标题： Floquet Möbius 拓扑绝缘体 显示英文标题

标题： Floquet Möbius topological insulators

摘要： 莫比乌斯拓扑绝缘体在动量空间中具有莫比乌斯扭曲的色散边缘带，并且这些边缘带由手性和 ${\mathbb Z}_2$ -投影平移对称性的组合保护。在这项工作中，我们揭示了一种独特的莫比乌斯拓扑绝缘体，其边缘带可以围绕周期驱动系统的准能带 $\pi$ 扭转，因此具有弗洛凯起源。通过对手动实现的莫比乌斯绝缘体模型施加时间周期性猝灭，我们在零和 $\pi$ 准能带周围获得了相互连接的弗洛凯莫比乌斯边缘带，这些边缘带可以与带隙或无带隙的体态共存。这些莫比乌斯带由一对广义缠绕数进行拓扑特征化，其量化由动量空间中高对称点处出现的手征对称性保证。准能带和纠缠谱的数值研究为存在此类莫比乌斯拓扑相提供了有力证据。进一步引入了一种基于边缘带群体绝热切换的协议，用于动态表征弗洛凯莫比乌斯边缘带的拓扑性质。因此，我们的发现扩展了莫比乌斯拓扑相在非平衡设置中的范围，并揭示了一类独特的没有静态对应物的莫比乌斯扭曲拓扑边缘态。 显示英文摘要

摘要： M\"obius topological insulators hold twofold-degenerated dispersive edge bands with M\"obius twists in momentum space, which are protected by the combination of chiral and ${\mathbb Z}_2$-projective translational symmetries. In this work, we reveal a unique type of M\"obius topological insulator, whose edge bands could twist around the quasienergy $\pi$ of a periodically driven system and are thus of Floquet origin. By applying time-periodic quenches to an experimentally realized M\"obius insulator model, we obtain interconnected Floquet M\"obius edge bands around zero and $\pi$ quasienergies, which can coexist with a gapped or gapless bulk. These M\"obius bands are topologically characterized by a pair of generalized winding numbers, whose quantizations are guaranteed by an emergent chiral symmetry at a high-symmetry point in momentum space. Numerical investigations of the quasienergy and entanglement spectra provide consistent evidence for the presence of such M\"obius topological phases. A protocol based on the adiabatic switching of edge-band populations is further introduced to dynamically characterize the topology of Floquet M\"obius edge bands. Our findings thus extend the scope of M\"obius topological phases to nonequilibrium settings and unveil a unique class of M\"obius twisted topological edge states without static counterparts.