Gate Tunable Infrared Phonon Anomalies in Bilayer Graphene

We observe a giant increase of the infrared intensity and a softening of the in-plane antisymmetric phonon mode $E_u$ ($\sim 0.2\mathrm{eV}$) in bilayer graphene as a function of the gate-induced doping. The phonon peak has a pronounced Fano-like asymmetry. We suggest that the intensity growth and the softening originate from the coupling of the phonon mode to the narrow electronic transition between parallel bands of the same character, while the asymmetry is due to the interaction with the continuum of transitions between the lowest hole and electron bands. The growth of the peak can be interpreted as a “charged-phonon” effect observed previously in organic chain conductors and doped fullerenes, which can be tuned in graphene with the gate voltage.

Figure 1

(a) A sketch of the infrared reflectivity experiment and the crystal structure of Bernal-stacked bilayer graphene. Atomic displacements corresponding to the antisymmetric mode $E_u$ are indicated by arrows; for the symmetric mode $E_g$, the displacements in one of the layers should be inverted. (b) A simplified band structure of bilayer graphene. Arrows indicate electronic transitions discussed in the text.

Figure 2

(a) Infrared reflectivity spectra of bilayer graphene on ${\mathrm{SiO}}_2(300\mathrm{nm})/\mathrm{Si}$ around the $E_u$ peak normalized by the reflectivity of the bare substrate at different gate voltages. (b) The same spectra with a baseline subtracted. The curves (except at $-100\mathrm{V}$) are vertically shifted.

Figure 3

(a) The real part of the optical conductivity $\Delta {\sigma }_1(\omega )$ of bilayer graphene at different gate voltages. The electronic baseline is subtracted. The curves (except at $-100\mathrm{V}$) are vertically shifted. (b) and (c) The expanded views of the $E_u$ peak at electron and hole doping.

Figure 4

(a)–(d) Fano parameters ${\omega }_0$, $\Gamma$, ${\omega }_p$ ($Z_{\mathrm{eff}}$), and $q$ of the phonon peak as a function of doping. At very low doping, the error bars for ${\omega }_0$ exceed the panel scale. The effective charge corresponding to the calculated static dipole is shown by the dashed line in panel (c). (e) The bare spectral phonon weight $W$ and the peak area $W^{\prime }$. (f) The background electronic conductivity at the phonon energy.