Flat Bands and Correlated Electronic States in Two Dimensional Atomic Crystals*

Stacking two-dimensional atomic crystals to form a moiré superstructure or applying an external periodic potential, can radically change the electronic properties. In particular, it is possible to engineer conditions leading to the creation of essentially flat energy bands with non-trivial topology, where the quenched kinetic energy facilitates the emergence of correlated electronic states, including superconductivity, Mott insulators or ferromagnetism. This talk will highlight two examples where the electronic ground state and Fermi surface topology depend sensitively on the filling of the flat bands: twisted graphene bilayers that develop a flat band at a magic twist-angle [1,2,3], and buckled graphene layers in which a strain-induced periodically modulated pseudo-magnetic field creates a post-graphene material with flat electronic bands [4].

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2. Y. Jiang, J. Mao, X. Lai, K. Watanabe, T. Taniguchi, K. Haule, E. Y. Andrei, Nature 573, (2019) 91
3. S. Wu1, Z. Zhang, K. Watanabe, T. Taniguchi, and E.Y. Andrei, Chern Insulators and Topological Flat-bands in Magic-angle Twisted Bilayer Graphene, arxiv 2007.03735 (2020)
4. J. Mao, S.P. Milovanović., M. Andelković., X. Lai, Yang Cao, K, Watanabe, T. Taniguchi, L. Covaci, F.M. Peeters, A.K. Geim, Y. Jiang, E.Y. Andrei, Nature 584, (2020) 215