Refractive properties of graphene in a medium-strong external magnetic field

Abstract

1-loop quantum corrections are shown to induce large effects on the refraction index $n$ inside a graphene strip in the presence of an external magnetic field $B$ orthogonal to it. To this purpose, we use the tools of Quantum Field Theory to calculate the photon propagator at 1-loop inside graphene in position space, which leads to an effective vacuum polarization in a brane-like theory of photons interacting with massless electrons at locations confined inside the thin strip (its longitudinal spread is considered to be infinite). The effects factorize into quantum ones, controlled by the value of $B$ and that of the electromagnetic coupling $\alpha$, and a "transmittance function" $U$ in which the geometry of the sample and the resulting confinement of electrons play the major roles. We consider photons inside the visible spectrum and magnetic fields in the range 1-20\; Teslas. At $B=0$, quantum effects depend very weakly on $\alpha$ and $n$ is essentially controlled by $U$; we recover, then, an opacity for visible light of the same order of magnitude $\pi \alpha_{vac}$ as measured experimentally.