Critical role of device geometry for the phase diagram of twisted bilayer graphene

In this talk, I will describe two approaches for understanding the electronic structure of twisted bilayer graphene. In the first approach, Wannier functions of flat band electrons are constructed and then matrix elements of the screened Coulomb interaction between those Wannier functions are calculated. It is demonstrated that screening by metallic gates results in significant qualitative changes of the effective Hamiltonian of the flat band electrons suggesting that the phase diagram of twisted bilayer graphene can be controlled through device engineering.
In the second approach, an atomistic Hartree theory calculation is used to describe the long-range part of the Coulomb interaction. We find that this results in important changes to the band structure which now becomes dependent on the Fermi level. This allows us to explain several features of recent scanning tunnelling spectroscopy experiments. Finally, we combine the Hartree theory description of the long-range part of the interaction with an atomic Hubbard model treatment of the short-range part. This analysis reveals that the phase diagram of twisted bilayer graphene is determined by an interesting interplay of long-ranged and short-ranged interactions.