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我们的工作研究了周期驱动下含次近邻跃迁的非厄米系统的拓扑相变行为。通过结合广义布里渊区理论与Floquet拓扑不变量方法，发现周期驱动不仅改变了零模的拓扑相边界，还诱导出独特的π模能隙，形成由零模相和π模相共同表征的复合拓扑相结构。次近邻跃迁的引入可以诱导大拓扑数，但与静态体系不同，周期驱动下大拓扑数仅在特定参数区间出现。即随着次近邻跃迁强度的增大，大拓扑数相反而消失，表明动态体系具有区别于平衡态的非单调调控特性。此外，次近邻跃迁相位的引入，能够改变拓扑相的边界，这为实验上实现拓扑态的可控调制提供了新思路。这些结果揭示了长程跃迁与外部周期驱动对拓扑性质的独特影响，为非厄米体系中长程与动态调控的交叉研究奠定了理论基础。Our work constructs a non-Hermitian system with long range hopping under periodic driving. The Hamiltonian has chiral symmetry, which implies that the topological invariant can be defined. Based on the non-Bloch band theory and the Floquet method, relevant operators and topological number can be defined, providing quantitative approaches for studying topological properties. For example, by calculating the non-Bloch time-evolution factor, the Floquet operator, etc., it is found that the topological invariant is determined by the change of the phase of $U^{+}_{\epsilon=0,\pi}(\beta)$ as it moves along the generalized Brillouin zone, corresponding to the emergence of quasi-energy zero mode and $\pi$ mode.
Results show that the topological structure of the static system can be affected by periodic driving significantly. The topological phase boundary of the zero mode can be changed. When there is no periodic driving, there is no $\pi$ mode in the energy spectrum. After the introduction of periodic driving, a gap appears at the quasi-energy $\epsilon=\pi$, inducing a non-trivial $\pi$-mode phase and enriching the topological phase diagram. Further, the next nearest neighbor hopping has a unique effect in this system. It can induce large topological numbers. However, different from the static system, large topological numbers only appear in specific parameter intervals under periodic driving. As the strength of the next nearest neighbor hopping increases, the large topological number phase disappears instead, reflecting the non-monotonic regulation characteristics of the Floquet system. In addition, the introduction of the phase of the next nearest neighbor hopping can change the topological phase boundary, providing new ideas for experimentally regulating topological states.
This research is of significance in the field of topological phase transitions in non-Hermitian systems. Theoretically, it reveals the synergistic effect of long-range hopping and periodic driving, and improves the theoretical framework for the cross-research of long-range and dynamic regulation in non-Hermitian systems. From an application perspective, it provides theoretical support for experimentally realizing the controllable modulation of topological states, which is helpful to promote the development of fields such as low energy consumption electronic devices and topological quantum computing.-
Keywords:
- non-Hermitian /
- Floquet /
- long-range hopping /
- topological phase transition
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