论文标题
拓扑电磁效应和四维间距的更高第二个Chern数字
Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
论文作者
论文摘要
较高的拓扑阶段在通过尺寸还原过程中理解较低维拓扑阶段和相关拓扑响应方面起着关键作用。在这项工作中，我们提出了一个由$ \ Mathcal {CP} $对称性保护的四维（4D）$ \ MATHBB {Z} _2 $ topological Insulator（Ti）的Dirac-type模型，其3D边界支持奇数的Dirac锥。特定的扰动将每个散装的巨大狄拉克锥体分为两个在能量摩托车空间中分离的山谷，而相反的第二个chern数字，其中3D边界模式成为鼻球或Weyl半金属相。通过引入电磁（EM）和伪EM磁场，揭示了我们4D系统的外来拓扑响应，在低能策略中发现了（4+1）D混合Chern-Simons理论所描述的。值得注意的是，$ \ Mathcal {cp} $ - 损坏的$ \ Mathbb {z} _2 $ ti从$ \ Mathbb {z} $ ti出现时，当散装间隙通过产生异国情调的双节点/nodal-nodal-nodal-hyodal-hydal-hydal-hyper-torlus papase spase时。最后，我们建议在冷原子中对这些拓扑作用进行实验探测。
Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of four-dimensional (4D) $\mathbb{Z}_2$ topological insulator (TI) protected by $\mathcal{CP}$-symmetry, whose 3D boundary supports an odd number of Dirac cones. A specific perturbation splits each bulk massive Dirac cone into two valleys separated in energy-momentum space with opposite second Chern numbers, in which the 3D boundary modes become a nodal sphere or a Weyl semimetallic phase. By introducing the electromagnetic (EM) and pseudo-EM fields, exotic topological responses of our 4D system are revealed, which are found to be described by the (4+1)D mixed Chern-Simons theories in the low-energy regime. Notably, several topological phase transitions occur from a $\mathcal{CP}$-broken $\mathbb{Z}_2$ TI to a $\mathbb{Z}$ TI when the bulk gap closes by giving rise to exotic double-nodal-line/nodal-hyper-torus gapless phases. Finally, we propose to probe experimentally these topological effects in cold atoms.
