论文标题
石墨烯的Attosend瞬时吸收光谱中的鱼骨共振结构
Fishbone resonance structure in the attosecond transient absorption spectroscopy of graphene
论文作者
论文摘要
我们通过数值求解四个波段密度 - 矩阵方程来研究石墨烯的Attsond瞬时吸收光谱（ATA），这表明了明显的鱼骨共振结构。为了深入了解这些有趣的结构，我们利用了一个简化的模型，该模型仅考虑$γ$和Brillouin区域中的M点。借助该模型，我们可以在分析中表达ATAS频谱作为零和一阶Bessel函数的总和，在红外泵场的强度和频率的变量中以及在$γ$和M点处的有效电子质量。吸收光谱中的Lorentzian和Fano线形状被解决。鱼骨结构由周期性V形结构组成，可以用一阶贝塞尔功能来解释，其倾斜角仅由泵激光的频率确定。鱼骨中V形结构的周期性源于吸收光谱的Lorentzian和Fano线形状的周期性依赖性，对泵和探测激光器之间的时间延迟。与数值结果相比，我们的分析理论可以在ATAS光谱的鱼骨结构中进行定性甚至定量预测零的零和一阶边缘。还讨论了数值模拟中的量规问题。
We investigate the attosecond transient absorption spectroscopy (ATAS) of graphene by numerically solving four-band density-matrix equations, which demonstrates apparent fish bone resonance structures. To gain insight into these interesting structures, we exploit a simplified model that only considers the electrons of $Γ$ and M points in the Brillouin zone. With the help of this model, we can analytically express the ATAS spectrum as the sum of zeroth- and first-order Bessel functions in the variables of the strength and frequency of the infrared pump field as well as the effective mass of electrons at the $Γ$ and M points. Lorentzian and Fano line shapes in the absorption spectrum are addressed. The fish bone structure consists of periodic V-shaped structure that can be explained by first-order Bessel functions and its tilt angle is solely determined by the frequency of the pump laser. The periodicity of the V-shaped structure in the fish bone originates from the periodic dependence of the Lorentzian and Fano line shapes of the absorption spectrum on the time delay between the pump and probe lasers. Compared with the numerical results, our analytical theory can qualitatively or even quantitatively predict the zeroth- and first-order fringes in the fish bone structures of the ATAS spectrum. The gauge issues in the numerical simulations are also discussed.
