhomogeneous electronic distribution under an applied direct current. In the skin effect, the exponential decay of alternating electromagnetic fields as they propagate into the medium gives rise to a so-called skin layer. The electronic distribution within the skin layer becomes inhomogeneous as the skin depth falls below the MFP. Here we study the size and skin effects in PdCoO₂, both experimentally and theoretically. While previous theoretical treatments of non-local electrical conductivity have assumed a free-electron dispersion, we observe that the anisotropic Fermi surface (FS) in PdCoO₂ results in behaviour that is incompatible with this assumption. Measurements of the size effect in PdCoO₂ revealed two novel phenomena, both of which are symmetry-forbidden for local conduction: anisotropy in the in-plane longitudinal resistivity, and a non-zero transverse resistivity at zero magnetic field. We developed a theory of the size effect for arbitrary FS geometry and used it to reproduce the key features of these measurements. Motivated by recent interest in the possibility that electrons in solids may behave viscously as a result of frequent internal momentum-conserving scattering, we developed a generalized theory of the skin effect, taking into account separate rates of momentum-conserving and momentum-relaxing scattering for arbitrary FS geometry. For an isotropic FS, our theory encompasses several known limiting behaviours. For anisotropic FSs, we explored geometries which lead to changes in the scaling of the surface impedance. By applying bolometric broadband microwave spectroscopy, we studied the skin effect in PdCoO₂ for three different directions of electromagnetic propagation. Using symmetry-based arguments, we determined that our measurements were neither in the local nor purely viscous regime. We argued instead that the data demonstrate a novel, predominantly ballistic effect as a result of the faceted FS.

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Graphene, the first truly 2D material to be isolated, is host to a wealth of remarkable properties. It can be modified in a variety of ways—strained, twisted, stacked, placed on a substrate, decorated with adatoms, etc.—to further enhance these properties or introduce new ones. In this thesis, we use several complementary surface characterization techniques to study two methods of modifying epitaxial graphene on a silicon carbide (SiC) substrate via the addition of other atoms.In the first method, we induce the Kekulé distortion—a periodic distortion of the bonds in graphene—using a small number of lithium atoms (
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Topological materials have been at the forefront of condensed matter physics research over the past few decades. Characterised by electronic bands with non-trivial topological invariants, topological materials exhibit a number of interesting electronic properties, such as conducting chiral boundary states and linear electronic dispersions, and have been theorised for use in a variety of applications ranging from spintronic devices to quantum computing. Recently, topological semimetals were discovered, where the bulk electronic bands are understood in the framework of the high-energy relativistic Dirac equation and its conditional variations, the Weyl and Majorana equations. Furthermore, the vast permutations of material compounds available results in a nearly infinite sandbox for researchers to study, which has resulted in topological semimetals that have no high-energy analogue. One of such material classifications is the nodal-line semimetal, characterised by linear electronic band crossings that form lines or loops in momentum space. These nodal-line semimetals also exhibit exotic surface states, named drumhead states, which are an interesting and exciting new state with promises in high-temperature superconductivity and quantum computation. A large effort is being placed to find materials that can be used to study the fundamental properties of these materials and their resultant surface states. Scanning tunnelling microscopy (STM) provides a perfect tool to study the topological properties of materials, able to atomically resolve the surface structure and also provide insight into scattering selection rules, which are deeply dependent on the band topology. Two topological materials were studied using STM in this thesis: the topological nodal-line semimetal ZrSiTe and the topological insulator (Bi$_x$Sb$_{1-x}$)$_2$Te$_3$. ZrSiTe was studied with an emphasis on the quasiparticle scattering characteristics, measured using Fourier-transform scanning tunnelling spectroscopy. Two main scattering features are examined, one relating to the nodal line, and the other arising from the drumhead surface state. These studies mark the first time a drumhead state has been observed using a real space measurement. (Bi$_x$Sb$_{1-x}$)$_2$Te$_3$ was studied with an emphasis on the nano-scale transport characteristics, measured using 4-probe STM and scanning tunnelling potentiometry. Effects of step edges and domain boundaries on the local resistance are studied for a fractional substitution of $x = 0.19$.

