Survival of the Dirac Points in Rippled Graphene

We study the effects of the rippling of a graphene sheet on quasiparticle dispersion. This is achieved using a generalization to the honeycomb lattice of the momentum average approximation, which is accurate for all coupling strengths and at all energies. We show that even though the position of the Dirac points may move and the Fermi speed can be renormalized significantly, quasiparticles with very long lifetimes survive near the Dirac points even for very strong couplings.

Figure 1

Spectral weight along high-symmetry cuts in the Brillouin zone, for $\Omega =0.25t$ and $\lambda =0.5$.

Figure 2

Imaginary part of the self-energy for $\Omega =0.07t$ (left) and $\Omega =0.25t$ (right).

Figure 3

Spectral weight near the Dirac points for (a) $\lambda =0.25$, (b) $\lambda =2.0$ and (c) $\lambda =4.0$ and $\Omega =0.07t$. The red (or gray) lines indicate the free-electron dispersion ($\lambda =0$).