Hofstadter butterflies of bilayer graphene

Norbert Nemec, Gianaurelio Cuniberti
2007 Physical Review B  
We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accommodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase $2\pi$. The resulting Hofstadter-like butterfly plots show a reduced symmetry, depending on the relative position of the two layers against each other. The split of the zero-energy relativistic Landau level differs by one order of magnitude between Bernal and
more » ... between Bernal and non-Bernal stacking.
doi:10.1103/physrevb.75.201404 fatcat:z2f73iylt5atdgz52ruoo7oubi