Interaction and disorder effects in graphene

该项目致力于石墨烯中相互作用和无序效应的理论研究，包括平衡附近和远离平衡的相互作用和无序效应。该提议的主要目标是探索石墨烯的量子输运性质，这些性质是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。这是在SPP的第一个资助期内开展的一项非常成功的研究的扩展，在该研究期间，我们(A)发展了一种有效的理论方法来研究无序体系中的电子输运--展开了T矩阵形式--并将其应用于具有强散射的石墨烯；(B)确定了具有手性对称的体系中Anderson局域化的一种新的涡旋驱动机制，这对于具有空位的石墨烯特别相关；(C)使用Keldysh形式研究了石墨烯中的EEI效应，这使得我们能够计算碰撞主导极限下的驰豫速率和电阻率；(D)发展了石墨烯中的库仑阻力理论，在肮脏和干净的极限下都是如此；(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)探索了无序石墨烯在经典和量子极限下的直流和交流磁输运，包括EEI。2010-2013年间，我们在该项目上发表了10篇论文、3份预印本、1份博士学位论文和2份文凭论文。2013-2016年方案在很大程度上受到最近的实验发展的推动，并扩大了在第一个资助期内取得的成果。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：DO，磁输运和屏蔽1.2库仑在石墨烯中的阻力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。WP2：强非平衡石墨烯的物理：磁场的影响2.1热电子的物理：远离平衡运动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。所提出的研究意味着先进的分析和数值方法的广泛使用和发展，包括非线性Sigma模型、重整化群、展开散射矩阵形式、凯尔什图解、凯尔什图相对论流体力学、玻色化、对称性和拓扑分析。我们预计将在SPP1459内部以及与国外领先的实验和理论小组进行广泛的合作。该项目的成功完成将提高我们对石墨烯结构的输运和非平衡性质的理解，并将推动新的实验，特别是在SPP中。工具包和MPI合作伙伴之间的密切合作对项目的成功至关重要，私营部门过去卓有成效的联合工作证明了这一点，也是在战略计划的第一个资助期内。

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.