辛 Hopf 绝缘体：玻色 Bogoliubov-de Gennes 系统中的精细拓扑
Symplectic Hopf Insulator: Delicate Topology in Bosonic Bogoliubov-de Gennes Systems
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中文总结 AI 辅助
本文构建了辛 Hopf 绝缘体，一种在弱相互作用玻色系统中具有整数量子化辛 Hopf 不变量、每个原胞需两个玻色模式且边界存在精细保护的表面态的拓扑相。
中文摘要 AI 辅助
拓扑相的最新进展凸显了辛（Krein 空间）拓扑在玻色 Bogoliubov-de Gennes（BBdG）系统分类中的作用。在本工作中，我们从 Moore-Ran-Wen 模型的微观 Bose-Hubbard 推广出发，在 Bogoliubov 近似下处理弱在位相互作用，构建了 Hopf 拓扑的 BBdG 实现，我们称之为辛 Hopf 绝缘体。由此产生的 BBdG 系统具有辛 Hopf 不变量，我们证明对于孤立能带，该不变量是整数量子化的。我们确定这种拓扑本质上是精细的，每个原胞恰好需要两个玻色模式，同时在一系列质量参数范围内对弱相互作用保持鲁棒性。当三维绝缘体在边界处终止时，我们发现在有限激发能量下存在受拓扑保护的非带隙表面态，其保护本身也是精细的。我们的结果确立了辛 Hopf 绝缘体作为弱相互作用玻色系统中一种鲁棒但精细的拓扑相，超越了十重方式分类。
英文摘要
Recent advances in topological phases have highlighted the role of symplectic (Krein-space) topology in the classification of bosonic Bogoliubov-de Gennes (BBdG) systems. In this work, we construct a BBdG realization of Hopf topology, which we dub the symplectic Hopf insulator, starting from a microscopic Bose-Hubbard generalization of the Moore-Ran-Wen model with weak on-site interactions treated within a Bogoliubov approximation. The resulting BBdG system admits a symplectic Hopf invariant, which we show to be integer-quantized for isolated bands. We establish that this topology is intrinsically delicate, requiring exactly two bosonic modes per unit cell, while remaining robust against weak interactions over a range of mass parameters. Upon terminating the three-dimensional insulator at a boundary, we find topologically protected in-gap surface states at finite excitation energy, whose protection is itself delicate. Our results establish the symplectic Hopf insulator as a robust yet delicate topological phase in weakly interacting bosonic systems lying beyond the tenfold-way classification.
发表机构
- Technische Universität Berlin（柏林工业大学）
- University of Coimbra（科英布拉大学）
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