Moiré bands in Twisted Bilayer Graphene under externally imposed periodic potential

Applying a periodic external potential in magic-angle twisted bilayer graphene (MATBG) having the same periodicity as the moiré pattern changes the curvature of either the conduction or valence band. However, the bandwidth at the centre of the moiré Brillouin zone remains unaffected. We study the MATBG in such external periodic potentials such that the bandwidth can be decreased further to enhance the flatness of both the conduction and valence bands simultaneously, which consequently enhances the strong correlation effects.