Raman 2D-Band Splitting in Graphene: Theory and Experiment

Abstract

We present a systematic experimental and theoretical study of the two-phonon (2D) Raman scattering in graphene under uniaxial tension. The external perturbation unveils that the 2D mode excited with 785 nm has a complex line-shape mainly due to the contribution of two distinct double resonance scattering processes (inner and outer) in the Raman signal. The splitting depends on the direction of the applied strain and the polarization of the incident light. The results give new insight into the nature of the 2D band and have significant implications for the use of graphene as reinforcement in composites since the 2D mode is crucial to assess how effectively graphene uptakes an applied stress or strain.

Theoretical2DRaman band of strained graphene

“…11 The shift rates of −49.4 and −57.4 cm −1 /%, calculated from first principles, overestimate the experimental values by more than 20% (in absolute value). In another paper, the pairs of shift rates −44.1 and −63.1 cm −1 /% (near-A-strain) and −26.0 and −67.8 cm −1 /% (near-Z-strain), measured at E L = 2.41 eV, have been reported.…”

“…Some authors have concluded that the contributions from these processes are comparable, 11,20 while others have found that the contribution from "outer" processes is negligible compared to that from "inner" ones. 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".…”

“…The asymmetry of the 2D band shape, namely, higher minor peak for perpendicular polarization than for parallel polarization, is also predicted here. In another experiment, 11 Raman measurement have been performed on a graphene flake at θ = 18.4…”

“…Raman measurements on strained graphene have been performed at different strain magnitude, strain direction, and laser photon energy. [9][10][11][12] In all these studies, only one or two peaks of the 2D band could be resolved and their shift rates have been derived. In two similar measurements, 10,12 the determined strains differ by a factor of 2, which shows that the calibration of strain can still be an issue.…”

“…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.…”