Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect

We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov–de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of $\lesssim 1\mathrm{V}/\mathrm{nm}$, below the electric breakdown of ${\mathrm{SiO}}_2$. The opening of a gap is clearly seen in the quantum Hall regime.

Figure 1

(a) Measured Hall conductivity of pristine (undoped) and chemically doped bilayer graphene ($n_0\approx 5.4\times {10}^{12}{\mathrm{cm}}^{-2}$), showing a comparison of the QHE in both systems. (b) Cyclotron mass vs $n$, normalized to the free electron mass, $m_{\mathrm{e}}$. Experimental data are shown as ○. The solid line is the result of the self-consistent procedure and the dashed line corresponds to the unscreened case. The inset shows an electron micrograph (in false color) of one of our Hall bar devices with a graphene ribbon width of $1\mu \mathrm{m}$.

Figure 2

(a) Lattice structure of bilayer graphene and parameters of our model (see text). (b) Band structure of bilayer graphene near the Dirac points for $\mathrm{eV}=150\mathrm{meV}$ (solid line) and $V=0$ (dashed line). (c) $eV$ as a function of $n$: solid and dotted lines are the result of the self-consistent procedure (see text) for $t_{\perp }=0.2\mathrm{eV}$ and $t_{\perp }=0.4\mathrm{eV}$, respectively; dashed line is the unscreened result; circles represent $eV$ vs $n$ measured by ARPES [8]. (d) Band gap as a function of $n$ (bottom axis) and $V_g$ (top): solid and dashed lines are for the screened and unscreened cases, respectively. The thin dashed-dotted line is a linear fit to the screened result at small biases.

Figure 3

Energy spectrum for a ribbon of bilayer graphene with zigzag edges, $t_{\perp }/t=0.2$, $B=30\mathrm{T}$, and width $N=400$ unit cells: (a) $eV=0$; (b) $eV=t_{\perp }/10$. (c) Sketch of the bands close to zero energy (for the biased bilayer) with indication of bulk (solid lines) or edge (dotted lines) states and their left ($L$) or right ($R$) positions along the ribbon. Quasidegeneracies have been removed for clarity.