Interplay of Superconductivity and Localization

凝聚态物理学的一个中心研究领域是理论预测、分类和描述，以及对不同相态物质的实验研究。该项目致力于在二维无序相互作用系统中超导，金属和绝缘状态之间相变的理论研究。该提案中提出的基本理论问题是超导性，无序和电子关联的相互作用。该项目的主要方向是低维无序超导结构。这个方向的核心问题之一是无序系统中超导体-绝缘体转变的性质，其普遍性程度及其附近的输运特性。超导体-绝缘体相变（SIT）属于无序诱导量子相变的一个大类，包括安德森金属-绝缘体相变和量子霍尔相变。定域-离域量子相变是凝聚态物理中一个非常活跃的研究领域。电子-电子相互作用在相变过程中的作用是研究的热点之一。在相应的量子临界区的临界性质是由无序和相互作用控制的量子相干效应的相互作用。该项目旨在开发一个无序超导体的连贯图像，涉及所有关键成分：超导相关性，无序诱导的多重分形，以及各种通道中的电子-电子相互作用。重点将放在薄膜的超导性能，展示了超导体-绝缘体转变和高温超导新材料。主要的预期结果是描述强关联低维系统的不同状态的相图。该项目的目标预计将与在新材料中寻找高温超导性特别相关。在方法论上，我们计划推广具有库珀通道中相互作用的相互作用σ模型，以包括额外的相关机制和非常规对称性。工作计划包括三个相互关联的任务：1.发展薄膜SIT的综合理论.研究无序薄膜中的有限T超导转变，超越平均场的束缚.确定在新材料和纳米系统中无序诱导超导性增强的可能性。

A central research area in condensed matter physics is theoretical prediction, classification, and description as well as experimental investigation of different phases of matter. The project is devoted to the theoretical study of phase transitions between superconducting, metallic, and insulating states in two-dimensional disordered interacting systems. The fundamental theoretical problem addressed in the proposal is that of the interplay of superconductivity, disorder, and electronic correlations. The major direction of the project is related to low-dimensional disordered superconducting structures. One of the central questions within this direction is the nature of the Superconductor-Insulator Transition in disordered systems, its degree of universality, and character of transport in its vicinity. The Superconductor-Insulator Transition (SIT) belongs to a broad class of disorder-induced quantum phase transitions which includes Anderson metal-insulator transition and quantum Hall transition. Localization-delocalization quantum phase transitions form an actively developing field of condensed matter physics. Electron-electron interaction effects at the transitions represent one of central research directions. Critical properties in the corresponding quantum critical regimes are governed by interplay of disorder- and interaction-controlled quantum-coherent effects. The project is intended to develop a coherent picture of disordered superconductors involving all the key ingredients: superconducting correlation, disorder-induced multifractality, and electron-electron interactions in various channels. The emphasis will be put on superconducting properties of thin films demonstrating the supeconductor -insulator transition and novel materials for high temperature superconductivity. The main expected result is the phase diagram describing different states of strongly correlated low-dimensional systems. The objectives of the project are expected to be particularly relevant for searching high-temperature superconductivity in novel materials. Methodologically, it is planned to generalize the interacting sigma-model with the interaction in the Cooper channel to include additional correlation mechanisms and unconventional symmetries.The Work Plan consists of the three inter-related Tasks:1. To develop a comprehensive theory of the SIT in thin films.2. To investigate the finite-T superconducting transition in disordered films, going beyond the mean-field description.3. To identify possibilities of disorder-induced enhancement of superconductivity in novel materials and nanosystems.