The higher-order topological insulator (HOTI) is a new type of topological system which has special bulkedge correspondence compared with conventional topological insulators. In this work, we propose a scheme to realize Floquet HOTI in ultracold atom systems. With the combination of periodically spin-dependent driving of the superlattices and a next-next-nearest-neighbor d-wave-like anisotropic coupling term between different spin components, a Floquet second-order topological insulator with four zero-energy corner states emerges, whose Wannier bands are gapless and exhibit interesting bulk topology. Furthermore, the anisotropic coupling with nearest-neighbor form will also induce some intriguing topological phenomena, e.g. non-topologically protected corner states and topological semimetal for two different types of lattice structures respectively. Our scheme may give insight into the construction of different types of higher-order topological insulators in synthetic systems. It also provides an experimentally feasible platform to research the relations between different types of topological states and may have a wide range of applications in future.
Directed motion of doublons and holes in periodically driven Mott insulators
周期性驱动的系统可以导致粒子的定向运动。我们研究了玻色子莫特绝缘体的棘轮效应，其中交错跳跃和交错局部电位随时间周期性变化。如果驱动频率小于相互作用强度，并且激发的密度很小，则可以有效地获得描述双占据位置（doublons）和空位置（holes）运动的单粒子量子棘轮。这种简单的量子机器可以用来操纵莫特绝缘体的激发。对于适当选择的参数，例如，孔和双孔以相反的方向移动。为了研究周期性驱动是否可以用于使颗粒“上坡”移动，即，研究了线性势$- g x$对外力的影响。在很长一段时间内，只有当驱动频率$ω$和外力$n_0 g = m_0 ω$与$\frac{n_0}{2},m_0 \in \mathbb{Z}$相当时，才能进行运输。
Topological Floquet edge states in periodically curved waveguides
研究了用调制的Su-Schrieffer-Heeger模型描述的周期弯曲光波导阵列中的Floquet边缘态。除了散装边缘对应，我们的研究探讨了频带拓扑结构和周期性调制之间的相互作用。通过分析准能谱和Zak相位，我们发现，虽然拓扑和非拓扑边缘状态可以存在相同的参数，\emph{they can not appear in the same spectral gap}。在高频极限下，我们分析发现不同相位之间的所有边界，并研究拓扑和非拓扑边缘状态的共存。与未调制的系统相比，边缘状态的出现是由于能带拓扑结构或调制引起的缺陷。这意味着周期性调制不仅可以调整具有非平凡拓扑的参数区域，而且还可以支持新的边缘状态。
Anomalous multi-gap topological phases in periodically driven quantum rotors
Institute of Science and Technology Austria（奥地利科学技术研究院）；TCM Group, Cavendish Laboratory, Department of Physics, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom（英国剑桥大学卡文迪许实验室物理系）
