Polarization Selection Rules for Inter-Landau-Level Transitions in Epitaxial Graphene Revealed by the Infrared Optical Hall Effect

We report on the polarization selection rules of inter-Landau-level transitions using reflection-type optical Hall effect measurements from 600 to $4000{\mathrm{cm}}^{-1}$ on epitaxial graphene grown by thermal decomposition of silicon carbide. We observe symmetric and antisymmetric signatures in our data due to polarization preserving and polarization mixing inter-Landau-level transitions, respectively. From field-dependent measurements, we identify that transitions in coupled graphene monolayers are governed by polarization mixing selection rules, whereas transitions in decoupled graphene monolayers are governed by polarization preserving selection rules. The selection rules may find explanation by different coupling mechanisms of inter-Landau-level transitions with free charge carrier magneto-optic plasma oscillations.

Figure 1

Optical Hall effect experimental data (green, dotted lines) and best-model fit data (red, solid lines) for epitaxial graphene at $B_c=+(5.66\pm 0.02)\mathrm{T}$ and $T=1.5\mathrm{K}$. The angle of incidence is ${\Phi }_a=45°$. DTC, BLG, and SLG denote contributions assigned in this Letter to Drude-type carriers, bilayer graphene LL, and single-layer graphene LL, respectively. Signatures indicated by SLG are isotropic and do not occur in off-diagonal-block elements $\delta M_{13}$, $\delta M_{23}$, $\delta M_{31}$, and $\delta M_{32}$ (shaded background), while features labeled with DTC and BLG are anisotropic and cause polarization mixing. A schematic representation of the optical Hall effect experimental setup is given in the left upper corner.

Figure 2

Selected on- and off-diagonal-block optical Hall effect spectra ($T=1.5\mathrm{K}$, ${\Phi }_a=45°$) for $B_c=+(0.707\pm 0.002)\mathrm{T}$ to $B_c=+(5.66\pm 0.02)\mathrm{T}$ in 0.07 T increments. The graphs are stacked by 0.006. (a) $\delta M_{33}$: Isotropic inter-Landau-level transitions, indicated by letters according to Sadowski et al. [13]. (b) $\delta M_{32}$: Anisotropic inter-Landau-level transitions, indicated by blue and red arrows.

Figure 3

Symmetric [(a) isotropic] and antisymmetric [(b) anisotropic] inter-Landau-level transition energies in epitaxial graphene determined from optical Hall effect measurements at 1.5 K. Solid lines denote single-layer graphene [(a) black solid lines and dots], bilayer graphene [(b) blue solid lines and dots], and trilayer graphene [(b) red dashed lines and dots] dependencies on the magnetic field.