Electronic properties of strained graphene

Hence, the Umklapp electron-electron scattering processes have fun- damental role in order that the system sustains the high-energy plasmon mode. More- over, we have found an intermediate energy pseudo-plasmon mode, associated with a logarithmic divergence of the polarization, which can be related to an interband transi- tion between the Van Hove singularities in the valence and conduction bands of graphene, and it can be identified with a ! transition. In graphene, to date there are measure- ments about the low energy plasmon (Nature 487, 77 (2012), Nature Photonics 6, 749 (2012)) and the pseudo-plasmon excitation (Phys. Rev. B 77, 233406 (2008)), whereas there is no clear experimental evidence about the high energy plasmon. Usually, experi- mental methodologies to detect plasmon dispersion relation, such as electron energy loss spectroscopy (EELS), measure the collective excitation at small wavevectors (q ! 0). The detection of the high energy branch at small wavevector could be difficult, first of all, because of the reduced spectral weight associated with the high energy branch, but also because these plasmons could be damped by the promotion of electrons from the valence band into the higher ( ) energy band. Due to the robustness of the Dirac cones with respect to the application of uniax- ial strain, for sufficiently small strain modulus, it is possible to use the massless Dirac approximation in order to describe the low energy electronic properties. In particular, exploiting the massless Dirac approximation, we have st