论文标题
编织量子结：二维系统中的拓扑相变
Knitting quantum knots: Topological phase transitions in Two-Dimensional systems
论文作者
论文摘要
我们首先描述了一种蜂窝组的2D平面形式-V及其非琐碎热电动响应的对称性强制性淋巴结线半金属（NLSM）。然后，我们将继续证明，屈曲后，系统经历了其零dirac-Mersing相变。进一步的屈曲会导致这些未添加的狄拉克锥体以两个不同的临界角对成对an灭，从而导致第二个拓扑相过渡到绝缘状态。然后，我们证明这种看似无害的绝缘状态确实是薄弱的拓扑结晶绝缘子。此外，仔细观察时，这种绝缘状态被证明是一个由$ \ Mathcal {s} _6 $对称性保护的高阶拓扑绝缘子（HOTI）。在更广泛的背景下，我们将看到，屈服群的拓扑特性 - $ v $源于它们在拓扑上属于阻塞原子极限（OAL）绝缘子的类别。将所有这些结合起来，我们将证明，歼灭狄拉克费米子对从关键的半金属阶段到OAL绝缘体相的拓扑相过渡。在消灭狄拉克·费米子并使用纠缠熵研究其纠缠特性的情况下，我们还发现了相图中的丰富相位。最后，基于这些系统的非平凡拓扑结构，我们提出了受拓扑保护的量化开关的概念设计。论文的最后一部分涉及在众所周知的系统的表面上显着发现自旋极化的2D电子/孔气。
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.
