Figure 1

(Color online) Structure of a graphene bilayer with honeycomb lattice constant $a=2.46\mathrm{\AA }$ and interlayer separation $d=3.35\mathrm{\AA }$.Reuse & Permissions

Figure 2

(Color online) Schematic illustration of a circuit with a bilayer graphene channel sensitive to an external gate voltage. The graphene channel is separated from the front and back gates by a $\mathrm{Si}{\mathrm{O}}_2$ layer. The channel resistance change will be rapid and large when the graphene channel is undoped and isolated from the gate electrodes, as illustrated here. In this case, the total charge density in the bilayer system is fixed and the chemical potential lies in the gap opened by the gate voltage. This geometry could also be used to capacitively probe the correlation physics of the isolated bilayer system, as discussed in the text.Reuse & Permissions

Figure 3

(Color online) An averaged Coulomb potential of a cross section vs $z$ for total external potential $U_{\mathit{ext}}=0\mathrm{eV}$ and $U_{\mathit{ext}}=1\mathrm{eV}$. Here, $z_0$ is the superlattice period and the cross section was chosen to include equal number of atoms in each layer.Reuse & Permissions

Figure 4

(Color online) (a) Bilayer graphene band structure in the absence of an external electric field. (b) Bilayer graphene band structure near the $K$ point for $U_{\mathit{ext}}=0$, 0.5, and $1\mathrm{eV}$.Reuse & Permissions

Figure 5

(Color online) (a) Evolution of the graphene bilayer screened on-site energy difference $U$, extracted from the ab initio DFT bands as explained in the text, with the external potential $U_{\mathit{ext}}$. The external potential is strongly screened. (b) Evolution of the interlayer tunneling amplitude ${\gamma }_1$ with $U_{\mathit{ext}}$. (c) Comparison of band gap as a function of the on-site energy difference $U$ obtained from the ab initio DFT calculations (open circles) with the tight-binding result for ${\gamma }_3=0$ (dashed line) and ${\gamma }_3=0.3\mathrm{eV}$ (solid line).Reuse & Permissions

Figure 6

(Color online) The ratio of the external electric potential $U_{\mathit{ext}}$ to the interlayer energy difference inferred from the ab initio DFT calculation compared with the value of the same ratio in tight-binding model self-consistent Hartree calculations, both with and without crystalline inhomogeneity corrections. The tight-binding model calculations used ${\gamma }_0=2.6\mathrm{eV}$ for the intralayer tunneling amplitude, ${\gamma }_1=0.34\mathrm{eV}$ for the interlayer tunneling amplitude, and ${\gamma }_3=0.3\mathrm{eV}$ for the interlayer $A\text{−}\tilde{B}$ coupling.Reuse & Permissions

Figure 7

Splitting of Hartree potentials $({ϵ}_l^{\left(H\right)}-{ϵ}_h^{\left(H\right)})∕({ϵ}_l^{\left(H\right)}+{ϵ}_h^{\left(H\right)})$ as a function of (a) the external electric potential $U_{\mathit{ext}}$ and (b) the corresponding density inhomogeneity $(\Delta n_l-\Delta n_h)∕(\Delta n_l+\Delta n_h)$ in the lattice Hartree potential model.Reuse & Permissions