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，石墨烯与半导体层间的库仑阻力。B。 石墨烯中的应变诱导自旋轨道相互作用（SOI），硅烯中的输运。C. 拓扑绝缘体。 A. i）石墨烯（石墨的原子厚度、二维（2D）版本）中的载流子表现得像相对论性无质量粒子，其中“光速”被非常高的费米速度（~106 m/s）取代，完美地穿过势垒（克莱因悖论），显示出非常规的量子霍尔效应（QHE）等。我们将深入研究电子在单层或双层石墨烯在分数QHE制度的传输和评估的影响，电子-电子相互作用使用线性响应理论。ii）我们将研究动量传递，即，在石墨烯和空间分离的半导体2D层或衬底上的另一石墨烯层之间的库仑阻力。 B。 对石墨烯施加应变改变了原子间距离，并导致不同轨道之间的重新杂化和增强的SOI。我们将研究由于i）石墨烯中的应变诱导SOI和ii）硅单层中的SOI引起的自旋相关输运，硅烯是一种类似于石墨烯的材料，但在狄拉克点处具有间隙，在其附近具有线性光谱，并且具有非常强的SOI。 C. 拓扑绝缘体是在本体中是绝缘体但具有表面导电状态的材料。 我们将研究电子-电子相关性对石墨烯微结构和拓扑绝缘体的输运性质的影响，使用线性响应理论和二进制散射率，占交换。我们还将在应变石墨烯包括SOI中寻找拓扑状态。

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.