Faraday rotation in graphene

Abstract

We study magneto-optical properties of monolayer graphene by means of quantum field theory methods in the framework of the Dirac model. We reveal a good agreement between the Dirac model and a recent experiment on giant Faraday rotation in cyclotron resonance [19]. We also predict other regimes when the effects are well pronounced. The general dependence of the Faraday rotation and absorption on various parameters of samples is revealed both for suspended and epitaxial graphene.

Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

“…This relation between the Faraday angle and the Hall Conductivity has been already obtained in graphene [11], [13], [14] and here we have obtained it naturally from the 3D result after a dimensional compactification. It can be easily checked that our approach is equivalent to the one followed in Ref.…”

“…V we have obtained in 2D+1 limit. This result has been obtained theoretically in 2D+1 systems [12], [13], [24].…”

“…In Fig. 3 the 2D Ohm conductivity is plotted as a function of energy for fixed values of B = 7 × 10 4 G, chemical potential µ = 200 MeV and ǫ = 6.8 MeV, which are typical values for a graphenelike system [14] and [13]. The figure also shows the imaginary part of the conductivity.…”

“…51)-(52] must be multiplied by two, to account for the sublattice-valley degeneracy in graphene. The frequency must be substituted by ω → ω + iǫ where the imaginary part-ǫ is a phenomenological parameter associated with system disorder ( [13], [14]). In Fig.…”

“…Let us suppose that the graphene plate is located at x 3 = 0 and the incoming electromagnetic wave is linearly polarized along the x 1 direction, and travels in the positive x 3 direction. Due to the optical Faraday rotation of the polarization vector when the wave crosses the graphene sheet, both the reflected and transmitted component acquire a component along the x 2 direction ( [13], [14], [26]). …”