Ultrafast dynamics in the Floquet states of Dirac semiconductors are theoretically explored, which accentuates nonequilibrium dynamical nature of the Floquet state beyond the usually considered quasi-static band nature and then gives a missing connection between the two. Phase oscillation of the Fano resonance at the frequency of 2 ${\omega }_{\text{pump}}$ on the Floquet Dirac cone of graphene is disclosed from the transient absorption spectroscopy (TAS), which is due to the correlation between 2 ${\omega }_{\text{pump}}$-absorption paths. This establishes a driving of the petahertz (PHz) quantum oscillation from Dirac materials. On another Floquet Dirac cone of the graphene/h-BN (Gr/h-BN) heterostructure under the circularly polarized pulse pumping, we find a regime that exists between topologically trivial and optically induced nontrivial phases from the time-resolved dichroic photoemission spectroscopy (TRdPES), which we call the fluctuating topological order. The topological order fluctuation is a novel mixed phase, i.e., a dynamical mixture of trivial and nontrivial phases, as a precursor to the transient nontrivial phase.

理论上探索了狄拉克半导体 Floquet 态的超快动力学，这突出了 Floquet 态的非平衡动力学性质，超出了通常认为的准静态带性质，然后给出了两者之间缺失的联系。Fano 共振频率为 2 时的相位振荡${\omega }_{\text{泵}}$ 从瞬态吸收光谱 (TAS) 中公开了石墨烯的 Floquet Dirac 锥体，这是由于 2 ${\omega }_{\text{泵}}$- 吸收路径。这建立了由狄拉克材料驱动的太赫兹 (PHz) 量子振荡。在圆偏振脉冲泵浦下的石墨烯/h-BN（Gr/h-BN）异质结构的另一个 Floquet Dirac 锥上，我们发现了一种存在于拓扑微不足道和光学诱导的非微不足道相之间的机制，来自时间分辨二向色光发射光谱（ TRdPES)，我们称之为波动拓扑序。拓扑序涨落是一种新的混合相，即平凡和非平凡相的动态混合，作为瞬态非平凡相的前兆。