Topological insulators with weak and strong indices

具有弱指数和强指数的拓扑绝缘体

• 批准号: 314807712
• 负责人: Professor Dr. Piet W. Brouwer
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/314807712?language=en
• 关键词: Topological; insulators; weak; strong; indices

Topological insulators in three dimensions have weak and strong topological indices. Strong topological insulators have topologically protected surface states with an odd number of Dirac cones. In weak topological insulators line dislocations may carry topologically protected helical states (depending on the Burgers vector of the line dislocation). These two characteristics appear simultaneously in topological insulators that have nontrivial strong {\em and} weak indices.In a slab geometry, the helical states supported by dislocation lines may connect the surface states of the top and bottom surfaces. Preliminary results show that under suitable conditions this coupling leads to the opening of a gap in the surface state spectrum. In this proposal we present directions in which a more complete understanding of this observation can be reached, and how the dislocation line-induced coupling between surface states of top and bottom surfaces can be used to transfer nontrivial properties of electronic states from one surface to the other. The remarkable physics we discuss is here specific for strong topological insulators with nontrivial weak indices, a condition that is met in a small number of known topological insulator materials, including certain BiSb compounds. For strong topological insulators with trivial weak indices, which applies to most presently known topological insulator materials, dislocation lines to not carry protected helical states, so that the phenomena described here do not apply. For this reason, topological insulators with nontrivial weak {\em and} strong topological indices must be considered a special class of their own, separate from the purely weak or strong topological insulators. This proposal addresses the physics that sets this class apart: The combination of protected helical states at dislocation lines and protected surface states.

三维拓扑绝缘子有弱拓扑指数和强拓扑指数。强拓扑绝缘体具有具有奇数个狄拉克锥体的拓扑保护表面态。在弱拓扑绝缘体中，线位错可能带有拓扑保护的螺旋态(取决于线位错的Burgers矢量)。这两个特征同时出现在具有非平凡强{em和}弱指标的拓扑绝缘体中。在平板几何中，由位错线支撑的螺旋态可以连接顶面和底面的表面态。初步结果表明，在合适的条件下，这种耦合导致表面态光谱中的能隙打开。在这一建议中，我们提出了可以达到对这一观察结果更完整理解的方向，以及如何利用位错线诱导的顶面和底面表面态之间的耦合来将电子态的非平凡性质从一个表面转移到另一个表面。我们在这里讨论的非凡的物理学是专门针对具有非平凡弱指数的强拓扑绝缘体的，这一条件在少数已知的拓扑绝缘体材料中满足，包括某些BiSb化合物。对于具有平凡弱折射率的强拓扑绝缘体，这适用于目前大多数已知的拓扑绝缘体材料，位错线不携带保护的螺旋态，因此这里描述的现象不适用。因此，具有非平凡弱{em和}强拓扑指数的拓扑绝缘子必须被认为是它们自己的一类特殊类型，与纯粹的弱或强拓扑绝缘子是分开的。这一提议解决了区分这一类的物理问题：位错线上受保护的螺旋态和受保护的表面态的组合。