We present a theoretical study on the Landau levels (LLs) and magneto-optical absorption of a two-dimensional semi-Dirac electron system under a perpendicular magnetic field. Based on an effective k$·\mathrm{p}$ Hamiltonian, we find that the LLs are proportional to the two-thirds power law of the magnetic field and level index, which can be understood as a hybridization of the LL of Schrödinger and Dirac electrons with new features. With the help of the Kubo formula, we find the selection rule for interband (intraband) magneto-optical transition is anisotropic (isotropic). Specifically, the selection rules for interband magneto-optical transitions are $\mathrm{\Delta }n=0$, $\pm 2$ $(\pm 2,$ $\pm 4)$ for linearly polarized light along the linear (parabolic) dispersion direction, while the selection rules for the intraband transition are $\mathrm{\Delta }n=\pm 1,$ $\pm 3$ regardless of the polarization direction of the light. Further, the magneto-optical conductivity for interband (intraband) transition excited by linearly polarized light along the linear dispersion direction is two (one) orders of magnitude larger than that along the parabolic dispersion direction. This anisotropic magneto-optical absorption spectrum clearly reflects the structure of the LLs, and results in a strong linear dichroism. Importantly, a perfect linear dichroism with magnetic-field tunable wavelength can be achieved by using the interband transition between the two lowest LLs, i.e., from $E_{v0}$ to $E_{c0}$. Our results shed light on the magneto-optical property of the two-dimensional semi-Dirac electron systems and pave the way to design magnetically controlled optical devices.

中文翻译：

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二维半狄拉克电子系统中的各向异性磁光吸收和线性二向色性

我们对二维半狄拉克电子系统在垂直磁场下的朗道能级 (LLs) 和磁光吸收进行了理论研究。基于有效k $·\mathrm{p}$哈密​​顿量，我们发现LLs与磁场的三分之二幂律和能级指数成正比，可以理解为薛定谔和狄拉克电子LL具有新特征的杂化。借助久保公式，我们发现带间（intraband）磁光跃迁的选择规则是各向异性（isotropic）。具体来说，带间磁光跃迁的选择规则是$\mathrm{\Delta }n=0$, $\pm 2$ $(\pm 2,$ $\pm 4)$ 对于沿线性（抛物线）色散方向的线偏振光，带内跃迁的选择规则为 $\mathrm{\Delta }n=\pm 1,$ $\pm 3$与光的偏振方向无关。此外，由线性偏振光沿线性色散方向激发的带间（带内）跃迁的磁光导率比沿抛物线色散方向的磁光导率大两（一）个数量级。这种各向异性磁光吸收光谱清楚地反映了 LL 的结构，并导致强烈的线性二色性。重要的是，通过使用两个最低 LL 之间的带间跃迁，可以实现具有磁场可调波长的完美线性二向色性，即从${乙}_{v0}$ 到 ${乙}_{C0}$. 我们的结果阐明了二维半狄拉克电子系统的磁光特性，并为设计磁控光学器件铺平了道路。