Within the Floquet theory of periodically driven quantum systems, we developed the theory of light-induced modification of electronic states in semiconductor materials described by the Luttinger Hamiltonian (the electronic term ${\mathrm{\Gamma }}_8$). Particularly, exact solutions of the Floquet problem are found for the band edge in the cases of linearly and circularly polarized irradiation. It is shown that the irradiation changes electron effective masses near the band edge, induces anisotropy of the electron dispersion, and splits the bands. It is demonstrated that the light-induced band splitting strongly depends on the light polarization. Namely, the circularly polarized light acts similarly to a stationary magnetic field and lifts the spin degeneracy of electron branches, whereas a linearly polarized light does not affect the spin degeneracy and only splits the bands in the center of the Brillouin zone. The present theory can be applied to describe electronic properties of various semiconductor structures irradiated by an electromagnetic field in the broad frequency range.

中文翻译：

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Luttinger哈密顿量的球拍工程

在周期性驱动的量子系统的Floquet理论中，我们开发了由Luttinger Hamiltonian（电子术语， ${\mathrm{\Gamma }}_8$）。特别地，在线性和圆偏振辐射的情况下，对于带边缘发现了浮球问题的精确解。结果表明，辐照会改变能带边缘附近的电子有效质量，引起电子分散的各向异性，并分裂能带。已经证明，光诱导的带分裂强烈地取决于光的偏振。即，圆偏振光的作用类似于固定磁场，并提高了电子分支的自旋简并性，而线偏振光不影响自旋简并仅分裂布里渊区中心的能带。本理论可以用于描述在宽频率范围内由电磁场照射的各种半导体结构的电子特性。