Nonlinear strain effects in double-resonance Raman bands of graphite, graphene, and related materials

We analyze the influence of biaxial strain on the double-resonance ($D$ and 2$D$) Raman bands of graphite-related materials. A substantial nonlinear dependence of these bands with the strain is observed, evidencing a quite different effect on the electronic structure around the K and $\mathbf{\ensuremath{\Gamma}}$ points of the first Brillouin zone. The strain dependence of the Gr\"uneisen parameters is also analyzed and discussed. We suggest an application of Raman spectroscopy in graphite-related systems, based on the frequency difference observed between the $G$ and $D$ bands (or half the frequency of the 2$D$ features in undefective samples), to provide a measure of the local strain.