We compare the classification of the electron bands in graphene, obtained by group theory algebra in the framework of a tight-binding model (TBM), with that calculated in a density-functional-theory (DFT) framework. Identification in the DFT band structure of all eight energy bands (four valence and four conduction bands) corresponding to the TBM-derived energy bands is performed and the corresponding analysis is presented. The four occupied (three $\sigma$-like and one $\pi$-like) and three unoccupied (two $\sigma$-like and one $\pi$-like) bands given by the DFT closely correspond to those predicted by the TBM, both by their symmetry and their dispersion law. However, the two lowest lying at the $\Gamma$-point unoccupied bands (one of them of a $\sigma$-like type and the other of a $\pi$-like one), are not of the TBM type. According to both their symmetry and the electron density these bands are plane waves orthogonal to the TBM valence bands; dispersion of these states can be determined unambiguously up to the Brillouin zone borders. On the other hand, the fourth unoccupied band given by the TBM can be identified among those given by the DFT band calculations; it is situated rather high with respect to energy. The interaction of this band with the free-electron states is so strong that it exists only in part of the $k$ space.

We present the results of the first-principle calculations of the energy bands in graphene and their symmetry classification. The valence bands and four lowest conduction bands are classified according to their symmetry at points $\Gamma$ and $K$. Merging of the bands is interpreted in the framework of the group theory.

Variable-range hopping (VRH) conductance fluctuations in the gate-voltage characteristics of mesoscopic gallium arsenide and silicon transistors are analyzed by means of their full distribution functions (DF’s). The forms of the DF predicted by the theory of Raikh and Ruzin have been verified under controlled conditions for both the long, narrow wire and the short, wide channel geometries. The variation of the mean square fluctuation size with temperature in wires fabricated from both materials is found to be described quantitatively by Lee’s model of VRH along a one-dimensional chain. Armed with this quantitative validation of the VRH model, the DF method is applied to the problem of magnetoconductance in the insulating regime. Here a nonmonotonic variation of the magnetoconductance is observed in silicon metal-oxide-semiconductor field-effect transistors whose sign at low magnetic fields is dependent on the channel geometry. The origin of this effect is discussed within the framework of the interference model of VRH magnetoconductance in terms of a narrowing of the DF in a magnetic field. © 1996 The American Physical Society.

The localized running waves in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors, are analytically studied. The quasicontinuum approximation reduces calculation of the running wave properties to the problem of equilibrium of an elastic rod in the potential field. Making additional approximation, the problem is reduced to the motion of the fictitious Newtonian particle in the potential well. It is shown that there exist running waves in the form of supersonic kinks and solitons and their velocities and profiles are calculated. It is shown that the nonstationary smooth waves which are small perturbations on the homogeneous nonzero background are described by Korteweg–de Vries equation and those on zero background by modified Korteweg–de Vries equation. The effect of dissipation on the running waves in JTL is also studied and it is found that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves, whose profiles are also found. Finally, in the framework of Stocks expansion, the nonlinear dispersion and modulation stability in the discrete JTL are studied.

Broadening of the Raman scattering (RS) spectra was studied in monolayer graphene samples irradiated with various doses of ions followed by annealing of radiation damage at different temperatures. It is shown that the width Γ (full width at half maximum) of three main RS lines (G, D, and 2D) increases linearly with the increase of the density of irradiation-induced point defects N_d: ΔΓ = mN_d. The slope m is the same for one-phonon emitting G-line and D-line and almost double for a two-phonon emitting 2D-line. It is observed that the width of the D-line for slightly irradiated samples is larger than one half of the width of the 2D-line, which shows that, in the case of the D-line, elastic electron scattering on point defects leads to an additional linewidth. This difference decreases with the increase of N_d, which shows the decrease of the role of scattering on a single point defect because of the spreading of this mechanism over the whole disordered film. A theoretical model of the width of the D-line in disordered graphene is developed. The analytical expressions explain the experimental observations and allow one to determine the numerical coefficient in the in-plane transverse optical phonon dispersion in graphene.