Topology and Superconductivity In and Out of Equilibrium

凝聚态物理学领域关注的是理解和控制材料的性质。 材料的性质是由物质的微观组成部分-电子和原子决定的。 微观世界是由量子力学而不是经典力学的定律所支配的，并且是用专门为许多粒子系统（每立方厘米10^22个原子的数量级）开发的工具进行数学描述的。 这些工具已经存在了60多年，并且在从微观角度预测传导和磁性等性质方面非常成功。 特别是，朗道的费米液体理论描述了电子在有序的原子晶格中运动。 在这个框架中，非常普遍的论点允许物理学家对物质状态进行分类，并研究不同状态之间的转换。 然而，由于过去十年的进步，我们现在知道有些材料与以前提出的任何类别都不匹配。 更准确地说，应该细化分类。 虽然物质的“旧”分类是基于系统在某些坐标变换（如时间反演，自旋旋转，点群）下的对称性不变的概念，但新的分类应该包括拓扑方面以及对称性考虑。 例如，最近发现的新材料被称为拓扑绝缘体和拓扑超导体。 它们与非拓扑绝缘体和超导体的区别在于它们的拓扑结构，而不是对称性。 拓扑结构也有物理后果。 最值得注意的是，拓扑绝缘体具有绝缘体，同时在其表面上保持导电状态。 . 在发现基金的帮助下，我将继续从事物质拓扑状态的研究。 我特别感兴趣的是使用外场来驱动系统进入和离开拓扑状态。 特别地，可以施加依赖于时间的电磁场（如光）并驱动系统脱离热平衡。 非平衡系统可能不同于非驱动系统，可能具有不同的拓扑性质。 我的工作是理论性的，将侧重于预测材料和设备的性能，并提出可行的实验。 一旦可以通过施加外场来控制拓扑性质，电子学和自旋电子学领域的许多应用就可能随之而来。

The field of condensed matter physics is concerned with understanding and controlling the properties of materials. Material properties are determined by the microscopic components of matter - electrons and atoms. The microscopic world is governed by the laws of quantum mechanics, rather than classical mechanics and is described mathematically with tools specifically developed for systems of many particles (of the order of 10^22 atoms per cubic cm). Such tools have existed for over 60 years and have been very successful in predicting properties like conduction and magnetism from microscopic considerations. In particular, Landau's Fermi liquid theory describes the electrons as they move through an ordered lattice of atoms. In this framework very general arguments allow physicists to classify states of matter and study transitions between different states. However, thanks to advances over the past decade, we now know that some materials do not match any of the previously proposed classes. To be more precise, the classification should be refined. While the 'old' classification of matter is based on the notion of symmetry - invariance of the system under some coordinate transformation (like time reversal, spin rotation, point group), the new classification should include topological aspects as well as symmetry considerations. For example, new materials which were discovered recently are called topological insulators and topological superconductors. They can be distinguished from non-topological insulators and superconductors by their topology but not by their symmetry. The topology also has physical consequences. Most notably, topological insulators have an insulating bulk while maintaining conducting states on their surfaces. . With the help of the discovery grant I will continue to pursue the study of topological states of matter. I'm particularly interested in driving systems into and out of topological states using external fields. In particular, one can apply a time dependent electromagnetic field (like light) and drive the system out of thermal equilibrium. The non-equilibrium system may be different from the un-driven system and may posses different topological properties. My work is theoretical and will focus on predicting the properties of materials and devices and proposing feasible experiments. Once topological properties can be controlled by applying external fields many applications in the field of electronics and spintronics may follow.