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At the atomic scale, surfaces exhibit a rich variety of physical phenomena that can be probed using a scanning tunnelling microscope (STM). The STM measures the quantum tunnelling of electrons between a metallic tip and conducting sample and can be used to characterize the nanoscale surface. This thesis presents STM measurements taken at low-temperature in ultra-high vacuum, which are used to characterize two different nanoscale environments: the two-dimensional surface states of Ag(111) and Cu(111) and the magnetic moments of iron and cobalt atoms deposited on a thin-film of magnesium oxide.Fourier-transform scanning tunnelling spectroscopy (FT-STS) analysis of quasiparticle interference, created by impurity scattering on the surfaces of the noble metals Ag(111) and Cu(111), is used to compare the most common modes of acquiring FT-STS data and shows, through both experiment and simulations, that artifact features can arise that depend on how the STM tip height is stabilized throughout the course of the measurement. Such artifact features are similar to those arising from physical processes in the sample and are susceptible to misinterpretation in the analysis of FT-STS in a wide range of important materials. A prescription for characterizing and avoiding these artifacts is proposed, which details how to check for artifacts using measurement acquisition modes that do not depend on tip height as a function of lateral position and careful selection of the tunnelling energy.In a separate set of experiments a spin resonance technique is coupled to an STM to probe the spin states of individual iron atoms on a magnesium oxide bilayer. The magnetic interaction between the iron atoms and surrounding spin centres shows an inverse-cubic distance dependence at distances greater than one nanometre. This distance-dependence demonstrates that the spins are coupled via a magnetic dipole-dipole interaction. By characterizing this interaction and combining it with atomic manipulation techniques a new form of nanoscale magnetometry is invented. This nanoscale magnetometer can be combined with trilateration to probe the spin structure of individual atoms and nanoscale structures. The information gained characterizing these new forms of magnetic sensing sets the stage for the study of complex magnetic systems like molecular magnets.

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Organic semiconductors are a promising class of materials for many applications such as photovoltaics, light emitting diodes, and field-effect transistors. As these devices rely on the movement of charge at and near interfaces, understanding energy level alignment at these boundaries is essential to improve device performance. Differences in the local environment and surrounding molecular geometry have the potential to cause significant energy level shifts occurring on single molecule length scales, thus affecting device properties. Scanning Probe Microscopy is a family of techniques that allows investigation of materials on the molecular and submolecular level. Scanning Tunneling Spectroscopy (STS) allows for the mapping of electronic states with spatial and energetic resolution. Electrostatic Force Spectroscopic (EFS) mapping investigates the local charge distribution of surfaces even down to submolecular resolution. We utilize these techniques to investigate the prototypical semiconductors PTCDA and CuPc on NaCl(2ML)/Ag(111). Nanoislands of PTCDA were examined with STS, revealing strong electronic differences between molecules at the edges and those in the center, with energy level shifts of up to 400 meV. We attribute this to the change in electrostatic environment at the boundaries of clusters, namely via polarization of neighboring molecules. To further investigate the local electrostatics, we use EFS to probe the effect of adding charge to PTCDA molecules, both isolated and within clusters. We found that the charging energy depends on the initial local charge distribution by spatially resolving the charging events with sub-molecular resolution. In order to investigate the influence of interface geometry, we use pixel-by-pixel STS of the prototypical acceptor/donor system PTCDA/CuPc. We observe shifting of the donor and acceptor states in opposite directions, indicating an equilibrium charge transfer between the two. Further, we find that the spatial location of electronic states of both acceptor and donor is strongly dependent on the relative positioning of both molecules in larger clusters. The observation of these strong shifts illustrates a crucial issue: interfacial energy level alignment can differ substantially from the bulk electronic structure in organic materials. This has significant implications for device design, where energy level alignment strongly correlates to device performance.

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Organic-based technologies have recently attracted significant interest. Characterization of their structure and properties at native length scales are essential for their implementation in devices. On-surface self-assembly of metal-organic frameworks is a simple way to fabricate molecular systems with specific functionalities. In this thesis work, the morphology and electronic structure of self-assembled linear nanochains, featuring a triiron linkage between two bisterpyridine-based ligands on an Ag(111) surface, have been investigated with scanning tunneling microscopy and spectroscopy. An in situ, clean and reliable on-surface preparation technique was developed for thermally-activated self-assembly of complexes based on the metal-organic motif of dyes used in photovoltaic and catalysis applications. Tunneling spectroscopy on the metal-organic nanostructures obtained suggests the formation of a coordination bond with charge transfer between metal and ligand. Furthermore, the electronic structure indicates the presence of the desired metal-to-ligand charge transfer optical transitions, characteristic of the related complexes. The unprecedented triiron coordination link has potential for being an efficient reaction center for catalysis applications, as well as for having interesting magneto, spin, and electronic properties. Each step and aspect of the chains formation process has been characterized via scanning tunneling microscopy measurements and growth studies, and the results are supported by density functional theory calculations. Additionally, the relevance and influence of the silver metal substrate on both bare ligands and chains has been investigated. Bare molecules show a strong interaction with the substrate, as demonstrated by their specific adsorption configurations and an electronic structure which is distinct from when they are electronically decoupled from the surface by an NaCl bilayer. When the molecules are in chains the silver plays a key role in the structure of the coordination link. This work shows the potential of using on-surface self-assembly and scanning tunneling microscopy and spectroscopy, not only to prepare with high-fidelity clean and controlled structures but also as a flexible platform to investigate and tailor functional properties of different systems for a large variety of applications where a solid support is essential.

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