"Correlated and topological phases in multi-moiré graphene"
Moiré lattices formed by twisting two-dimensional materials are a powerful platform for exploring correlated and topological phases. Introducing a second moiré pattern extends this idea: interference between two independent moiré lattices produces a long-wavelength supermoiré modulation, offering new control over electronic structure. Twisted trilayer graphene naturally realizes such a system, with two distinct twist angles generating separate moiré patterns between adjacent layers. I will present experiments showing that correlated and topological phases in twisted trilayer graphene organize along two continuous lines in the two-angle parameter space [1]. Depending on lattice relaxation, these systems form either moiré polycrystals [2]—domains with locally commensurate moiré order that breaks C2z, where we observe an anomalous Hall effect—or moiré quasicrystals [3], where superconductivity appears generically and sometimes exhibits spatial modulation driven by the supermoiré structure. These results reveal the organizing principles of correlated phases in multi-moiré graphene and suggest that magic conditions arise not as isolated points but as continuous manifolds within multidimensional twist-angle spaces