Vibrational Characteristics of Graphene Nanostructures: Stability, Low-Dimensional Peculiarities and Peculiarities of Phonon Expansion and Localization

Among the large number of both fundamental and ordinary studies of various physical parts of nanomaterials, the study of graphene structures, such as nanofilms (bigraphene, trigraphene) and nanotubes is undoubtedly a priority. At first sight, from a practical point of view, the vibrational characteristics of these structures do not seem to be as relevant as the spectra of some of the other quasiparticle excitations and their properties (e.g., electronic and magnetic), this is clearly not the case. First of all, the phonon spectrum determines the stability of the structure, which is especially important for the building of nanostructures. Secondly, some properties that are manifested by investigated nanoobjects, or those that are already being applied and are currently being put into effect, or those that are still in demand (such as increased conductivity of graphene structures), manifest themselves with a significant and even decisive participation of phonons. One more thought is the theoretical background of the dynamic stability of carbon nanostructures, which is very important for “fine tuning” the process of their synthesis and determining the operating conditions of devices based on this structures. In addition, an analysis of the rms amplitudes of atomic displacements makes it real to define the limits of applicability of the harmonic approximation when considering vibrations of graphite and bigraphene, trigraphene, i.e., the use of phonons and phonons modes to explain heat capacity, root-mean-square (rms) atomic displacements, thermal expansion of the concepts themselves, which is not a priori obvious.