论文标题
少木诺博夫 - de Gennes Systems的非热性和拓扑不变性
Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
论文作者
论文摘要
由于理论上的预测和实验观察了镁的热厅效应，因此已经提出了在镁质系统中可能发生的各种新现象。在本文中，我们回顾了木核Bogoliubov-DE Gennes（BDG）系统的拓扑阶段研究的最新进展。在概述了先前关于电子拓扑绝缘子的作品和镁的热厅效应之后，我们为玻色粒BDG系统提供了必要的背景，并特别强调了它们是由BDG Hamiltonian的对角线化引起的。之后，我们介绍了$ \ mathbb {z} _2 $ topogical不变性的定义，用于带有伪时间 - 反转对称性的拓扑系统，以确保存在“ Kramers Pairs Pairs”的玻色子对应物。由于玻色粒BDG系统的固有非热性，因此必须根据玻色浆浆果连接和曲率来定义这些拓扑不变。然后，我们引入了理论模型，可以将其视为AII类二维拓扑绝缘子的宏伟类似物。我们在分析上和数值上证明了$ \ mathbb {z} _2 $拓扑不变性精确地表征了无间隙边缘/表面状态的存在。我们还预测，带有特定堆叠的BiLayer CRI $ _3 $将是实现二维镁质系统的理想候选者，其特征在于非平凡的$ \ Mathbb {Z} _2 _2 $拓扑不变性。对于三维拓扑镁质系统，预计将磁场施加到表面时，预计将发生木元素的热霍尔效应。
Since the theoretical prediction and experimental observation of the thermal Hall effect of magnons, a variety of novel phenomena that may occur in magnonic systems have been proposed. In this paper, we review the recent advances in the study of topological phases of magnon Bogoliubov-de Gennes (BdG) systems. After giving an overview of the previous works on electronic topological insulators and the thermal Hall effect of magnons, we provide the necessary background for bosonic BdG systems, with a particular emphasis on their non-Hermiticity arising from the diagonalization of the BdG Hamiltonian. After that, we introduce the definitions of $ \mathbb{Z}_2 $ topological invariants for bosonic systems with pseudo-time-reversal symmetry, which ensures the existence of bosonic counterparts of "Kramers pairs". Because of the intrinsic non-Hermiticity of the bosonic BdG systems, these topological invariants have to be defined in terms of the bosonic Berry connection and curvature. We then introduce theoretical models that can be thought of as magnonic analogues of two- and three-dimensional topological insulators in class AII. We demonstrate analytically and numerically that the $ \mathbb{Z}_2 $ topological invariants precisely characterize the presence of gapless edge/surface states. We also predict that bilayer CrI$_3$ with a particular stacking would be an ideal candidate for realization of a two-dimensional magnon system characterized by a nontrivial $ \mathbb{Z}_2 $ topological invariant. For three-dimensional topological magnon systems, the thermal Hall effect of magnons is expected to occur when a magnetic field is applied to the surface.
