编织量子结：二维系统的拓扑相变
Knitting quantum knots: Topological phase transitions in Two-Dimensional systems
摘要：
我们首先描述了一个对称强制节线半金属（NLSM）在二维平面形式的蜂窝V族和它的非平凡的热电响应。然后，我们将继续表明，在屈曲时，系统经历其dirac合并相变。进一步的屈曲导致这些未钉扎的狄拉克锥在两个不同的临界角处成对湮灭，导致第二次拓扑相变到绝缘状态。然后，我们表明，这种看似无害的绝缘状态确实是一个弱拓扑晶体绝缘体。此外，仔细观察，这种绝缘状态原来是一种高阶拓扑绝缘体（HOTI），它受到$\mathcal{S}_6$对称性的保护。在更广泛的背景下，我们将看到屈曲群- $V$的拓扑性质源于它们在拓扑上属于阻塞原子极限（OAL）绝缘体类的事实。结合所有这些，我们将证明，湮灭狄拉克费米子对需要一个拓扑相变从临界半金属相到OAL绝缘体相。我们还揭示了狄拉克费米子湮灭时相图中丰富的相集，并利用纠缠熵研究了它们的纠缠特性。最后，基于这些系统的非平凡拓扑结构，我们提出了一个拓扑保护的量化开关的概念设计。论文的最后一部分是在一个著名的系统LiCoO 2的表面发现了一个自旋极化的二维电子/空穴气体。
英文摘要：
We start by describing a symmetry enforced nodal line semi-metal (NLSM) in the 2D flat form of honeycomb Group - V and its non trivial thermo-electric response. We will then proceed to show that, upon buckling, the system undergoes its dirac-merging phase transitions. Further buckling leads to these unpinned Dirac cones annihilating in pairs at two distinct critical angle leading to a second topological phase transition to an insulating state. We then show that this seemingly innocuous insulating state is indeed a weak topological crystalline insulator. Furthermore, upon closer look, this insulating state turns out to be a Higher Order Topological Insulator (HOTI) that is protected by $\mathcal{S}_6$ symmetry. In a broader context, we will see that the the topological properties of buckled Group - $V$ stem from the fact that they topologically belong to the class of Obstructed Atomic Limit (OAL) insulators. Combining all these, we will prove that annihilating pairs of Dirac fermions necessitate a topological phase transition from the critical semi-metallic phase to an OAL insulator phase. We also uncover the rich set of phases in the phase diagram in case of annihilating Dirac fermions and study their entanglement properties using entanglement entropy. Finally, based on the non-trivial topology of these systems, we propose the conceptual design of a quantized switch that is protected by topology. Last part of the thesis involves the remarkable discovery of a spin polarized 2D electron/hole gas at the surfaces of a well known system - LiCoO2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
