From Quantum Field Theory to Nano-Optics : Refractive Properties of Graphene in a Medium-Strong Magnetic field

TL;DR

This paper uses quantum field theory to analyze how a magnetic field affects the refractive index of graphene, revealing significant quantum effects that depend on magnetic strength and sample geometry, especially in visible light.

Contribution

It introduces a quantum field theoretical approach to calculate the refractive index of graphene under magnetic fields, highlighting the role of confinement and quantum corrections.

Findings

Quantum corrections significantly alter the refractive index in magnetic fields.

Refractive index depends on magnetic field strength and sample geometry.

Quantum effects are weak at zero magnetic field, matching experimental opacity 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.