Four Flat Bands in Twisted Bilayer Graphene with an alternative magnetic field

The Moiré energy flat bands in twisted bilayer graphene serve as a fruitful playground for strong correlations and topological phases. We introduce a magnetic field that spatially alternates directions in the graphene layers so that the Dirac cones possess additional magnetic phases. By properly adjusting the phase and the twisted angle, in this twisted bilayer system, the energy spectrum for each valley can form FOUR moiré flat bands. In contrast, the conventional twisted bilayer graphene has only TWO moiré energy flat bands at magic angles. The doubled number of the flat bands in this magnetic platform might bring more rich correlation physics.