标题： 拓扑超导体中的时间反演不变涡旋和引力$\mathbb{Z}_2$拓扑 显示英文标题

标题： A time-reversal invariant vortex in topological superconductors and gravitational $\mathbb{Z}_2$ topology

摘要： 我们研究了在时间反演对称涡旋存在下的拓扑超导体。Bogoliubov-de-Genne (BdG) 亥姆霍兹的本征态表现出$\mathbb{Z}_2$拓扑结构：具有奇数绕数的时间反演对称涡旋在涡旋和边缘处支持一对螺旋马约拉纳零模，而当绕数为偶数时则没有这样的零模。我们发现这种$\mathbb{Z}_2$结构可以被解释为一种涌现的引力效应。将能隙函数识别为 2 +1 维引力理论中 vielbein 的空间分量，我们可以将 BdG 方程显式地转换为与非平凡引力背景耦合的狄拉克方程。我们发现涡旋核心处诱导了引力曲率，其总通量以$\pi$的整数倍量化，反映了$\mathbb{Z}_2$的拓扑结构。尽管曲率仅在涡旋核心处存在，但由于引力阿哈罗诺夫-博姆效应，费米子谱仍对总曲率通量敏感。 显示英文摘要

摘要： We study a topological superconductor in the presence of a time-reversal invariant vortex. The eigenmodes of the Bogoliubov-de-Genne (BdG) Hamiltonian show a $\mathbb{Z}_2$ topology: the time-reversal invariant vortex with odd winding number supports a pair of helical Majorana zero-modes at the vortex and the edge, while there is no such zero-modes when the winding number is even. We find that this $\mathbb{Z}_2$ structure can be interpreted as an emergent gravitational effect. Identifying the gap function as spatial components of the vielbein in 2 +1-dimensional gravity theory, we can explicitly convert the BdG equation into the Dirac equation coupled to a nontrivial gravitational background. We find that the gravitational curvature is induced at the vortex core, with its total flux quantized in integer multiples of $\pi$, reflecting the $\mathbb{Z}_2$ topological structure. Although the curvature vanishes everywhere except at the vortex core, the fermionic spectrum remains sensitive to the total curvature flux, owing to the gravitational Aharonov-Bohm effect.