Moiré patterns are well known in the visual arts and textile industries -- the term comes from the textured patterns seen in mohair silk fabrics. It arises whenever two periodic structures are superimposed giving new periodicities. Such translational symmetry breaking atomic positions is at the heart of condensed matter physics and twisting two atomically thin materials on top of each other yields designer materials where the material properties like bandwidth, electron velocity, and band topology can be controllably altered.
Less than 15 years after the first isolation of two dimensional materials, our experimental colleagues are now able to tune the twist angle between adjacent atomic monolayers to within 0.1 degrees allowing, for example, the change in electronic bandwidth from 10,000 K in monolayer graphene to less than 10 K in twisted bilayer graphene. Moreover, there are more than 1,000 possible “easily exfoliatable” materials to play with, giving billions of designer band structures. In the past decade, we have achieved a good handle on building non-interacting models for these materials, however, we do not have a good way to include Coulomb interactions in such moiré van der Waals systems. I will discuss our successful work on adding Coulomb interactions to the bands of monolayer graphene  where we found that contrary to expectation, the interactions are strong. However, this is masked by the effective competition between the short-range (i.e. “Hubbard-U”) and long-range (i.e. “Coulomb tail”) interaction . I will speculate on how similar ideas might be applied to twisted bilayer graphene .
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 Jia Ning Leaw, Ho-Kin Tang, Maxim Trushin, Fakher F Assaad, Shaffique Adam, “Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions”, Proc. Natl. Acad. Sci. (USA) 116 26431 (2019).
 Girish Sharma, Maxim Trushin, Oleg Sushkov, Giovanni Vignale, and Shaffique Adam
“Superconductivity from collective excitations in magic-angle twisted bilayer graphene”, Phys. Rev. Research, Rapid Comm. 2, 022040 (2020).
† This work is supported by the Singapore National Science Foundation Investigator Award (NRF-NRFI06-2020-0003).