| Summary: | Two-dimensional solids often exhibit carrier bands with Berry phase in 𝑘 space, resulting in carriers behaving like spinning objects and generating orbital magnetization in position space. This thesis explores the impact of orbital magnetization arising in this way on the correlated electron phases. The effect of Berry phase is particularly interesting for magnetic phases with spin and valley polarization originating from Stoner instability, such as those seen in moiré graphene and other narrow-band systems. Despite recent advances in the field, these questions remain largely unexplored, and this thesis aims to address this gap in research. Interesting physics arises due to an interplay between two distinct effects: geometric phases in 𝑘 space due to band Berry curvature and geometric phases in position space arising for spin-polarized carriers traversing a spin texture. This results in an interaction that we term the “chiral interaction,” a form of an emergent spin-orbital interaction that arises solely from electron exchange, in the absence of microscopic spin-orbit couplings. The chiral interaction, in contrast to microscopic spin-orbit coupling, respects the SU(2) spin rotation symmetry and exhibits other interesting characteristics. In this thesis, we establish the existence of this interaction through a general symmetry argument and microscopic calculations, and investigate its consequences. Specifically, we explore the emergence of chiral edges that support spin excitations propagating without back-scattering and the occurrence of skyrmions, the topologically protected particle-like objects stabilized by the chiral interaction in the ground state of the system.
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