Landau Level optical Hall effect spectroscopy on two- and three-dimensional layered materials with graphene and graphite as examples

Abstract

We present a comprehensive study of the band structure of two- and three-dimensional hexagonal layered materials using Landau Level optical Hall effect spectroscopy investigations, employing graphene and graphite as model systems. We study inter-Landau-level transitions in highly oriented pyrolytic graphite and a stack of multilayer graphene on C-face 6\textit{H}-SiC, using data from reflection-type optical Hall effect measurements in the mid-infrared spectral range at sample temperatures of $T=1.5$~K and magnetic fields up to $B=8$~T. We describe a comprehensive dielectric polarizability model for inter-Landau-level transitions, which permits analysis of the optical Hall effect data. From their magnetic field dependence we identify sets of H- and K-point inter-Landau-level transitions in graphite and sets of inter-Landau-level transition from decoupled graphene single, and coupled graphene bi-, tri-, and quad-layer for the multilayer graphene stack. For inter-Landau-level transitions in decoupled graphene single-layers and H-point transitions in graphite we observe polarization mode preserving behavior, requiring symmetric magneto-optical contributions to the corresponding dielectric tensors. Inter-Landau-level transitions in coupled graphene layers as well as K-point transitions in graphite exhibit polarization mode mixing behavior, requiring antisymmetric magneto-optical contributions to the corresponding dielectric tensors. From the circular-polarization-averaged inter-Landau-level transition energies and the energy splitting between right- and left-handed circular polarized inter-Landau-level transitions we determine the model parameters in the Slonczewski-Weiss-McClure band structure approximation for two- and three-dimensional hexagonal layered materials, with graphene and graphite as examples.