Topological materials: from fundamentals to applications

***最近拓扑绝缘体、超导体和半金属的发现，通过将量子物理学与拓扑（数学的一个分支）结合起来，彻底改变了对固体的理解。在这些所谓的“拓扑材料”中，电子结构的特征是被称为“拓扑不变量”的非零整数。这些不变量不受材料缺陷的影响，并通过在样品边界或表面定位的不寻常的电子状态在物理上表现出来。******拓扑材料的出现，是基础科学的一项非凡壮举，同时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“马约拉纳模式”是量子计算机的有希望的候选者。此外，拓扑绝缘体的表面状态有助于实现低耗散磁电子（自旋电子）器件。******尽管最近取得了进展，但拓扑材料向变革性量子技术的过渡仍处于起步阶段，并面临各种挑战。首先，马约拉纳模式很难检测和操纵，因为它们没有电荷和磁性。此外，基于拓扑材料的潜在自旋电子学器件利用了拓扑材料所不特有的特性（如“自旋动量锁定”）。在这一点上，尚不清楚这些特性是否足够有效地用于有用的设备。******我们的研究目标是通过开发新的方案来检测和操纵马约拉纳模式，通过引入新的优化算法，以及通过构想利用真正拓扑效应的自旋电子学设备，帮助推进拓扑材料从基础到应用的转变。沿着这些方向取得进展不仅有助于基于拓扑材料的有用器件的发展，而且还将提高对这类令人兴奋的新材料的基本理解。

***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.