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

TL;DR

This paper investigates how quantum corrections in a graphene strip under a strong magnetic field significantly alter its refractive index, with effects depending on magnetic field strength, sample geometry, and quantum electrodynamics.

Contribution

It provides a quantum field theoretical calculation of the photon propagator in graphene under magnetic fields, revealing large effects on refraction index influenced by sample geometry and external magnetic fields.

Findings

Quantum effects induce large changes in graphene's refractive index under magnetic fields.

Refraction index depends on magnetic field strength and sample geometry.

Visible light opacity in graphene is comparable to experimental measurements.

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.