Blue and red shifted temperature dependence of implicit phonon shifts in graphene

Abstract

We have calculated the implicit shift for various modes of frequency in a pure graphene sheet. Thermal expansion and Grüneisen parameter which are required for implicit shift calculation have already been studied and reported. For this calculation, phonon frequencies are obtained using force constants derived from dynamical matrix calculated using VASP code where the density functional perturbation theory (DFPT) is used in interface with phonopy software. The implicit phonon shift shows an unusual behavior as compared to the bulk materials. The frequency shift is large negative (red shift) for ZA and ZO modes and the value of negative shift increases with increase in temperature. On the other hand, blue shift arises for all other longitudinal and transverse modes with a similar trend of increase with increase in temperature. The q dependence of phonon shifts has also been studied. Such simultaneous red and blue shifts in transverse or out plane modes and surface modes, respectively leads to speculation of surface softening in out of plane direction in preference to surface melting.