论文标题
Floquet在广场格子及其有效的汉密尔顿的霍夫史塔特蝴蝶工程
Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian
论文作者
论文摘要
在本文中，我们使用Floquet理论来理论上研究单色圆形和线性极化的光对方形晶格中Hofstadter蝴蝶的影响，该光线是由均匀的垂直磁场引起的。在没有激光器的情况下，蝴蝶具有分形的，相似的结构粒子孔对称性和磁通量$ ϕ = 1/2 $的反射对称性。这些对称性分别由子晶格和时间反向对称性保存。当系统暴露于圆形的光线时，通过打破粒子 - 孔对称性和镜像对称性，将原始的hofsatdter蝴蝶变形了，而对能量$ e = 0 $的反转对称性则保留了对称性。我们的研究表明，圆形极化的灯光对称性和时间交流对称性均均匀。保留了反转对称性，因为磁通量$ ϕ $的哈密顿量和$ 1-ϕ $通过子晶格变换连接。为了关注小型通量区域，我们研究了Landau水平以及圆形光线对Landau水平的影响。相反，线性极化的光通过打破旋转对称性而在保留子晶格和时间反转对称性的同时破坏原始的Hofstadter蝴蝶。此外，我们研究了周期性驱动器对非谐和制度中最低频段的Chern数量的影响。我们发现强烈的圆形光线将改变Chern数量。对于线性极化的光，Chern数不会改变，并且值与激光极化方向保持独立。我们的工作突出了方格上定期驱动的Hofstadter问题所期望的通用功能，并提供了用激光来设计Hofstadter Butterfly的策略。
In this paper, we use Floquet theory to theoretically study the effect of monochromatic circularly and linearly polarized light on the Hofstadter butterfly in the square lattice, which is induced by uniform perpendicular magnetic field. In the absence of laser, the butterfly has a fractal, self-similar structure particle-hole symmetry and reflection symmetry about magnetic flux $ϕ= 1/2$. These symmetries are preserved by the sub-lattice and the time-reversal symmetry, respectively. As the system is exposed to circularly polarized light, the original Hofsatdter butterfly in equilibrium is deformed by breaking both the particle-hole symmetry and the mirror symmetry, while the inversion symmetry about energy $E=0$ and magnetic flux $ϕ=1/2$ is preserved. Our study show that, the circularly polarized light break both the sub-lattice symmetry and the time-reversal symmetry. The inversion symmetry is preserved because the Hamiltonian at magnetic flux $ϕ$ and $1-ϕ$ is connected through the sub-lattice transformation. Focusing on the small flux region, we study the Landau level and the influence of circularly polarized light on the Landau level. On the contrary, the linearly polarized light deforms the original Hofstadter butterfly by breaking the rotational symmetry while preserving sub-lattice and the time-reversal symmetry. Further, we study the influence of the periodic drive on the Chern number of the lowest band in middle Floquet copy within the off-resonance regime. We found strong circularly polarized light will change the Chern number. For linearly polarized light, the Chern number will not change and the values stay independent of laser polarization direction. Our work highlights the generic features expected for the periodically driven Hofstadter problem on square lattice and provide the strategy to engineering the Hofstadter butterfly with laser.
