Titlebook: Low-Dimensional Functional Materials; Reinhold Egger,Davron Matrasulov,Khamdam Rakhimov Conference proceedings 2013 Springer Science+Busin

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Two-Dimensional Lattice Fermions with Random Gap,umerical results are analyzed for finite-size scaling and they exhibit a metal-insulator and a insulator-insulator transition. At these transitions we calculate the critical exponent of the localization length.

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On the Electron-Phonon Interactions in Graphene,ted in pristine graphene. We present an analytical method to calculate the ground-state of the electron-phonon system within the framework of the Lee-Low-Pines theory. We show that the degenerate band structure of the graphene promotes the chiral polaron formation. Within our theoretical analysis, w

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Landau Levels and Edge States in Graphene with Strong Spin-Orbit Coupling,eractions (SOI). For a homogeneous field we provide analytical results for the Landau level eigenstates for arbitrary intrinsic and Rashba SOI, including also the effect of a Zeeman field. We then study the edge states in a semi-infinite geometry in the absence of the Rashba term. We find that, for

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Wave Packet Propagation Through Randomly Distributed Scattering Centers in Graphene,are performed within the continuum model, and the time propagation is made by a simple computational technique, based on the split-operator method. Our results show that, despite the Klein tunnelling effect, the presence of these potential steps significantly reduces the transmission probabilities,

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