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Vibrational instabilities in multilayer graphene and graphite: Effects of strain and number of layers

Abstract:

We study the rippling instabilities of multilayer graphene and graphite as a function of strain and number of layers using density-functional theory and density-functional perturbation theory calculations. We find that, for multilayer graphene, a small but finite compressive strain is needed to induce a rippling instability, signaled by the onset of imaginary frequencies near the center of the Brillouin zone. For monolayer graphene, this critical strain is zero within numerical uncertainty. Using insights from continuum elasticity theory, we fit the phonon dispersion of the ZA mode near the zone center to a function ω2(q)=C2q2+C4q4 and determine the C2 and C4 coefficients as a function of strain and number of layers. In particular, the C2 coefficient is positive for multilayers in the absence of strain and shows a linear dependence with strain. It assumes negative values for compressive strains beyond a critical value and it is responsible for the appearance of imaginary frequencies in the ZA mode. We discuss these results in light of both continuum and atomistic approaches. Critical parameters vary smoothly with the number of layers from monolayer graphene (two-dimensional) to graphite (three-dimensional).