Band Structure Asymmetry of Bilayer Graphene Revealed by Infrared Spectroscopy

We report on infrared spectroscopy of bilayer graphene integrated in gated structures. We observe a significant asymmetry in the optical conductivity upon electrostatic doping of electrons and holes. We show that this finding arises from a marked asymmetry between the valence and conduction bands, which is mainly due to the inequivalence of the two sublattices within the graphene layer and the next-nearest-neighbor interlayer coupling. From the conductivity data, the energy difference of the two sublattices and the interlayer coupling energy are directly determined.

Figure 1

$T(V)/T(V_{CN})$ spectra of bilayer graphene. (a),(b) Data for $E_F$ on the hole side and electron side. Inset of (a): A schematic of the device and infrared measurements. Inset of (b): A schematic of bilayer graphene with the interlayer coupling parameters shown. The $A$ and $B$ sublattices are shown in different colors. The sublattice $A_2$ is right on top of the sublattice $A_1$.

Figure 2

The optical conductivity of bilayer graphene. (a),(b) ${\sigma }_1(\omega ,V)$ data for $E_F$ on the hole side and electron side. (c) ${\sigma }_2^{\mathrm{diff}}(\omega ,V)$ spectra in the low frequency range, after subtracting the Lorentzian oscillators describing the main resonance around $3000{\mathrm{cm}}^{-1}$ from the whole ${\sigma }_2(\omega ,V)$ spectra. Inset of (a): Schematics of the band structure of bilayer with zero values of ${\Delta }^{\prime }$ and $v_4$ [gray curve (red)] and finite values of ${\Delta }^{\prime }$ and $v_4$ (black curve), together with allowed interband transitions. Inset of (b): ${\sigma }_1(\omega ,V)$ at 0 V ($V_{CN}$) and 40 V on the hole side with assignments of the features.

Figure 3

(a) Symbols: The $2E_F$ values extracted from the optical conductivity detailed in the text. The error bars are estimates of the uncertainties of ${\sigma }_2^{\mathrm{diff}}(\omega ,V)$ spectra in Fig. 2c. Solid lines: The theoretical $2E_F$ values using $v_F=1.1\times 106\mathrm{m}/\mathrm{s}$ and ${\gamma }_1=450\mathrm{meV}$. (b) Solid symbols: The energy of the main peak ${\omega }_{\mathrm{peak}}$ in the ${\sigma }_1(\omega ,V)$ spectrum. Open symbols: The energy of the dip feature ${\omega }_{\mathrm{dip}}$ in the $T(V)/T(V_{CN})$ spectra. Note that ${\omega }_{\mathrm{peak}}$ in ${\sigma }_1(\omega ,V)$ is shifted from ${\omega }_{\mathrm{dip}}$ in the raw $T(V)/T(V_{CN})$ data with an almost constant offset, which is due to the presence of the substrate. Solid lines: Theoretical values of the transitions at $e_2$, $e_3$, and $(e_2+e_3)/2$ with $v_F=1.1\times {10}^6\mathrm{m}/\mathrm{s}$, ${\gamma }_1=404\mathrm{meV}$, ${\Delta }^{\prime }=18\mathrm{meV}$, and $v_4=0.04$. Red dashed lines: $e_3$ with similar parameters except $v_4=0$.