What is the effect of the applied perpendicular magnetic for graphene?

Graphene is subjected to an electric field with the gate control, resulting in the opening bandgap. For example, the bilayer shows a tunable bandgap and the trilayer displays an overlapping bandgap.

So, I want to know the effect of the perpendicular magnetic field. Does it have a similar effect to open the bandgap? Or what are others, i.e. the opening excitonic condensation gap?

Additionally, I put the four-terminal graphene device on the perpendicular magnetic field; the observed resistance (not Hall Effect resistance) shows a nonlinear increase with the increasing magnetic field. What is the origin of the nonlinear magneto resistance?