Vibrational stability of graphene under combined shear and axial strains

We study the vibrational properties of graphene under combined shear and uniaxial tensile strain using density-functional perturbation theory. Shear strain always causes rippling instabilities with strain-dependent direction and wavelength; armchair strain contrasts this instability, enabling graphene stability in a large range of combined strains. A complementary description based on membrane elasticity theory nicely clarifies the competition of shear-induced instability and uniaxial tension. We also report the large strain-induced shifts of the split components of the G optical phonon line, which may serve as a shear diagnostic. As to the electronic properties, we find that conical intersections move away from the Brillouin zone border under strain, and they tend to coalesce at large strains, making the opening of gaps difficult to assess. By a detailed search, we find that even at large strains, only small gaps in the tens-of-meV range open at the former Dirac points.