Magnetic breakdown in twisted bilayer graphene

We consider magnetic breakdown in twisted bilayer graphene where electrons may hop between semiclassical k-space trajectories in different layers. These trajectories within a doubled Brillouin zone (BZ) constitute a network in which an S matrix at each saddle point (SP) is used to model interlayer tunneling. Although semiclassical orbits at a given energy all have the same shape, we find that the doubled BZ supports two distinct quantization conditions above the SP, versus only one below it, yielding a more intricate spectrum. Possible experimental signatures are discussed.