High critical-temperature (Tc) superconductivity in the cuprates has been a defining challenge of condensed matter physics for the 35 years since their discovery. One strategy to address this challenge has been to look for "cuprate analog'' materials: alternative transition metal oxides that exhibit ingredients that are considered proxies for cuprate physics. These key ingredients include a quasi-2D structure based on the CuO2 planes, a nominal oxidation state for Cu2+: 3d9 with a single hole in the uppermost dx2-y2 orbital, and a strong O(2p) and Cu(3d) hybridization. Nickelates have been an obvious choice of study in this context due to the proximity of Ni to Cu on the periodic table. After a 30 year wait, superconductivity in nickelates was realized for the first time in 2019 in hole-doped NdNiO2 (Li et al, 2019). This material contains NiO2 planes (analog to the CuO2 planes of the cuprates), and realizes a Ni1+ oxidation state (analog to Cu2+). NdNiO2 is simply the infinite-layer member of a larger family of materials represented by the chemical formula Rn+1NinO2n+2 (R= La, Pr, Nd; n >= 2), where n refers to the number of NiO2 planes along the c axis. In this thesis, a comprehensive description of the electronic structure of the Rn+1NinO2n+2 family of layered rare-earth nickelates (for n= oo and n=2-6) using state-of-the-art first-principles methods is presented. Specifically, different levels of theory are used to describe the electronic structure of this family of materials: from density-functional band theory (DFT) to incorporating correlation effects at the mean-field level via DFT+U, and finally including dynamical many-body effects via DFT+dynamical mean-field theory (DFT+DMFT). It is shown that the cuprate-like character of the layered nickelate series increases from the n=oo to the n=3 members. Namely, as n decreases the electronic structure becomes more single-band-like, and the degree of p-d hybridization increases while correlations are dominated by the dx2-y2 orbitals. Insights from these calculations allowed for the prediction of the n=4-6 nickelates as ideal candidates for nickelate superconductivity. Indeed, superconductivity was subsequently observed in the quintuple layer nickelate Nd6Ni5O12 (Pan et al, 2021). That superconductivity arises in this layered rare-earth nickelate series, suggests that a new family of superconductors has been uncovered, currently with two members, n=oo and n=5.

The performance of kilometer-scale electron accelerators, which are used for high energy physics and next-generation light sources as well as meter-scale ultra-fast electron diffraction setups is limited by the brightness of electron sources. A potential emerging candidate for such applications is the family of alkali and bi-alkali antimonides. Much of the physics of photoemission from such semiconductor photocathodes is not fully understood even today, which poses a hindrance to the complete exploration and optimization of their photoemission properties. This thesis presents the theoretical and experimental measurements which lead to advances in the understanding of the photoemission process and properties of cesium-antimonide photocathodes. First, the growth of high quantum efficiency (QE), atomically smooth and chemically homogeneous Cs$_3$Sb cathodes on lattice-matched strontium titanate substrates (STO) is demonstrated. The roughness-induced mean transverse energies (MTE) simulations indicate that the contribution to MTE from nanoscale surface roughness of Cs$_3$Sb cathodes grown on STO is inconsequential over typically used field gradients in photoinjectors. Second, the formulation of a new approach to model photoemission from cathodes with disordered surfaces is demonstrated. The model is used to explain near-threshold photoemission from thin film Cs$_3$Sb cathodes. This model suggests that the MTE values may get limited to higher values due to the defect density of states near the valence band maximum. Third, the detailed measurements of MTE and kinetic energy distribution spectra along with QE from Cs$_3$Sb cathodes using the photoemission electron microscope are presented. These measurements indicate that Cs$_3$Sb cathodes have a work function in the range of 1.5-1.6 eV. When photoemitting near this work function energy, the MTE nearly converges to the thermal limit of 26 meV. However, the QE is extremely low, of the order of 10$^{-7}$, which limits the operation of these photocathodes for high current applications. Lastly, the growth of Cs$_3$Sb cathodes using the ion beam assisted molecular beam deposition (IBA-MBE) technique is demonstrated. This technique has the potential to grow epitaxial Cs$_3$Sb cathodes in a more reproducible, easier fashion. Structural characterization of such cathodes via tools such as reflection high energy electron diffraction (RHEED) and x-ray diffraction (XRD) will be necessary to investigate the role of the IBA-MBE technique in facilitating the epitaxial, ordered growth of alkali-antimonides.

Producing a brighter electron beams requires the smallest possible emittance from the cathode with the highest possible current. Several materials like ordered surface, single-crystalline metal surfaces, ordered surface, epitaxially grown high quantum efficiency alkali-antimonides, topologically non-trivial Dirac semimetals, and nano-structured confined emission photocathodes show promise of achieving ultra-low emittance with large currents. This work investigates the various limitations to obtain the smallest possible emittance from photocathodes, and demonstrates the performance of a novel electron gun that can utilize these photocathodes under optimal photoemission conditions. Chapter 2 discusses the combined effect of physical roughness and work function variation which contributes to the emittance. This is particularly seen in polycrystalline materials and is an explanation for their higher than expected emittance performance when operated at the photoemission threshold. A computation method is described for estimating the simultaneous contribution of both types of roughness on the mean transverse energy. This work motivates the need for implementing ordered surface, single-crystalline or epitaxially grown photocathodes. Chapter 3 investigates the effects of coulomb interactions on electron beams from theoretically low emittance, low total energy spread nanoscale photoemission sources specifically for electron microscopy applications. This computation work emphasizes the key role that image charge effects have on such cold, dense electron beams. Contrary to initial expectations, the primary limiter to beam brightness for theoretically ultra-low emittance photocathodes is the saturation current. Chapters 4 and 5 describe the development and commissioning of a high accelerating gradient, cryogenically cooled electron gun and photoemission diagnostics beamline within the Arizona State University Photoemission and Bright Beams research lab. This accelerator is unique in it's capability to utilize photocathodes mounted on holders typically used in commercial surface chemistry tools, has the necessary features and tools for operating in the optimal regime for many advanced photocathodes. A Pinhole Scan technique has been implemented on the beamline, and has shown a full 4-dimensional phase space measurement demonstrating the ability to measure beam brightness in this gun. This gun will allow for the demonstration of ultra-high brightness from next-generation ultra-low emittance photocathodes.

The performance of accelerator applications like X-ray free electron lasers (XFELs)and ultrafast electron diffraction (UED) and microscopy (UEM) experiments is limited by the brightness of electron beams generated by photoinjectors. In order to maximize the brightness of an electron beam it is essential that electrons are emitted from photocathodes with the smallest possible mean transverse energy (MTE). Metallic photocathodes hold the record for the smallest MTE ever measured at 5 meV from a Cu(100) single crystal photocathode operated near the photoemission threshold and cooled to 30 K. However such photocathodes have two major limitations: poor surface stability, and a low quantum efficiency (QE) which leads to MTE degrading non-linear photoemission effects when extracting large charge densities. This thesis investigates the efficacy of using a graphene protective layer in order to improve the stability of a Cu(110) single crystalline surface. The contribution to MTE from non-linear photoemission effects is measured from a Cu(110) single crystal photocathode at a variety of excess energies, laser fluences, and laser pulse lengths. To conclude this thesis, the design and research capabilities of the Photocathode and Bright Beams Lab (PBBL) are presented. Such a lab is required to develop cathode technology to mitigate the practical limitations of metallic photocathodes.