Criticality, fractionalization, and superconductivity in two-dimensional quantum materials.

Abstract

Emergence is a foundational concept in modern condensed matter physics, capturing the idea that interactions between many degrees of freedom can give rise to phenomena that have no analog at the level of individual constituents. Superconductivity stands as one of the most celebrated exam- ples of emergence, where electronic correlations give rise to a macroscopically observable coherent quantum-mechanical state. More recent developments in the field include the study of emergent gauge theories, which describe the highly entangled states of matter that can appear in frustrated and strongly interacting systems. As increasingly exotic phases of matter are discovered, a deeper understanding of how strong correlations give rise to these phases and the transitions between them becomes essential. In this dissertation, we will explore the concept of emergence in the context of two-dimensional quantum materials. In the first part, we will discuss the exotic phenomenology of high-temperature cuprate superconductors and present a theory for a fractionalized parent state of superconductivity. We will describe how such a parent state can account for several experimental observations made in both the superconducting and charge-ordered phases. We will describe how our normal state can be understood as an emergent gauge theory, with possible applications to the study of deconfined critical points. Furthermore, we will study the critical properties of out theory through a renormal- izationgroupN1 analysis. We will also explore the strange metallic phase of the cuprate superconductors, presenting a study at large M of a simplified, zero-dimensional model that captures the spin glass phase observed at low doping, the Planckian metal phase near criticality, and the Fermi-liquid-like phase at high doping. Additionally, we will examine the 1/M corrections demonstrate that they always lead to spin glass ordering at low doping. In the final part of this dissertation, we will discuss several examples of superconducting and in- sulating phases observed in moiré materials. First, we will investigate the possibility of deconfined criticality in twisted bilayer graphene and identify the potential superconducting pairing states com- patible with a direct second-order transition between the superconductor and insulator. Next, we will present a mean-field analysis of insulating and superconducting instabilities in several stacked van der Waals materials. We will further discuss the consequences of inter-band coherence on ob- servables in the superconducting state.