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Special condensed matter seminar: Incommensurability-driven phases, flat bands, and topology in two-dimensional materials

Justin Wilson, Louisiana State University

(Hybrid seminar - available both in person (in Physics 18/19) and via zoom)

(Note time change)

By quenching electron kinetic energy, one can reveal correlated phases in previously weakly correlated materials, such as in twisted bilayer graphene. Disorder typically obscures correlated phases; for instance, it might just lead to localized electron wave functions. Incommensurability-driven phases provide a platform to observe both phase transitions typically associated with disorder (Anderson-like transitions) as well as flat bands and correlated phases. In this talk, I will discuss our work to understand this, particularly within the context of topological band structures. In both two-dimensional semimetals and topological insulators, we see that disorder induces a delocalization eigenstate transition in momentum space. The wave functions exhibit multifractality in this phase, and in the case of two-dimensional semimetals, it occurs at the “magic-angle” as for twisted bilayer graphene. Concomitantly, there is a precise sense in which the “bands” become increasingly flat at these transitions. In the case of the topological insulator, the Berry curvature also becomes more uniform as the wave functions near criticality: clearing the way for potential fractional Chern insulators in these systems.