Vibrational stability of graphene under combined shear and axial strains

Abstract

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 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 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.

The shear strain energy fluctuations caused by random porosities in graphene based on the stochastic finite element model

“…In comparison, the stability of armchair graphene nanoribbons is improved with the increase of ribbon width under the shear strain [13]. Last but not least, the shear strain causes the rippling instability with strain-dependent direction and wavelength, and the large strain-induced shifts of the split components of the G optical phonon line, which may serve as a shear diagnosis [14].…”

Tunability of the Berry phase in gapped graphene

“…From the practical viewpoint, our suggestion is easy to countercheck and exploit. Gaps from 20 meV upwards can be produced by strain [11], epitaxy [12], nanostructuration [13]. Doping would be in the typical currentlyreachable range.…”

“…So far we have implicitly assumed that the perturbation opening the gap has the periodicity of graphene itself (which is the case, for example, for combined sheartension strains preserving vibrational stability [11]). This consideration is relevant in view of a recent report of quantum Hall effect measurements [16] for graphene on h-BN, which suggest that the system has a gap of order 20 meV and no n=0 Landau level-that is, the Berry phase would be essentially zero.…”