Observation of an Electric-Field-Induced Band Gap in Bilayer Graphene by Infrared Spectroscopy

It has been predicted that application of a strong electric field perpendicular to the plane of bilayer graphene can induce a significant band gap. We have measured the optical conductivity of bilayer graphene with an efficient electrolyte top gate for a photon energy range of 0.2–0.7 eV. We see the emergence of new transitions as a band gap opens. A band gap approaching 200 meV is observed when an electric field $\sim 1\mathrm{V}/\mathrm{nm}$ is applied, inducing a carrier density of about ${10}^{13}{\mathrm{cm}}^{-2}$. The magnitude of the band gap and the features observed in the infrared conductivity spectra are broadly compatible with calculations within a tight-binding model.

Figure 1

Experimental spectra of the IR conductivity $\sigma (\hslash \omega )$ in units of $\pi e^2/2h$ (displaced vertically by 1.3 units from one another) of graphene bilayer under varying gate bias voltages $│V│<4\mathrm{V}$. (a) corresponds to hole doping for $V=-0.5$, $-0.8$, $-1.0$, $-1.2$, $-1.4$, $-1.6$, $-1.8$, $-2.0$, $-2.2$, $-2.4$, $-2.6$, $-2.8$, and $-3.0\mathrm{V}$ (from bottom to top) and (b) to electron doping for $V=-0.5$, $-0.4$, $-0.3$, $-0.2$, 0.0, 0.2, 0.4, 0.8, 1.2, 1.6, 2.0, 2.4, 2.8, 3.2, and 3.6 V (from bottom to top). Charge neutrality occurs for $V=V_{\mathrm{CN}}=-0.5\mathrm{V}$, as determined by the minimum in source-drain current [inset of (a)].

Figure 2

Band structure of graphene bilayer with (solid) and without (dashed) the presence of a perpendicular electric field as calculated within the TB model described in the text. Transitions 1 and 2 are the strongest optical transitions near the $K$ point for electron doping.

Figure 3

Dependence of the energy gap at the $K$ point $\Delta E_K$ (symbols) on the gate voltage and the charge doping density of the graphene bilayer. The error bars arise primarily from uncertainties in determining the peak position of the broad absorption features. The results of TB model for both $\Delta E_K$ and the band gap $E_g$ are plotted as well to compare with the experimental data.

Figure 4

Simulated spectra of the IR conductivity $\sigma (\hslash \omega )$ from the Kubo formula for gated bilayer graphene under the same doping as in Fig. 1. Panels (a) and (b) show the results obtained with the predictions of TB model for the electronic structure described in the text (including the electron-hole asymmetry). For comparison, (c) is a reference calculation in which the bilayer graphene band structure is assumed to remain unchanged (without an induced gap) and the spectral modifications reflect only population changes.