MAGNETOTRANSPORT IN GRAPHENE, SILICENE, AND TOPOLOGICAL INSULATORS: INFLUENCE OF ELECTRON-ELECTRON CORRELATIONS

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The main areas of the proposed research will be: A. FRACTIONAL QUANTUM HALL EFFECT IN GRAPHENE, COULOMB DRAG BETWEEN GRAPHENE AND A SEMICONDUCTOR LAYER. B. STRAIN-INDUCED SPIN-ORBIT INTERACTION (SOI) IN GRAPHENE, TRANSPORT IN SILECENE. C. TOPOLOGICAL INSULATORS.A. i) Carriers in graphene, the atomically thick, two-dimensional (2D) version of graphite, behave like relativistic massless particles with the "speed of light" replaced by the very high Fermi velocity (~106 m/s), transmit perfectly through barriers (Klein paradox), show an unconventional quantum Hall effect (QHE), etc.. We will thoroughly study electron transport in single-layer or bilayer graphene in the fractional QHE regime and assess the influence of the electron-electron interaction using linear-response theory. ii) We will study momentum transfer, i.e., the Coulomb drag, between graphene and a spatially separated semiconductor 2D layer or another graphene layer on a substrate. B. Applying a strain to graphene changes the interatomic distances and leads to a rehybridization between different orbitals and an enhanced SOI. We will study spin-dependent transport due to i) strain-induced SOI in graphene, and ii) SOI in a monolayer of silicon, called silicene, a material similar to graphene but with a gap at the Dirac point, a linear spectrum near it, and very strong SOI. C. Topological insulators are materials that are insulators in the bulk but possess surface conducting states. We will study the influence of electron-electron correlations on the transport properties of graphene microstructures and topological insulators using linear-response theory and binary scattering rates that account for exchange. We will also search for topological states in strained graphene including SOI.