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

拟议研究的主要领域将是：A.石墨烯中的分数量子霍尔效应，石墨烯和A半导体层之间的库仑阻力。B.石墨烯中应变诱导的自旋-轨道相互作用(SOI)，硅中的输运。A.)石墨烯中的载流子，原子厚度很大的二维(2D)版本的石墨，其行为就像相对论的无质量粒子，“光速”被极高的费米速度(~106m/S)取代，完全通过势垒传输(克莱因悖论)，显示出非传统的量子霍尔效应(QHE)等。我们将深入研究单层或双层石墨烯在分数QHE区域的电子输运，并利用线性响应理论评估电子-电子相互作用的影响。Ii)我们将研究石墨烯与空间分离的半导体2D层或衬底上的另一层石墨烯之间的动量转移，即库仑阻力。B.对石墨烯施加一种菌株会改变原子间的距离，并导致不同轨道之间的重新杂交和增强的SOI。我们将研究自旋相关的输运，这是由于i)应变诱导的石墨烯中的SOI，以及ii)硅单层中的SOI，硅烯是一种类似于石墨烯的材料，但在Dirac点有一个间隙，在它附近有一个线性光谱，并且SOI非常强。拓扑绝缘体是指具有表面导电态的体绝缘体材料。我们将使用线性响应理论和考虑交换的二元散射率来研究电子-电子关联对石墨烯微结构和拓扑绝缘体输运性质的影响。我们还将在应变石墨烯中寻找拓扑态，包括SOI。

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.