Interaction and disorder effects in graphene

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The Project is devoted to theoretical investigation of interaction and disorder effects in graphene, both near and far from equilibrium. The main goal of the proposal is to explore quantum transport properties of graphene that are determined by the interplay of disorder-induced effects and electron-electron interaction (EEI) in a system of Dirac fermions. This is an extension of a very successful research carried out during the first funding period of SPP, within which we have (a) developed an efficient theoretical approach to studying electron transport in disorderedsystems--unfolded T-matrix formalism--and applied it to graphene with strong scatterers; (b) identified a novel vortex-driven mechanism of Anderson localization in systems with chiral symmetries, that is particularly relevant for graphene with vacancies; (c) studied EEI effects in graphene using Keldysh formalism, which allowed us to compute relaxation rates and resistivity in collision-dominated limit; (d) developed theory of Coulomb drag in graphene, both in dirty and clean limits; (e) investigated transport in suspended graphene taking into account both scattering by flexural phonons and EEI; (f) explored dc and ac magnetotransport in disordered graphene both in classical and quantum limits, including EEI. During 2010-2013 our work on the Project resulted in 10 published papers, 3 preprints, 1 PhD and 2 diploma theses. The program for 2013-2016 is largely motivated by recent experimental developments and also extends the results obtained during the first funding period. The Project is structured in two mutually related Work Packages: WP1: Interactions and disorder effects in graphene at equilibrium1.1 Vacancies and strong impurities: DoS, magnetotransport, and screening1.2 Coulomb drag in graphene1.3 Instabilities in disordered graphene 1.4 Magnetotransport in suspended graphene.WP2: Physics of strongly non-equilibrium graphene2.1 Hot electrons: relaxation and influence of magnetic field2.2 Hydrodynamic description of far-from-equilibrium kinetics2.3 Nonequilibrium tunneling spectroscopy2.4 Nonequilibrium phenomena and magnetotransport in graphene nanoribbons.The proposed research implies extensive use and development of advanced analytical and numerical methods including non-linear sigma models, renormalization group, unfolded scattering matrix formalism, Keldysh diagrammatics, relativistic hydrodynamics, bosonization, symmetry and topology analysis. We foresee extensive cooperation within SPP1459 and with leading experimental and theoretical groups from abroad. Successful completion of the project will boost our understanding of transport and non-equilibrium properties of graphene-based structures and should motivate new experiments, in particular, within SPP. A close collaboration between the KIT and MPI partners will be crucial for the success of the Project, as proven by very fruitful past joint work by Pis, also within the first funding period of SPP.