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Explore the fascinating world of spin-resolved topology in quantum materials through this comprehensive lecture. Delve into the intricacies of topological insulating phases, focusing on their disorder-robust bulk responses and boundary states. Examine the shift in focus from 2D Chern insulators to time-reversal-invariant 2D and 3D topological insulators and topological crystalline insulators. Investigate higher-order topological crystalline insulators (HOTIs) in materials such as bismuth, α-BiBr, and MoTe2, and learn about their unique 1D hinge states. Discover novel tools for characterizing bulk topological properties of spinful 3D insulators, including nested spin-resolved Wilson loops and layer constructions. Gain insights into the three distinct spin-resolved phases of helical HOTIs: 3D quantum spin Hall insulators, "spin-Weyl" semimetal states, and T-doubled axion insulator states. Understand the quantitative robustness of these phases to large deformations of the bulk spin-orbital texture and their implications for 3D spin-magnetoelectric bulk responses.
