Recently, second harmonic generation (SHG) for the yellow exciton series in cuprous oxide was demonstrated [Phys. Rev. B 98, 085203 (2018)]. Assuming perfect $O_{\mathrm{h}}$ symmetry, SHG is forbidden along certain high-symmetry axes. Perturbations can break this symmetry and forbidden transitions may become allowed. We investigate theoretically the effect of external magnetic fields on the yellow exciton lines of cuprous oxide. We identify two mechanisms by which an applied magnetic field can induce a second harmonic signal in a forbidden direction. First of all, a magnetic field by itself generally lifts the selection rules. In the Voigt configuration, an additional magneto-Stark electric field appears. This also induces certain SHG processes differing from those induced by the magnetic field alone. Complementary to the paper by Farenbruch et al. [Phys. Rev. B 101, 115201 (2020)], we perform a full numerical diagonalization of the exciton Hamiltonian including the complex valence-band structure. Numerical results are compared with experimental data.

中文翻译：

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磁场中氧化亚铜的二次谐波产生

最近，证明了在氧化亚铜中黄色激子系列的二次谐波产生（SHG）。版本B 98，085203（2018）]。假设完美${Ø}_{\mathrm{H}}$在对称性方面，SHG沿某些高对称轴被禁止。扰动会破坏这种对称性，并且可能会允许禁止的跃迁。我们从理论上研究了外部磁场对氧化亚铜的黄色激子线的影响。我们确定了两种机制，通过这种机制，施加的磁场可以沿禁止方向感应二次谐波信号。首先，磁场本身通常会提升选择规则。在Voigt配置中，会出现一个附加的Stark磁场。这也会引起某些SHG过程，不同于仅由磁场引起的SHG过程。作为对Farenbruch等人论文的补充。[物理 B版 101，115201（2020）]，我们对激子哈密顿量进行了完整的数值对角化，包括复杂的价带结构。将数值结果与实验数据进行比较。