UC Berkeley

Interest has been rising in systems, such as the iridates, where both spin-orbit coupling and Coulomb correlations play a prominent role, with theoretical proposals for a variety of exotic states. One such state, the spin-orbit Mott insulator, was discovered by Kim et al in Sr$_2$IrO$_4$ using angle-resolved photoemission spectroscopy, the experimental technique used in this work. Such states were later discovered in a variety of materials, including Sr$_3$Ir$_2$O$_7$, Na$_2$IrO$_3$, and RuCl$_3$ and provide a concrete testing ground for the physics of Mott insulators. This includes, naturally, the search for nearby exotic states which are the frequent companion of the Mott state. Indeed, significant attention has been given to doped Sr$_2$IrO$_4$ as an analog to the cuprate high-temperature superconductors, and to Na$_2$IrO$_3$, Li$_2$IrO$_3$, and RuCl$_3$ as candidates for hosting a spin-liquid state.

This work focuses on (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$, which is notable in the weakness of its parent Mott state and thus its likely proximity to other ground states. The substitution of La on the Sr site adds electrons as carriers to the system. This eventually destroys the insulating state, though manifestations of both Coulomb correlations and spin-orbit coupling remain well beyond the insulator-metal transition. Chapter 1 covers the physics relevant to the ground state of (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$, starting from the effects of Coulomb correlations and spin-orbit coupling in general and including an overview of the current experimental results in doped and undoped Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$. Chapter 2 summarizes the theory of (spin- and) angle-resolved photoemission spectroscopy (ARPES), and describes analysis techniques used in the later chapters. The main experimental results of the work obtained using spin-integrated photoemission are in chapter 3, including evidence for a novel ground state in lightly-doped (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ and a thorough exploration of the evolving role of Coulomb correlations with doping. Chapter 4 goes into more recent results from several spin-resolved ARPES measurements and their possible implications, including some outstanding puzzles in the results.