周期性驱动 Creutz 阶梯的拓扑性质
Topological properties of a periodically driven Creutz ladder
AI总结：
本文研究了周期性驱动 Creutz 阶梯在正弦和 $δ$-kick 两种协议下的拓扑性质，发现高频与静态物理特性一致，但零能模式在高低频下表现不同，且 $δ$-kick 会产生更高的拓扑不变量和大量边缘模式。
摘要：
我们研究了在两种不同驱动协议下的周期性驱动 Creutz 阶梯，即正弦驱动和以固定时间间隔施加于阶梯的 $δ$-kick。具体而言，我们通过计算合适的拓扑不变量，研究了静态（非驱动）情形下平庸和非平庸极限所对应的拓扑性质。在手性对称性保持不变的情形下，除了零能模式外，这两种情况下还会出现 $π$ 能模式。此外，驱动协议出现了两种不同的频率区间，其中特别采用 Floquet-Magnus 展开来研究正弦驱动的高频区间。除了高频和静态场景中的物理特性相同外，零能模式在低频和高频下表现出截然不同的特征。对于正弦驱动，存在一个尖锐的频率阈值，超过该阈值时零能模式仅存在于拓扑极限中，而在平庸极限中，它仅存在至该阈值频率。在存在 $δ$-kick 的情况下，Creutz 阶梯表现出更高的拓扑不变量值，因此系统拥有大量的边缘模式。
英文摘要：
We have investigated a periodically driven Creutz ladder in presence of two different driving protocols, namely, a sinusoidal drive and a $δ$-kick imparted to the ladder at regular intervals of time. Specifically, we have studied the topological properties corresponding to the trivial and the non-trivial limits of the static (undriven) case via computing suitable topological invariants. Corresponding to the case where the chiral symmetry is intact, in addition to the zero energy modes, $π$ energy modes appear in both these cases. Further, two different frequency regimes of the driving protocol emerge, where Floquet-Magnus expansion is particularly employed to study the high frequency regime for the sinusoidal drive. Apart from the physics being identical in the high frequency and the static scenarios, the zero energy modes show distinctive features at low and high frequencies. For the sinusoidal drive, there exists a sharp frequency threshold beyond which the zero energy mode only exists in the topological limit, while in the trivial limit, it exists only upto the threshold frequency. In presence of the $δ$-kick, the Creutz ladder demonstrates higher values of the topological invariant, and as a consequence the system possesses large number of edge modes.
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