Graphene phonon softening and splitting by directional straining

Abstract

Strain-induced graphenephonon softening and phonon band splitting are indeed fascinating, which were attributed to the phonon double resonant scattering without intrinsic involvement of C-C bond relaxation. Here, we show that the lengthening and weakening of the C-C bond softens the phonon and that the mismatching between the uniaxial strain and the C3vbond geometry splits the band. In addition to the force constant of 11.8 N/m for a C-C bond in graphene, consistency between theory and measurements derives that if the strain is along a bond, maximal band splitting happens; if the strain is perpendicular, no band splitting occurs.