Figure 1

(Color online) Transverse view (bottom) along the dashed-dotted line (top left) of the lattice distortion considered in the text. Only the atoms ${\text{A}}_1$ and ${\text{B}}_2$, which are connected via the hopping $t_{\perp }$, are displaced toward each other in the distorted phase. The vertical displacement of the carbon atoms connected by $t_{\perp }$ is represented by the parameter $u$. In the top right we schematically represent the band structure in the vicinity of the Dirac point.Reuse & Permissions

Figure 2

(Color online) Phonon modes along the $c$ axis in graphite, using the notation of Ref. 17. The modes $A_{2u}$ and $B_{1g_2}$ are nearly degenerate at the center of the Brillouin zone, with $\omega \simeq 870{\text{cm}}^{-1}$ (Refs. 17, 18).Reuse & Permissions

Figure 3

(Color online) Energy as a function of distance between layers measured with respect to the equilibrium position, and calculated within the GGA. The positive direction indicates a displacement toward the other graphene sheet. The zero-value energy is the energy of the fully relaxed sample.Reuse & Permissions

Figure 4

(Color online) (a) Total energy, $E_t$, per unit cell as a function of the deformation parameter $u$, and for different values of $K$. The left (right) vertical axis pertains to the solid (dashed) curves. [(b)–(d)] The equilibrium radius as a function of the bias voltage, $V$. In all panels dashed lines refer to the Dirac approximation, whereas full lines have been calculated using the full tight-binding dispersion in Eq. (6). Notice that in panels (c) and (d) the vertical axis is amplified ten and 100 times, respectively. Other parameters used are $t_{\perp }^0=0.3\text{eV}$, $t=3.0\text{eV}$, $\alpha =1.5{\text{Å}}^{-1}$.Reuse & Permissions

Figure 5

(Color online) Equilibrium deformation, $u_{\text{eq}}$, as a function of the electron density per unit cell $\left(n_e\right)$ and the bias voltage $\left(V\right)$. The lines drawn on the surface represent level curves. The parameters used are $t_{\perp }^0=0.3\text{eV}$, $t=3.0\text{eV}$, $K=0.2\text{eV}{\text{Å}}^{-2}$, and $\alpha =1.5{\text{Å}}^{-1}$.Reuse & Permissions

Figure 6

(Color online) (a) Selected cuts from Fig. 5 at constant bias $V$. For clarity, successive curves have been shifted vertically by 0.002 in the order of increasing $V$. (b) The densities $n_e^{\ast }$ and $n_e^{\ast \ast }$ defined in Eq. (23), plotted as a function of $V$ for the same parameters used in Fig. 5.Reuse & Permissions

Figure 7

(Color online) Schematic representation of an arbitrary cut of the band structure of bilayer graphene close to the Dirac point.Reuse & Permissions