Minimum light transmission in graphene in the presence of a magnetic field

Abstract

We show that, on general theoretical grounds, transmission of light in graphene always presents a non-vanishing minimum value independently of any material and physical condition, the transmission coefficient being higher in the presence of a substrate, and getting increasing when QED corrections higher than α come into play. Explicit numerical calculations for typical cases are carried out when an external magnetic field is applied to the sample, showing that, in epitaxial graphene, a threshold effect exists leading to a non trivial minimum transmission, for a non vanishing light frequency, only for field values larger than a critical one, both in the large and in the intermediate chemical potential regime. Such a threshold effect manifests even in the maximum Faraday rotation polarization of light, which is substantially controlled by the applied magnetic field. Instead, more transmission minima in suspended graphene enters in the considered light frequency region for increasing magnetic field, displaying an effective shift of frequency bands where the sample gets more or less absorptive with a suitable tuning of the external field. Two transition regions in different magnetic field ranges are found, where the shift effect towards higher frequency values occurs both in the transmission coefficient and in the Faraday rotation angle. Potential technological application of the results presented are envisaged.The naturally-occurring single sheet of carbon atoms in graphene [1] has attracted considerable interest in the last decade in different areas of research and technology [2]-[5], due to the peculiar and particularly intriguing properties of such 2D material. Its hardness, yet flexibility, indeed, as well as high electron mobility and thermal conductivity, has put graphene in the spotlight of applied research in condensed matter physics. Also, the simple theoretical description [6] -confirmed by experimental evidences [7] -has showed that the properties of charge carriers in graphene are completely similar to those of ultrarelativistic electrons [8], the corresponding quasiparticles obeying a linear dispersion relation, so that a new era of Dirac materials has opened with potential applications in nanotechnology.Particularly extraordinary are the optical properties of monolayer graphene which, despite being only one atom thick, presents a surprisingly huge effect of absorption of a significant 2.3% fraction of the incident light [9], as a consequence of its unique conical electronic band structure [8]. This is just the behavior expected for ideal Dirac fermions [10]- [13], and the result proved to be valid for a wide range of frequencies. Graphene's opacity 1 − T πα 2.3% can be indeed obtained by calculating the absorption of light by two-dimensional Dirac particles with Fermi's golden rule, and its only dependence on the fine structure function α is a consequence of the fact that the optical conductivity σ = πe 2 /2h (e and h being the electron charge and the Planck constant, respectively) is independent of a...