Wannier functions have been widely applied in the study of topological properties and Floquet–Bloch bands of materials. Usually, the real-space Wannier functions are linked to the k-space Hamiltonian by two types of Fourier transform (FT), namely lattice-gauge FT (LGFT) and atomic-gauge FT (AGFT), but the differences between these two FTs on Floquet–Bloch bands have rarely been addressed. Taking monolayer graphene as an example, we demonstrate that LGFT gives different topological descriptions on the Floquet–Bloch bands for the structurally equivalent directions which are obviously unphysical, while AGFT is immune to this dilemma. We introduce the atomic-laser periodic effect to explain the different Floquet–Bloch bands between the LGFT and AGFT. Using AGFT, we showed that linearly polarized laser could effectively manipulate the properties of the Dirac fermions in graphene, such as the location, generation and annihilation of Dirac points. This proposal offers not only deeper understanding on the role of Wannier functions in solving the Floquet systems, but also a promising platform to study the interaction between the time-periodic laser field and materials.

Wannier 函数已广泛应用于材料的拓扑性质和 Floquet-Bloch 带的研究。通常，实空间 Wannier 函数与k-空间哈密顿量通过两种类型的傅里叶变换 (FT)，即格子规范 FT (LGFT) 和原子规范 FT (AGFT)，但是这两种 FT 在 Floquet-Bloch 频带上的差异很少得到解决。以单层石墨烯为例，我们证明了 LGFT 对 Floquet-Bloch 带给出了明显非物理的结构等效方向的不同拓扑描述，而 AGFT 则不受这种困境的影响。我们引入原子激光周期效应来解释 LGFT 和 AGFT 之间的不同 Floquet-Bloch 带。使用AGFT，我们证明了线偏振激光可以有效地控制石墨烯中狄拉克费米子的性质，例如狄拉克点的位置、产生和湮灭。