Infrared spectroscopy of electronic bands in bilayer graphene

We present infrared spectra (0.1–1 eV) of electrostatically gated bilayer graphene as a function of doping and compare it with tight-binding calculations. All major spectral features corresponding to the expected interband transitions are identified in the spectra: a strong peak due to transitions between parallel split-off bands and two onset-like features due to transitions between valence and conduction bands. A strong gate voltage dependence of these structures and a significant electron-hole asymmetry are observed that we use to extract several band parameters. The structures related to the gate-induced band gap are less pronounced in the experiment than predicted by the tight-binding model that uses parameters obtained from previous experiments on graphite and recent self-consistent band-gap calculations.

Figure 1

(Color online) (a) Schematic view and a micrograph of the used bilayer graphene device. The flake is seen as a darker area between the contacts. (b) Infrared reflectance of graphene flake (blue solid line) and of bare substrate (red dotted line) (taken at $T=10\text{K}$ and $V_g=+100\text{V}$). Left inset: Bernal stacking of bilayer graphene and relevant hopping terms. Right inset: resistivity at 10 K as a function of the gate voltage.

Figure 2

(Color online) (a) Midinfrared spectra of $\Delta R$ at $T\approx 10\text{K}$ as a function of the gate voltage $V_g$. The curves are separated by 0.005; the dashed line is the zero level for the $+100\text{V}$ curve. (b) Real part of the infrared sheet conductance of bilayer graphene $\tilde{G}\left(\omega \right)$, derived from the reflectance curves [panel (a)] using a Kramers-Kronig inversion. The curves are separated by $0.5G_0$. Note that $\tilde{G}\left(\omega \right)$ possibly differs from the true conductance $G\left(\omega \right)$ by a spectrally featureless gate-independent background, as explained in the text. The dashed line is the correction (shown relative to the $+100\text{V}$ spectrum) used to generate Fig. 3b.

Figure 3

(Color online) (a) and (b) Color plots of the raw $\Delta R\left(\omega \right)$ and the derived $\text{Re}G\left(\omega \right)$ spectra as a function of $\omega$ and $V_g$. (c) and (d) $\Delta R$ and $\text{Re}G\left(\omega \right)$ calculated using the tight-binding model assuming that the band gap is zero. (e) The four bands of bilayer graphene in the absence (left) and in the presence (right) of the band gap, with the interband transitions shown with arrows. (f) $\text{Re}G\left(\omega \right)$ calculated assuming that the band gap ${\Delta }_g$ is present as given by the red solid curve (Ref. 17).