Determination of two-dimensional phonon dispersion relation of graphite by Raman spectroscopy

Phonon dispersion relations of a two-dimensional (2D) graphite are obtained by fitting dispersive Raman modes that originate from nonzone center phonons near the $\Gamma$ or K point in the Brillouin zone (BZ). A new set of 12 force constants of 2D graphite up to the fourth neighbor are determined by a self-consistent fitting procedure, combined with double-resonance Raman theory. Analytical expressions for eigenvalues and eigenvectors at high symmetry points of the BZ are presented.