Phonons in graphene with point defects

Abstract

The phonon density of states (DOS) of graphene with different types of point defects (carbon isotopes, substitution atoms, vacancies) is considered. Using a solvable model which is based on the harmonic approximation and the assumption that the elastic forces act only between nearest neighboring ions we calculate corrections to the graphene DOS dependent on the type and concentration of defects. In particular the correction due to isotopic dimers is determined. It is shown that a relatively small concentration of defects may lead to significant and specific changes in the DOS, especially at low frequencies, near the Van Hove points and in the vicinity of the K points of the Brillouin zone. In some cases defects generate one or several narrow gaps near the critical points of the phonon DOS as well as resonance states in the Brillouin zone regular points. All types of defects are characterized by the appearance of one or more additional Van Hove peaks near the (Dirac) K points and their singular contribution may be comparable with the effect of electron-phonon interaction. Besides, for low frequencies and near the critical points the relative change in density of states may be many times higher than the concentration of defects.

Thermoelectric properties of finite graphene antidot lattices

“…24 Several ways to reduce the thermal conductivity have already been examined, such as interface mismatching between graphene and nanoribbons, 25,26 the presence of isotopes, [27][28][29][30] cross-plane phonon coupling in a few layers of graphene, 31 strain, 32 random hydrogen vacancies in graphene, 33 and point defects. [34][35][36] Edge disorder has been predicted theoretically to suppress heat conductance of graphene nanoribbons, [37][38][39] and ZT exceeding 3 has been theoretically predicted for such systems in the diffusive limit. 40 GALs have been proposed as a flexible platform for creating a semiconducting material with a band gap which can be tuned by varying the antidot size, shape, or lattice symmetry.…”

Thermal conductivity reduction in graphene with silicon impurity

“…Both calculation models predict that the additional peaks arise at the same frequencies, K 1-2 and K 4-5 . These additional peaks accompany the splitting of the intersected modes, which is analogous to the bandgap opening in the doped graphene [43,45]. It has been suggested that the shapes of the additional peaks are the result of optical phonons that occupy a narrow band with relatively low phonon group velocity [45].…”

“…The most remarkable change in the DOS distribution is that the increased concentration rate reduces or broadens all of the M point peaks of the pure sheet. In Adamyan's calculations [43] for sheets doped with aluminum atoms, which have a mass comparable to silicon atoms, the peaks are lower near the van Hove singularities. Generally, peak broadening indicates that the scattering rates increase [33,44] for all phonons.…”

Discrete breathers above phonon spectrum

“…However, in graphene the atomic interactions are determined by covalent forces. These forces cause the stiffness of the planes with respect to the transverse short-range displacements of atoms [1]. In accordance with the Mermin-Wagner theorem [39] the plane of graphene remains unstable with respect to longrange transverse distortions, resulting in the appearance of ripples [12,40].…”

“…The distances between an atom and three neighboring atoms equal In the pair potential approximation the potential energy of the vibrations of atoms depends on the distances R n = r n -a (explicit form of this energy in harmonic approximation, see e.g. in [1]). The expansion of these distances over the displacements x n , y n and z n depends on the powers R m = (bx + cy + (x 2 + y 2 + z 2 )/a) m (here the subscript n is omitted for simplicity).…”