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

这是KIT小组和朗道理论物理研究所（俄罗斯）在德俄联合项目提案征集框架内的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）的安德森定位和相互作用方面的世界领先专家组成，这对项目的成功至关重要。费米子的无序相互作用系统具有丰富的相图，其拓扑相由Anderson局域-离域跃迁分离。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。量子霍尔效应在二维空间中有两个近亲：自旋霍尔效应和热量子霍尔效应。这些现象发生在粒子-空穴对称存在的情况下，即在超导有序的系统中——拓扑超导体中。拓扑材料是当前凝聚态物理中最活跃的研究方向之一。由于相应的激发——马约拉纳费米子——可能在量子信息处理中得到应用，对拓扑超导体的兴趣也随之增强。在这个项目中，我们计划在没有相互作用的情况下，开发超导对称类C和D中广义多重分形的全面图景，然后，利用所获得的见解来阐明电子-电子相互作用存在时可能的拓扑相。该项目获得的结果有望与d波无序超导体、磁场中的粒状超导薄膜、三重态奇宇称超导体、非阿贝尔分数量子霍尔系统、自旋液体和三维拓扑超导体表面相关。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课上发展广义多重分形理论。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将解决导致失相和量子相变热展宽的实际非弹性散射过程。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，研究存在相互作用时的相图和相之间的转变。任务4将致力于研究具有热量子霍尔效应的D类系统中的多重分形、相互作用、相图和相变。

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.