标题： 二维拓扑性质的双层$α-T_{3}$晶格由偏振光诱导 显示英文标题

标题： Topological Properties of Bilayer $α-T_{3}$ Lattice Induced by Polarized Light

摘要： 在本研究中，我们探讨了双层$\alpha-T_{3}$晶格中光子修饰能带的拓扑性质，在非共振圆偏振光的影响下，重点关注对齐和循环堆叠配置。 我们推导出了对齐堆叠情况下准能带的精确解析表达式，而在循环堆叠情况下，通过在狄拉克点获得数值结果。 我们的发现表明，由圆偏振光引起的时间反演对称性破缺完全消除了这些狄拉克点处$t^{a,c}$点交汇处的简并。 为了研究驱动的$\alpha-T_{3}$晶格的拓扑特征，我们通过异常磁性和热响应来考察贝里相位。 值得注意的是，在$\alpha = 1/\sqrt{2}$处，波纹带和平坦带相关的轨道磁矩表现出相反的符号，以及它们的贝里曲率。 对于$0 < \alpha < 1$的值，非共振光在狄拉克点附近的能带引起变形，导致准能谱中出现两个大小相等的间隙。 化学势在这些间隙中的位置显著影响轨道磁化。 我们观察到磁化率的线性变化与$\alpha = 1/\sqrt{2}$两侧的陈数相关。 这些拓扑特征表现为两种堆叠类型之间异常霍尔电导的不同量化值... 显示英文摘要

摘要： In this study, we explore the topological properties of the photon-dressed energy bands in bilayer $\alpha-T_{3}$ lattices, focusing on both aligned and cyclic stacking configurations under the influence of off-resonant circularly polarized light. We derive precise analytical expressions for the quasi-energy bands in the aligned stacking case, while numerical results for cyclic stacking are obtained at the Dirac points. Our findings reveal that the time-reversal symmetry breaking caused by circularly polarized light completely lifts the degeneracy at the $t^{a,c}$-point intersections at these Dirac points. To investigate the topological signatures of the driven $\alpha-T_{3}$ lattices, we examine the Berry phase through anomalous magnetic and thermal responses. Notably, at $\alpha = 1/\sqrt{2}$, we find that the orbital magnetic moments associated with both corrugated and flat bands exhibit opposite signs, along with their Berry curvatures. For values of $0 < \alpha < 1$, off-resonant light induces deformations in the bands near the Dirac points, leading to two equally sized gaps in the quasi-energy spectrum. The position of the chemical potential within these gaps significantly influences the orbital magnetization. We observe that linear variations in magnetization correlate with Chern numbers on either side of $\alpha = 1/\sqrt{2}$. These topological features manifest as distinct quantized values of anomalous Hall conductivity across both stacking types...