Interaction and disorder effects in graphene

该项目致力于石墨烯中的相互作用和无序效应的理论研究，包括接近和远离平衡的情况。该提案的主要目标是探索石墨烯的量子输运性质，这些性质由狄拉克费米子系统中的无序诱导效应和电子-电子相互作用（EEI）的相互作用决定。这是SPP第一个资助期内开展的一项非常成功的研究的延伸，在该研究中，我们（a）开发了一种研究无序系统中电子输运的有效理论方法-展开的T矩阵形式-并将其应用于具有强散射体的石墨烯;（B）确定了具有手征对称性的系统中安德森局域化的一种新的涡旋驱动机制，（c）使用Keldysh形式主义研究了石墨烯中的EEI效应，这使我们能够计算碰撞主导极限中的弛豫速率和电阻率;（d）发展了石墨烯中的库仑阻力理论，无论是在脏极限还是干净极限;（e）研究了悬浮石墨烯中的输运，同时考虑了弯曲声子和EEI的散射;（f）研究了无序石墨烯中经典和量子极限下的直流和交流磁输运，包括EEI。在2010-2013年期间，我们在该项目上的工作导致了10篇发表论文，3篇预印本，1篇博士论文和2篇文凭论文。2013-2016年的计划主要是由最近的实验发展推动的，也扩展了第一个资助期内获得的结果。该项目由两个相互关联的工作包组成：WP 1：平衡状态下石墨烯中的相互作用和无序效应1.1空位和强杂质：DoS、磁输运和屏蔽1.2石墨烯中的库仑阻力1.3无序石墨烯中的不稳定性1.4悬浮石墨烯中的磁输运。WP 2：强非平衡石墨烯的物理学2.1热电子：弛豫和磁场的影响2.2远离平衡动力学的流体动力学描述2.3非平衡隧穿光谱2.4石墨烯纳米带中的非平衡现象和磁输运。拟议的研究意味着广泛使用和发展先进的分析和数值方法，包括非线性西格玛模型，重整化群，展开散射矩阵形式，Keldysh数学，相对论流体力学，玻色化，对称性和拓扑分析。我们预见到SPP 1459内部以及与国外领先的实验和理论小组的广泛合作。该项目的成功完成将促进我们对石墨烯基结构的传输和非平衡性质的理解，并应激发新的实验，特别是在SPP内。KIT和MPI合作伙伴之间的密切合作对于项目的成功至关重要，正如Pis过去在SPP的第一个资助期内非常富有成效的联合工作所证明的那样。

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.