Multifractality and interaction at localization transitions between topological phases in superconducting systems

超导系统拓扑相之间局域化转变时的多重分形和相互作用

• 批准号: 465126062
• 负责人: Professor Dr. Alexander Mirlin
• 金额: --
• 依托单位: Landau Institute for Theoretical Physics
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/465126062?language=en
• 关键词: Multifractality; interaction; localization; transitions; between

This is a DFG-RSF cooperation project between the KIT group and the Landau Institute for Theoretical Physics (Russia) in the framework of the call for joint German-Russian project proposals. Cooperation with the Russian team which is lead by Prof. Igor Burmistrov and consists of world-leading experts in Anderson localization and interactions in disordered systems (including topological insulators and disordered superconductors) is crucial for success of the project. Disordered interacting systems of fermions can have rich phase diagrams with topological phases separated by Anderson localization-delocalization transitions. The hallmark of Anderson criticality is multifractality. The primary example of such situation is the integer quantum Hall effect. There are two close cousins of the quantum Hall effect that occur in two dimensions: spin and thermal quantum Hall effects. These phenomena take place in the presence of particle-hole symmetry, i.e., in systems with superconducting order---topological superconductors. Topological materials represent currently one of most active research directions in condensed matter physics. The interest to topological superconductors is additionally enhanced by the fact that corresponding excitations---Majorana fermions---may find applications in quantum information processing. In this project we plan to develop a comprehensive picture of generalized multifractality in the superconducting symmetry classes C and D in the absence of interactions and, then, armed with the obtained insights to shed light on possible topological phases in the presence of electron-electron interaction. The results obtained in the project are expected to be relevant for d-wave disordered superconductors, granular superconducting films in a magnetic field, triplet odd-parity superconductors, non-abelian fractional quantum Hall systems, spin liquids, and surfaces of 3D topological superconductors.The work program consists of four interconnected tasks. In Task 1 we will develop a theory of generalized multifractality in class C. In Tasks 2 and 3 we will explore the interplay of multifractality and interactions in the spin quantum Hall effect. Specifically, Task 2 will address real inelastic-scattering processes leading to dephasing and to thermal broadening of quantum phase transitions. The goal of Task 3 is to investigate renormalization phenomena induced by interplay of disorder and interaction and, on this basis, the phase diagrams and transitions between phases in the presence of interaction. Task 4 will be devoted to investigation of multifractality, interactions, phase diagram, and phase transitions in systems of class D hosting the thermal quantum Hall effect.

这是KIT集团和朗道理论物理研究所（俄罗斯）在呼吁德国-俄罗斯联合项目提案框架内开展的DFG-RSF合作项目。与由Igor Burmistrov教授领导的俄罗斯团队合作，该团队由无序系统（包括拓扑绝缘体和无序超导体）中安德森局部化和相互作用的世界领先专家组成，对于该项目的成功至关重要。 费米子的无序相互作用系统可以具有丰富的相图，其拓扑相被安德森定域-离域跃迁分开。安德森临界性的标志是多重分形。这种情况的主要例子是整数量子霍尔效应。量子霍尔效应有两个近亲发生在两个维度：自旋和热量子霍尔效应。这些现象发生在粒子-空穴对称性的存在下，即，在超导有序的系统中--拓扑超导体。拓扑材料是当前凝聚态物理中最活跃的研究方向之一。对拓扑超导体的兴趣还由于相应的激发-马约拉纳费米子-可能在量子信息处理中找到应用而得到加强。在这个项目中，我们计划在没有相互作用的情况下，在超导对称类C和D中开发一个全面的广义多重分形图，然后，用所获得的见解来阐明电子-电子相互作用存在下可能的拓扑相。该项目所获得的结果预计将与d波无序超导体、磁场中的颗粒超导膜、三重态奇宇称超导体、非阿贝尔分数量子霍尔系统、自旋液体和3D拓扑超导体的表面相关。该工作计划由四个相互关联的任务组成。在任务1中，我们将在C类中建立一个广义多重分形理论。在任务2和任务3中，我们将探索多重分形和自旋量子霍尔效应中的相互作用。 具体来说，任务2将解决真实的非弹性散射过程导致的退相和量子相变的热加宽。任务3的目标是研究由无序和相互作用的相互作用引起的重整化现象，并在此基础上，相图和存在相互作用时的相变。任务4将致力于研究多重分形，相互作用，相图，和D类系统的相变托管热量子霍尔效应。