Moiré lattice effects on the orbital magnetic response of twisted bilayer graphene and Condon instability

We analyze the orbital magnetic susceptibility from band structure of twisted bilayer graphene. Close to charge neutrality, out-of-plane inherits strong diamagnetic response Increasing doping, a crossover diamagnetism paramagnetism is obtained and logarithmic divergence develops at van Hove singularity Moir\'e lattice in first band. The enhanced stronger for relatively large angle but gets suppressed by flat spectrum towards vicinity magic angle. A diverging paramagnetic indicates an instability ferromagnetism with magnetization Landau level structure. region however found be practically very small, parametrically ratio electron velocity speed light. also discuss in-plane neutrality where we find associated negative counterflow current two layers does not admit semiclassical description.