Graphene transparency in weak magnetic fields

TL;DR

This paper calculates how a weak magnetic field affects the optical properties of graphene, specifically its transparency and polarization rotation, by analyzing the vacuum polarization tensor and conductivity modifications.

Contribution

It provides an explicit calculation of the vacuum polarization tensor in graphene under a weak magnetic field, extending previous theoretical and experimental results.

Findings

Corrections to light transmission and polarization are proportional to (eB)^2/ω^4.

The vacuum polarization tensor remains transverse, ensuring gauge invariance.

Derived expressions relate conductivity changes to magnetic field strength and light frequency.

Abstract

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 radiated with monochromatic light of frequency $\omega$ along the external field direction, from the modified Maxwell's equations we derive the intensity of transmitted light and the angle of polarization rotation in terms of the longitudinal ($\sigma_{xx}$) and transverse ($\sigma_{xy}$) conductivities. Corrections to these quantities, both calculated and measured, are of order $(eB)^2/\omega^4$. Our findings generalize and complement previously known results reported in literature regarding the light absorption problem in graphene from the experimental and theoretical points of view, with and without external magnetic fields.