Multicomponent magneto-optical conductivity of multilayer graphene on SiC

Far-infrared diagonal and Hall conductivities of multilayer epitaxial graphene on the C face of SiC were measured using magneto-optical absorption and Faraday rotation in magnetic fields up to 7 T and temperatures between 5 and 300 K. Multiple components were identified in the spectra, including (i) a quasiclassical cyclotron resonance, originating from the highly doped graphene layer closest to SiC, (ii) transitions between low-index Landau levels (LLs), which stem from weakly doped layers, and (iii) a broad optical absorption background. Electron- and hole-type LL transitions are optically distinguished and shown to coexist. An electron-hole asymmetry of the Fermi velocity of about 2% was found within one graphene layer, while the Fermi velocity varies by about 10% across the layers. The optical intensity of the LL transitions is several times smaller than is theoretically expected for isolated graphene monolayers without electron-electron and electron-phonon interactions.

Figure 1

The diagonal (a) and Hall (b) optical conductivity at 3 T and 5 K, normalized to the universal conductivity ${\sigma }_0$, and results of the multicomponent modeling described in the text. The components in the graph are the individual contributions needed to create the total fit shown by the black dotted line on top of the data. The components in (b) have an offset indicated by the blue dashed line at the right side of the graph. (c),(d) The optical conductivities in the circular basis ${\sigma }_{+}(\omega )$ and ${\sigma }_{-}(\omega )$ corresponding to the absorption of right and left circular polarized light respectively. In the insets the low-index LL transitions allowed in the corresponding polarizations are shown.

Figure 2

Magneto-optical conductivity of multilayer graphene at 5 K, normalized to the universal conductivity ${\sigma }_0$, for several magnetic fields up to 7 T. The curves in all panels are offset as indicated by the dashed lines. Larger offsets correspond to higher magnetic fields. (a) and (b) show the measured spectra of ${\sigma }_{\mathit{xx}}(\omega )$ and ${\sigma }_{\mathit{xy}}(\omega )$ (solid lines) and multicomponent fits (black dotted lines). In (c) and (d) the model-derived ${\sigma }_{+}(\omega )$ and ${\sigma }_{-}(\omega )$ are shown.

Figure 3

Parameters of various components as a function of magnetic field obtained from the multicomponent fits to ${\sigma }_{\mathit{xx}}(\omega )$ and ${\sigma }_{\mathit{xy}}(\omega )$ of Fig. 2. (a) The transition energies of the CR (triangles) and the LL${}_{1\to 2}$ transition (diamonds). The solid lines are fits using Eqs. (10) and (1), respectively. (b) The transition energies of LL${}_{0\to 1,a}$ (squares), LL${}_{0\to 1,b}$ (triangles), and LL${}_{-1\to 0}$ (circles) transitions. The solid lines are fits using Eq. (1). (c) Spectral weight of the LL${}_{1\to 2}$ transition. (d) Spectral weight of the CR peak. (e) Spectral weights of the LL${}_{0\to 1,a}$, LL${}_{0\to 1,b}$, and LL${}_{-1\to 0}$ transitions. (f) The broadening of the LL${}_{1\to 2}$ transition. (g) The broadening of the CR transition. (h) The broadening of LL${}_{0\to 1,a}$, LL${}_{0\to 1,b}$, and the $-1\to 0$ transitions. Error bars in all figures are the standard deviation of several fitting results. The error bars in (a) and (b) are within the symbol size.

Figure 4

Magneto-optical conductivity of multilayer graphene at 3 T, normalized to the universal conductivity ${\sigma }_0$, for several temperatures between 5 and 300 K. The curves in all panels are offset as indicated by the dashed lines. Larger offsets correspond to higher temperatures. (a) and (b) show the measured spectra of ${\sigma }_{\mathit{xx}}(\omega )$ and ${\sigma }_{\mathit{xy}}(\omega )$ (solid lines) and multicomponent fits (black dotted lines, only at 5, 100, and 200 K). In (c) and (d) the model-derived ${\sigma }_{+}(\omega )$ and ${\sigma }_{-}(\omega )$ are shown.

Figure 5

The effect of environmental doping on the LL transitions at $B=3$ T and $T=5$ K. (a) The contributions of the LL${}_{0\to 1,a}$ and LL${}_{0\to 1,b}$ transitions to ${\sigma }_{+}(\omega )$. (b) The contribution of the LL${}_{-1\to 0}$ transition to ${\sigma }_{-}(\omega )$. In both panels, the red dash-dotted lines correspond to the measurement series as a function of temperature at constant magnetic field (Fig. 4), while the blue solid lines correspond to the measurement series as a function of magnetic field at constant temperature (Fig. 2). The curves are derived from the multicomponent fits of experimental data.

Figure 6

Total spectral weight of the LL${}_{0\to 1,a}$, LL${}_{0\to 1,b}$, and LL${}_{-1\to 0}$ transitions (circles) as compared to the theoretical prediction for the spectral weight of the sum of the LL${}_{0\to 1}$ and LL${}_{-1\to 0}$ transitions in ideal monolayer graphene (solid line) with the chemical potential between $E$${}_{-1}$ and $E$${}_1$.