B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkov 61103, Ukraine
Received April 3, 2009
It is shown that the spectral density of phonons polarized along c axis has in graphite the V-type singularity analogous to so-called Dirac singularity
typical for the graphene electron density of states. We study the appearance of quasilocalized states which increase number of quasiparticles near this
singularity by using as examples the phonon spectra of graphite intercalated by metals and electron spectra of graphene containing vacancies. It is
proved that in the electron spectrum of graphene with isolated vacancy the quasilocalized states exist only for atoms from sublattice not containing
PACS: 63.20.–e Phonons in crystal lattices; PACS: 63.22.+m Phonons or vibrational states in low-dimensional structures and nanoscale materials; PACS: 73.20.At Surface states, band structure,electron density of states.
Key words: quasiparticle spectrum, quasi-two-dimensional crystals, graphene, graphite, Green function.