Interaction and disorder effects in graphene

该项目致力于石墨烯的相互作用和无序效应的理论研究，包括接近和远离平衡。该提案的主要目标是探索由狄拉克费米子系统中无序诱导效应和电子-电子相互作用（EEI）的相互作用决定的石墨烯的量子输运性质。这是SPP第一个资助期进行的一项非常成功的研究的延伸，在该研究中，我们(a)开发了一种有效的理论方法来研究无序系统中的电子传输-展开t矩阵形式-并将其应用于具有强散射体的石墨烯；(b)在具有手性对称性的系统中确定了一种新的涡驱动的安德森局域化机制，这与具有空位的石墨烯特别相关；(c)使用Keldysh公式研究了石墨烯中的EEI效应，这使我们能够计算碰撞主导极限下的弛豫率和电阻率；(d)发展了石墨烯的库仑阻力理论，包括脏极限和干净极限；(e)考虑到弯曲声子和EEI的散射，研究了悬浮石墨烯中的输运；(f)在经典极限和量子极限（包括EEI）下探索无序石墨烯中的直流和交流磁输运。在2010-2013年期间，我们在该项目上发表了10篇论文，3篇预印本，1篇博士论文和2篇文凭论文。2013-2016年的项目主要受近期实验发展的推动，并扩展了第一个资助期取得的成果。该项目由两个相互关联的工作包组成：WP1：石墨烯在平衡状态下的相互作用和无序效应；1.1空位和强杂质；DoS、磁输运和筛选；1.2石墨烯中的库伦阻力；1.3无序石墨烯的不稳定性；1.4悬浮石墨烯中的磁输运。WP2：强非平衡石墨烯物理学2.1热电子：磁场的弛豫和影响2.2非平衡动力学的流体动力学描述2.3非平衡隧道光谱2.4石墨烯纳米带中的非平衡现象和磁输运。所提出的研究意味着广泛使用和发展先进的分析和数值方法，包括非线性sigma模型，重整化群，展开散射矩阵形式化，Keldysh图，相对论流体动力学，玻色子化，对称性和拓扑分析。我们期待在SPP1459内部以及与国外领先的实验和理论团队进行广泛的合作。该项目的成功完成将促进我们对石墨烯基结构的输运和非平衡性质的理解，并应激发新的实验，特别是在SPP中。KIT和MPI合作伙伴之间的密切合作对项目的成功至关重要，Pis过去非常富有成效的联合工作证明了这一点，也是在SPP的第一个资助期内。

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.