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

TL;DR

This study uses Landau Level optical Hall effect spectroscopy to analyze the electronic band structure of layered graphene and graphite, revealing polarization behaviors and extracting band parameters for these materials.

Contribution

It introduces a comprehensive dielectric polarizability model for inter-Landau-level transitions and applies it to analyze complex magneto-optical data in layered materials.

Findings

Identification of inter-Landau-level transitions in graphite and multilayer graphene.

Observation of polarization mode preserving and mixing behaviors in different transitions.

Extraction of band structure parameters using the Slonczewski-Weiss-McClure model.

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.