Magneto-transport in topological nanostructures due to novel spin states and trajectories

在1980年，量子霍尔（QH）效应被观察到在二维电子气受到外部磁场。QH态是第一个表现出拓扑不变量的电子结构的例子：它的行为只取决于系统的拓扑结构，因此不受杂质和几何扰动的散射事件的影响。四分之一个世纪后，二维拓扑绝缘体（TI）被发现是量子自旋霍尔效应的一种实现，它是由强自旋轨道耦合而不是外部磁场驱动的，并且在拓扑上受到时间反演对称性的保护。TI是用于未来电子和自旋电子技术的有趣材料。2D TI的发现引发了对其他拓扑材料的研究，包括TI（即三维TI），Weyl和Dirac半金属。当这样的拓扑材料受到外加磁场的作用时，QH和拓扑状态结合，甚至可以杂化形成新的磁状态，例如相空间中不寻常的自旋动量锁定磁轨道。这样的状态和轨道收集了极大的兴趣，因为它们表现出奇异的磁性和自旋输运性质。除了新的磁状态，在拓扑纳米结构中测量的磁阻（MR）通常是非饱和的;随场增加的MR斜率可以是线性的、二次的或平方根的，在这个项目中，我们将研究新的磁状态和轨道，同时考虑到电子-状态拓扑和纳米结构几何形状。我们建议并寻找：（1）在TI纳米结构中表现出不同自旋轨道动力学的丰富形式的磁轨迹，以及（2）在拓扑半金属板中的新的磁状态，即共振Weyl轨道。我们的目标是了解奇异的MR和自旋输运拓扑纳米结构在量子和经典的运输制度，通过整合这些磁状态和轨迹的贡献。这些研究将为设计基于拓扑材料的先进自旋电子学和磁电子学提供多功能平台。

In 1980, the quantum Hall (QH) effect was observed in a two-dimensional electron gas subject to an external magnetic field. The QH state was the first example of an electronic structure exhibiting a topological invariant: its behavior depends only on the system’s topological structure and is thus immune to scattering events from impurities and geometric perturbations. A quarter of a century later, the two-dimensional (2D) topological insulator (TI) was discovered as a realization of the quantum spin Hall effect, which is driven by a strong spin-orbit coupling rather than an external magnetic field, and is topologically protected by time-reversal symmetry. TIs are interesting materials for use in future electronic and spintronic technologies. The discovery of the 2D TI triggered the search for other topological materials, including the TI (i.e. three-dimensional TI), and Weyl and Dirac semimetals.When such a topological material is subject to an applied magnetic field, the QH and topological states join and can even hybridize to form new magnetic states, like for instance unusual spin-momentum-locked magnetic trajectories in phase space. Such states and trajectories gather great interest since they exhibit exotic magnetic and spin transport properties. In addition to new magnetic states, the magnetoresistance (MR) measured in topological nanostructures is generally non-saturating; the MR slope increasing with the field can be either linear, quadratic, or square root, depending on the class of the topological material and the geometry.In this project we will study new magnetic states and trajectories by taking into account effects of both the electronic-state topology and the nanostructure geometry. We propose and search for: (1) rich forms of magnetic trajectories exhibiting different spin-orbital dynamics in a TI nanostructure, and (2) a new magnetic state, namely, the resonant Weyl orbit, in a topological-semimetal slab. We aim at understanding the exotic MR and the spin transport in topological nanostructures in both quantum and classical transport regimes by integrating the contributions of these magnetic states and trajectories. The investigations will provide versatile platforms for designing advanced spintronics and magneto-electronics based on topological materials.