Euler–Heisenberg effective action and magnetoelectric effect in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field BB (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field EE at E/B≪1E/B≪1 and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field EE and the lowest order correction to it due to the magnetic field (B/E≪1B/E≪1).

► The low energy effective field model for the multilayer graphene (at ABC stacking) is constructed.
► We have calculated the effective action in the presence of external electric (EE) and magnetic (BB) fields, E≪BE≪B.
► Electromagnetic analog of Hořava quantum gravity with anisotropic scaling is obtained.
► Strong magnetoelectric effect due to degeneracy of zero-energy Landau level is predicted.
► Schwinger pair production rate in multilayer graphene is calculated at E≫BE≫B.