Topological materials: from fundamentals to applications

*最近发现的拓扑绝缘体、超导体和半金属通过将量子物理与拓扑学(数学的一个分支)相结合，彻底改变了人们对固体的理解。在这些所谓的“拓扑材料”中，电子结构由称为“拓扑不变量”的非零整数来表征。这些不变量对材料的缺陷免疫，并通过位于样品边界或表面的不寻常的电子态在物理上表现出来。*拓扑材料的出现，这是基础科学的一项非凡壮举，也为实际应用带来了巨大的希望。例如，在拓扑超导体中出现的“Majorana模”是量子计算机的很有前途的候选者。此外，拓扑绝缘体的表面态有助于实现低损耗的磁电子(自旋电子学)器件。尽管最近取得了一些进展，但拓扑材料向变革性量子技术的过渡仍处于起步阶段，并面临着各种挑战。首先，Majorana模式很难检测和操纵，因为它们没有电荷，也没有磁性。此外，基于拓扑材料的潜在自旋电子学设备利用了并非拓扑材料独有的特性(如“自旋-动量锁定”)。在这一点上，还不清楚这些特性对于有用的设备是否足够有效。*我们的研究目标是通过开发新的方案来检测和操纵Majorana模，通过引入新的优化算法，并通过设想利用真正的拓扑效应的自旋电子器件，来帮助推动拓扑材料从基础到应用的转变。在这些方向上取得进展，不仅有助于开发基于拓扑材料的有用设备，还将提高对这一令人兴奋的新材料类别的基本理解。

***The recent discovery of topological insulators, superconductors and semimetals has revolutionized the understanding of solids by combining quantum physics with topology (a branch of mathematics). In these so--called "topological materials", the electronic structure is characterized by nonzero integers known as "topological invariants". These invariants are immune to the imperfections of the material and manifest themselves physically through unusual electronic states localized at sample boundaries or surfaces. ******The advent of topological materials, a remarkable feat of fundamental science, harbors in addition a significant promise for practical applications. For example, the "Majorana modes" emerging in topological superconductors are promising candidates for quantum computers. In addition, the surface states of topological insulators could help realize low-dissipation magneto-electronic (spintronics) devices.******In spite of the recent advances, the transition of topological materials towards transformative quantum technologies remains in its infancy and faces various challenges. To begin with, Majorana modes are difficult to detect and manipulate because they have no charge and no magnetic properties. Also, potential spintronics devices based on topological materials exploit properties (such as the "spin-momentum locking") that are not unique to topological materials. At this point, it is unclear that these properties are sufficiently efficient for useful devices. ******The objective of our research is to help advance the transition of topological materials from fundamentals to applications by developing novel schemes to detect and manipulate Majorana modes, by introducing new optimization algorithms, and by conceiving spintronics devices that exploit genuine topological effects. Making progress along these directions will not only help the development of useful devices based on topological materials, but will also improve the fundamental understanding of this exciting new class of materials.