构造依赖的圆驱动$N$层Su-Schrieffer-Heeger链中的Floquet拓扑

中文摘要 AI 辅助

我们研究了由共位子晶格轨道堆叠Su-Schrieffer-Heeger（SSH）链形成的二维晶格中构造依赖的Floquet拓扑。在退耦链极限下，我们提出了两种构造。构造I：组成SSH链是拓扑平凡的，缠绕数$w=0$。构造II：组成SSH链是拓扑非平凡的，$w=1$。尽管这些构造在静态极限下是幺正等价的，但圆驱动将它们区分开来，因为由变换联系的跳跃过程对应于不同的物理键矢量，因此获得不同的Peierls相位。利用Floquet-Sambe形式，我们确定了准能量谱和相图，用下带陈数$C_L$和方向性Zak相位$(Z_x, Z_y)$表示。我们发现了不同的Floquet相结构，包括两种构造中具有$C_L=-3$和$C_L=-4$的低频相。由于陈数不能分别分辨两个准能量间隙的拓扑，我们进一步计算了动力学缠绕数$W_0$和$W_\pi$，并验证了相应的手性边缘态。特别地，在相同的驱动参数下，两种构造可以具有相同的陈数$C_L=-2$，而它们的间隙分辨缠绕数分别为$(W_0, W_\pi)=(0, +2)$和$(-2, 0)$。我们还计算了时间平均光学霍尔电导率，并表明$C_Le^2/h$决定了理想全带占据下的直流值。同时，其有限频率响应包含光子辅助贡献。我们的结果表明，组成链的物理构造虽然与静态体谱无关，但可以在Floquet拓扑结构中起决定性作用。我们讨论了驱动模型可能的实验实现。

英文摘要

We investigate construction-dependent Floquet topology in a two-dimensional lattice formed by stacking Su-Schrieffer-Heeger (SSH) chains with co-located sublattice orbitals. We present two constructions in the decoupled-chain limit. Construction-I: the constituent SSH chains are topologically trivial with winding number $w=0$. Construction-II: the constituent SSH chains are topologically nontrivial with $w=1$. Although these constructions are unitarily equivalent in the static limit, circular driving distinguishes them because the hopping processes related by the transformation correspond to different physical bond vectors and therefore acquire different Peierls phases. Using the Floquet-Sambe formalism, we determine the quasienergy spectra and phase diagrams in terms of the lower-band Chern number $C_L$ and directional Zak phases $(Z_x,\, Z_y)$. We find distinct Floquet phase structures, including low-frequency phases with $C_L = -3$ and $C_L = -4$ in the two constructions. Since the Chern number does not resolve the topology of the two quasienergy gaps separately, we further calculate the dynamical winding numbers $W_0$ and $W_π$, and verify the corresponding chiral edge states. In particular, at identical driving parameters, both constructions can have the same Chern numbers $C_L=-2$, while their gap-resolved winding numbers are $(W_0,\, W_π)=(0,\,+2)$ and $(-2,\,0)$, respectively. We also calculate the time-averaged optical Hall conductivity and show that $ C_Le^2/h$ determines its dc value for ideal full-band occupation. At the same time, its finite-frequency response contains photon-assisted contributions. Our results demonstrate that the physical construction of the constituent chains, although irrelevant to the static bulk spectrum, can play a decisive role in the Floquet topological structure. We discuss possible experimental realizations of the driven model.

发表机构

• Korea Institute for Advanced Study（韩国高等研究院）
• Birla Institute of Technology and Science, Pilani（皮拉尼博拉理工学院）

机构由 AI 辅助整理，请以论文原文为准。