Layering two-dimensional periodic materials to form moiré patterns is a convenient method of constructing emergent periodicity with on-demand length scales. This scheme has proven fruitful for engineering new electronic systems hosting superconductivity, strong electronic interactions, and topology. In contrast, quasicrystals, without periodicity or a Bloch description, have proven more challenging to engineer and thus are much less explored. In my talk, I will demonstrate how moiré lattices can be used to generate emergent quasiperiodicity with a high degree of tunability and favorable conditions for interacting electronic phenomena. I will discuss a graphene-based realization of a moiré quasicrystal that exhibits a wide array of phenomena, including superconductivity, flavor symmetry-breaking, quantum oscillations, and signatures of both periodic-like and quasiperiodic regimes in the electronic structure [1].

[1] A. Uri*, S. C. de la Barrera*, M. T. Randeria*, D. Rodan-Legrain*, T. Devakul, P. J. D. Crowley, N. Paul, K. Watanabe, T. Taniguchi, R. Lifshitz, L. Fu, R. C. Ashoori, and P. Jarillo-Herrero,  Superconductivity and strong interactions in a tunable moiré