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Delve into the fascinating world of moiré 2D materials and topological quasicrystals in this comprehensive tutorial talk. Gain a theoretical perspective on the exceptional electronic properties that emerge when distinct 2D materials with varying periodicities are overlaid, creating moiré interference patterns. Explore the fundamental long-range continuum model, essential for describing electronic characteristics in systems like twisted bilayer graphene (TBG), graphene/hBN superlattices, and twisted topological insulators. Discover recent theoretical advancements in moiré systems beyond TBG, with a focus on trilayer systems where multiple moiré patterns interfere to create quasiperiodic structures. Examine the twist-angle-dependent electronic spectrum, which exhibits fractal minigaps reminiscent of the Hofstadter butterfly, and learn about their distinct topological numbers expressed as second Chern numbers through a connection with the quantum Hall effect in four-dimensional space.
