Towards Phonon Spectrum of Graphene

TL;DR

This paper demonstrates that including second neighbor interactions is crucial for accurately modeling the phonon spectrum of graphene, and provides detailed derivations for various lattice models.

Contribution

It introduces the importance of second neighbor force constants in phonon spectrum calculations for graphene and related lattice models.

Findings

Nearest neighbor coupling is insufficient for accurate phonon spectra.

Second neighbor interactions are essential for realistic modeling.

Provides detailed derivations for 1D and 2D lattice phonon spectra.

Abstract

It is shown that the nearest neighbor coupling between the carbon atoms is not enough to reproduce the phonon spectrum as observed in graphene, the second neighbor force constant is essential. For completeness we have rederived the phonon spectrum of one dimensional chains and two dimensional lattices like square lattice and triangular lattice with nearest and next nearest neighbor coupling among the atoms. This article is essentially an account of the technical details of a review talk on phonon spectrum of graphene presented at Institute of Physics.