Bi2Se3 is an ideal three-dimensional topological insulator in which chemical modifications such as doping and intercalation can be used to engineer surface properties or to further functionalize the topological surface state. In this work, we study the Bi2Se3 system of materials with three experimental techniques: 1) ultrafast optical pump-probe spectroscopy (OPP), 2) angle-resolved photoemission spectroscopy (ARPES), and 3) X-ray photoelectron spectroscopy (XPS). These spectroscopic techniques are utilized to study the out-of- equilibrium carrier properties, surface chemistry, and band structure of Bi2Se3, Bi2–xSbxSe3, and CuxBi2Se3.

The photoexcited carrier decay in Bi2–xSbxSe3 nanoplatelets was studied with ultrafast optical pump-probe spectroscopy, demonstrating a substantial slowing of the bulk carrier relaxation time in bulk-insulating Bi2–xSbxSe3 as compared to n-type bulk-metallic Bi2Se3 at low temperatures, which approaches 3.3 ns in the zero pump fluence limit. This long-lived decay is correlated across different fluences and antimony concentrations, revealing unique decay dynamics not present in n-type Bi2Se3, namely the slow bimolecular recombination of bulk carriers.

Using ambient pressure X-ray photoelectron spectroscopy, copper migration in interca- lated CuxBi2Se3 is demonstrated, occurring on a timescale of hours to days after initial surface cleaving. The increase in near-surface copper proceeds along with the oxidation of the sample surface and large changes in the selenium content, with the development of copper and selenium gradients. These complex changes are further modelled with core level spectroscopy simulations (SESSA), which suggest a composition gradient near the surface which develops with oxygen exposure. These results shed light on a phenomenon that must be considered in intercalated topological insulators and intercalated materials in general.

Photoemission experiments are an information rich probe into the electronic structure of materials. Angle-resolved photoemission spectroscopy (ARPES) focusing on the valence bands and X-ray photoemission spectroscopy (XPS) focusing on tightly bound core electrons give a wholistic view into the features of occupied electronic states. In this dissertation I: (1) perform the first ARPES studies of LaNiGa$_2$, (2) develop an autonomous machine learning control system to improve the speed at which ARPES data can be taken, and (3) analyze the correlation between spatially resolved XPS and ARPES studies on Co$_3$Sn$_2$S$_2$. These together demonstrate the utility of ARPES and XPS for studying quantum materials as well as incorporating modern machine learning practices to extract otherwise hidden data from these rich datasets.

LaNiGa$_2$ is an unconventional superconductor that is reported to break time-reversal symmetry in its superconducting state, despite the absence of nearby magnetism. LaNiGa$_2$ has a nonsymmorphic Cmcm space group, which enforces symmetry-protected electronic degeneracies in its band structure. ARPES measurements across the three-dimensional Brillouin zone reveal features broadly consistent with density functional theory calculations. These measurements provide direct evidence for both predicted symmetry-enforced degeneracies and accidental near-degeneracies throughout the electronic structure. These findings suggest that the interplay between these degeneracies and the Fermi surface topology may play a role in the superconducting pairing mechanism of LaNiGa$_2$. This work on LaNiGa$_2$, detailed in Chapter 3, lead to two publications [1,2].

ARPES experiments often require substantial time to locate optimal sample regions for detailed study. AARDVARK, an autonomous machine learning control system, addresses this challenge by analyzing data in real time to guide measurements efficiently. The system uses uniform manifold approximation and projection (UMAP) for dimensionality reduction, followed by Gaussian process modeling to map spatial inhomogeneity. This pipeline reduces the number of measurements needed by approximately 75\% compared to traditional grid-search approaches while providing the same spatial heuristics to users. AARDVARK demonstrates the potential for integrating machine learning into photoemission spectroscopy workflows, enhancing the speed of collection of spatially resolved studies. This project is detailed in Chapter 4 and constitutes a manuscript that at the time of writing this dissertation is in preparation to be submitted for peer review.

Co$_3$Sn$_2$S$_2$ exhibits surface heterogeneity with distinct sulfur, tin, and mixed terminations, which influence its local electronic structure. ARPES and XPS measurements were performed across a $500 \, \mu\text{m} \times 300 \, \mu\text{m}$ area using a micro-focused beam ($15 \, \mu\text{m} \times 15 \, \mu\text{m}$), providing spatially resolved insight into the correlation between valence and core-level spectra. By combining traditional spectral integration methods with machine learning, the analysis captures termination-dependent variations in the electronic structure, forming a basis for interpreting spatial heterogeneity in hyperspectral datasets. These experiments highlight the critical role of synchrotron light sources in enabling simultaneous, high-resolution ARPES and XPS measurements, which are essential for studying spatially complex quantum materials. The study of surface heterogeneity in Co$_3$Sn$_2$S$_2$ in Chapter 5 is a portion of a manuscript that is still being prepared at the time of writing this dissertation.