Temperature dependence of phonon energies and lifetimes in single- and few-layered graphene

In this work, we have studied the phonon properties of multilayered graphene with the use of molecular dynamics simulations and the $k$-space velocity autocorrelation sequence method, for which we provide a theoretical proof. We calculate the phonon dispersion curves, densities of states, and lifetimes $\ensuremath{\tau}$ of few-layered graphene consisting of 1--5 layers and graphite. $\mathrm{\ensuremath{\Gamma}}$-point phonon energies and lifetimes are investigated for different temperatures ranging from 80 to 1000 K. The study focuses on the impact of the interlayer interaction and temperature on the energies and lifetimes of the $\mathrm{\ensuremath{\Gamma}}$-point phonons, as well as the type of interlayer potential used. For the latter we used the Kolmogorov-Crespi and the Lennard-Jones potentials. We have found that the number of layers $N$ has little effect on the intralayer ZO and $G$ mode energies and greater effect on the interlayer shear and breathing modes, while $\ensuremath{\tau}$ is generally affected by $N$ for all modes, except for the layer shear mode. The influence of $N$ on the lifetimes was also found to be independent of the type of potential used. For the Raman-active $G$ phonon, our calculations show that the lifetime increases with $N$ and that this increase is directly connected to the strength of the interlayer coupling and how this is modeled.