The correlation between the vibrational and electron excitation modes in the energy spectra of single-layer graphene and crystalline graphite, as well as the dispersion dependences of those modes, has been studied. The methods of the theory of projective representations of the point and spatial symmetry groups are used for the first time in order to interpret those correlations. The correlations of vibrational and electron excitation spectra and the compatibility conditions for irreducible projective representations in the descriptions of quantum states of graphene and crystalline graphite at various points of their Brillouin zones are determined. For the projective representations of all projective classes belonging to the hexagonal system, standard factor-systems are constructed for the first time. In particular, the factor-systems for electron states are first determined. The results obtained are used to calculate, also for the first time, the correct spinor multiplication tables, i.e. the multiplication tables for elements in double symmetry groups. The developed method is applied to classify all high-symmetry points in the Brillouin zones of single-layer graphene and crystalline graphite with respect to the symmetry type of vibrational excitations.K e y w o r d s: spinor representation of symmetry groups, factor-system, dispersion of elementary excitations.

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Potential applicability of undoped, B-, and N-doped carbon nanotubes (CNTs) for elaboration of the working materials of gas sensors of hydrogen halide molecules HX (X 5 F, Cl, Br) is analyzed in computational studies of molecular adsorption on the CNTs surfaces. Density Functional Theory (DFT)-based geometryoptimized calculations of the electronic structure of undoped, B-, and N-doped CNTs of (3,3) and (5,5) chiralities with adsorbed HX (X 5 F, Cl, Br) molecules are performed within molecular cluster approach. Relaxed geometries, binding energies between the adsorbates and the nanotubes, charge states of the adsorbates and the electronic wave function contours are calculated and analyzed in the context of gas sensing applications. Obtained results are supplemented by calculations of adsorption of hydrogen halides on B(N)-doped graphene sheets which are considered as model approximation for large-diameter CNTs. It is found that the B-doped CNTs are perspective for elaboration of sensing materials for detection of HCl and HBr molecules. The undoped and the N-doped CNTs are predicted to be less suitable materials for detection of hydrogen halide gases HX (X 5 F, Cl, Br).

Micro-Raman spectra of single-walled carbon nanotubes in the range of two-phonon 2D bands are investigated in detail. The fine structure of two-phonon 2D bands in the low-temperature Raman spectra of the mixture and individual single-walled carbon nanotubes is considered as the reflection of structure of their π-electron zones. The dispersion behavior of 2D band fine structure components in the resonant Raman spectra of single-walled carbon nanotube mixture is studied depending on the energy of excitating photons. The role of incoming and outgoing electron-phonon resonances in the formation of 2D band fine structure in Raman spectra of single-walled carbon nanotubes is analyzed. The similarity of dispersion behavior of 2D phonon bands in single-walled carbon nanotubes, one-layer graphene, and bulk graphite is discussed.

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In the present work, we used Raman spectroscopy as sensitive tool for characterization of dispersion of electron-phonon resonances in one-layer graphene. We analyzed Stokes and anti-Stokes components of the Raman spectra to investigate the temperature dependence of the graphene G-band on the power of exciting radiation. Appearance and drastic intensity increase of zone-edge D-like modes caused by introduction of structural defects and/or deformations in the graphene layer were observed in the Raman spectra at high powers of excitation. We investigated phonon dispersion of one-layer graphene for iTO phonon branch at K point along K-M direction, which is involved in double-resonance Raman scattering. Raman dispersion slope of D-band is in good agreement with results of theoretical calculations based on the Green's functions approach based on the screened electron-electron interaction. Deviation of the experimental iTO phonon frequency from the linear dependence on excitation energy was observed at excitation E(exc) = 3.81 eV. Self-consistent classification of phonon states according to the symmetry for all dispersion branches of one-layer graphene was carried out.

The dispersion dependences of electron excitations in crystalline graphite and single-layer graphene have been studied taking the electron spin into consideration. The correlations of the energy spectra of electron excitations and, for the first time, the compatibility conditions for two-valued irreducible projective representations characterizing the symmetry of spinor excitations in the indicated structures are determined, as well as the distributions of spinor quantum states over the projective classes and irreducible projective representations for all high-symmetry points in the corresponding Brillouin zones. With the help of theoretical symmetry-group methods for the spatial symmetry groups of crystalline graphite and single-layer graphene (in particular, the splitting of п-bands at the Dirac points), the spin-dependent splittings in their electron energy spectra are found. The splitting magnitude can be considerable, e.g., for dichalcogenides of transition metals belonging to the same spatial symmetry group. But it is found to be small for crystalline graphite and single-layer graphene because of a low spin-orbit interaction energy for carbon atoms and, as a consequence, carbon structures.