Dominant phonon wave vectors and strain-induced splitting of the2DRaman mode of graphene

Theoretical2DRaman band of strained graphene

“…It has been argued that this strain might be about three times larger than the actual one. 13 As shown above, our strain rates overestimate the experimental ones of Ref. 10 by ≈ 100%.…”

“…12,21 It has also been argued that the phonon wavevector for a seemingly "outer" process can be transformed by a reciprocal lattice vector to a phonon wavevector for an equivalent "inner" process, "thereby dismissing the notion of inner and outer processes". 13 In a recent study, we have proposed a quantitative criterion for distinction between the two processes. 19 We have noted that (1) the phonons with largest contribution to the 2D band belong exclusively to the TO phonon branch and (2) the TO branch is the fifth one close to the ΓK direction and the sixth one close to the KM direction (in order of increasing frequency).…”

“…The complexity of these calculations at the ab-initio level hinders the detailed investigation of the dependence of this band on strain and laser photon energy. The theoretical work has so far been limited to the calculation of the 2D peak position, [11][12][13] while the intensity of the peaks is either treated approximately, 11,12 or, in a limited number of cases, is calculated from first principles. 13 Despite the success in modeling the 2D Raman band of graphene, a detailed investigation of its behavior under strain is mandatory for monitoring strain in this material by means of Raman spectroscopy.…”

Interaction between graphene and copper substrate: The role of lattice orientation

“…Numerous theoretical and experimental works, e.g. [61,62,[64][65][66][67][68], appeared in the last decade describing various aspects of the origin and properties of this intense, narrow and dispersive line, yet there are still several debatable issues. The 2D band has been regarded as a single Lorentzian with FWHM of ~ 24 cm -1 for graphene on Si/SiO 2 or broader depending on the substrate and/or environment [34,69].…”

“…Earlier works usually assumed a preferential contribution of the latter to the 2D mode [66,68,69], but recent works point to a larger importance of the inner phonons [62,72,73,75]. However, the simple one-dimensional picture is now being superseded by a full two-dimensional description of the electronic bands and phonon dispersion and matrix elements [62], in which the notation of inner or outer phonons is of a weaker relevance [67]. The 2D mode is dispersive, and its frequency changes with the excitation energy with the slope ∂Pos(2D)/∂E L of approx.…”