Infrared of thin film graphene in a magnetic field and the Hall effect

Abstract

The infrared absorption of a mono-atomic thin film of carbon, called graphene, in a magnetic field is studied. Its interpretation in terms of the square root of the product of the cyclotron frequency and the Fermi energy is examined. The interpretation in terms of the Dirac points which are at the centre of the positive and negative energies, is examined and found not to fit well. The spin properties are used to obtain the energy levels correctly. A set of fractional values are tabulated which give the correct Hall effect plateaus. The energy levels arising from the Landau levels are usually of the type of a harmonic oscillator. In the present problem, the harmonic oscillator type levels are just like the equally spaced spin levels in which the number of levels is not limited by 2S+1. The oscillator type series and the proper spin properties are sufficient to get the correct fractions. The flux quantization is needed to get the plateaus in the Hall effect. We are thus able to obtain the correct fractions without the use of relativistic effects. The theory presented is thus non-relativistic. The normal infrared absorption arises from the equally spaced energy levels so that there is only one line. The additional lines occur due to spin properties.