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

Abstract

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