We show that bilayer graphene in the presence of a 2D superlattice potential provides a highly tunable setup that can realize a variety of flat band phenomena. We focus on two regimes: (i) topological flat bands with nonzero Chern numbers, , including bands with higher Chern numbers and (ii) an unprecedented phase consisting of a stack of nearly perfect flat bands with . For realistic values of the potential and superlattice periodicity, this stack can span nearly 100 meV, encompassing nearly all of the low-energy spectrum. We further show that in the topological regime, the topological flat band has a favorable band geometry for realizing a fractional Chern insulator (FCI) and use exact diagonalization to show that the FCI is in fact the ground state at filling. Our results provide a realistic guide for future experiments to realize a new platform for flat band phenomena.
- Received 8 July 2022
- Revised 6 February 2023
- Accepted 12 April 2023
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Condensed Matter, Materials & Applied Physics