Graphene transparency in weak magnetic fields

We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energy model of monolayer graphene in the presence of a weak magnetic field of intensity B perpendicularly aligned to the membrane. By expanding the quasiparticle propagator in the Schwinger proper time representation up to order (eB)2, where e is the unit charge, we find an explicitly transverse tensor, consistent with gauge invariance. Furthermore, assuming that graphene is irradiated with monochromatic light of frequency ω along the external field direction, from the modified Maxwell equations we derive the intensity of transmitted light. Corrections to this quantity, both calculated and measured, are of the order of (eB)2/ω4. Our findings generalize and complement previously known results reported in the literature regarding the light absorption problem in graphene from the experimental and theoretical points of view, with and without external magnetic fields.