UC Berkeley

The two most prevalent classes of ordered states in quantum materials are those arising from spontaneous symmetry breaking (SSB) and from topological order. However, a systematic study for their coexistence in interacting systems is still lacking. In this thesis, we will investigate how the topological configuration in order parameter spaces from SSB interplays with the symmetry protected/enriched topological orders in two spatial dimensions. We start from a phenomenological model of the domain wall structure in chiral spin liquids with domains of opposite chiralities. Based on a standard model, we obtain a spatially varying, self-consistent mean-field solution for the spinons that describes both the gapless edge modes and the change of chirality at the domain wall. We derive the non-universal properties, such as the velocity of the topologically protected domain wall edge states and its modification to domain wall tension. Then we discuss the interplay between topological orders from a more formal point of view. We consider two-dimensional topologically ordered systems with coexisting long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. We show that the universal properties of point defects and textures are determined by the remnant symmetry enriched topological order in the symmetry-breaking ground state with non-fluctuating order parameters, and provide a classification for their properties using algebraic topology. We further investigate the quantum dynamics that can happen at the domain wall of topological orders, where particle-hole scattering leads to linear-in-temperature resistivity of edge modes. Finally, we introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators.