Effects of Pseudopotentials on the Phonon Dispersion of Graphene

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The dependence of the various curves in the phonon dispersion of graphene on the particular pseudopotential used is analysed. By using three different pseudopotentials, we did a first principle calculation using the Quantum-ESPRESSO. It was found that the phonon frequencies of the various branches of graphene and some few layers graphene (FLGs) in addition to the crossings at some special symmetry points were dependent on the pseudopotential used. Keyword: Graphene, phonon dispersion, pseudopotential, first principle, force constant -1 , leading to differences in the slopes and even in the general shapes of the calculated phonon dispersions. The contradiction in most existing calculations as spelt out above is the motivation behind this study. We calculate the phonon dispersion of graphene and some FLGs using the density functional theory (DFT) performed using Quantum ESPRESSO (QE) codes (27) with the local density approximation (LDA). We used the Trouller Martin (TM) norm-conserving pseudopotentials and Rappe Rabe Kaxiras Joannopoulos ultra-soft (RRKJUS) pseudopotential, which is a Perdew-Zunger (LDA) exchange correlation functional. The wave functions were expanded using energy cut-off between 25 50 Ryd depending on the pseudopotential. We used Methfessel Paxton smearing (28) in the calculations with an energy cut off of 0.02 Ryd. A Monkhorst-Pack grid of 16 × 16 × 1was used for the Brillouin zone sampling. An in-plane lattice constant of 4.6595 a.u. (or 2.466 A) and an interlayer distance of 10 were used in the calculation. The results are fitted to the experimental data of Refs. (9, 10). We also compared the correlations and discrepancies between the experimental data and the calculated ones.