We compute binding energies, Stark shifts, electric-field-induced dissociation rates, and the Franz-Keldysh effect for excitons in phosphorene in various dielectric surroundings. All three effects show a pronounced dependence on the direction of the in-plane electric field with the dissociation rates, in particular, decreasing by several orders of magnitude upon rotating the electric field from the armchair to the zigzag axis. To better understand the numerical dissociation rates, we derive an analytical approximation to the anisotropic rates induced by weak electric fields thereby generalizing the previously obtained result for isotropic two-dimensional semiconductors. This approximation is shown to be valid in the weak-field limit by comparing it to the exact rates. The anisotropy is also apparent in the large difference between armchair and zigzag components of the exciton polarizability tensor, which we compute for the five lowest-lying states. As expected, we also find much more pronounced Stark shifts in either the armchair or the zigzag direction, depending on the symmetry of the state in question. Finally, an isotropic interaction potential is shown to be an excellent approximation to a more accurate anisotropic interaction derived from the Poisson equation, confirming that the anisotropy of phosphorene is largely due to the direction dependence of the effective masses.

中文翻译：

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各向异性斯塔克位移，场致离解和磷中激子的电吸收

我们计算了在各种介电环境中磷中激子的结合能，斯塔克位移，电场诱导的解离速率和弗朗茨-凯尔迪什效应。所有这三种效应都显示出与平面内电场的方向具有明显的解离关系，尤其是在将电场从扶手椅旋转到曲折轴时，减小了几个数量级。为了更好地理解数值解离速率，我们导出了由弱电场引起的各向异性速率的解析近似值，从而概括了先前获得的各向同性二维半导体的结果。通过将其与精确速率进行比较，可以证明该近似值在弱场限制中有效。激子极化率张量的扶手椅分量和之字形分量之间的巨大差异也很明显，我们针对最低的五个躺着状态进行了计算。不出所料，根据相关状态的对称性，我们还发现扶手椅或锯齿形方向的Stark位移更为明显。最后，各向同性的相互作用势被证明是从泊松方程推导的更精确的各向异性相互作用的极好的近似值，这证明磷的各向异性很大程度上是由于有效质量的方向依赖性所致。取决于所讨论状态的对称性。最后，各向同性的相互作用势被证明是从泊松方程推导的更精确的各向异性相互作用的极好的近似值，这证明磷的各向异性很大程度上是由于有效质量的方向依赖性所致。取决于所讨论状态的对称性。最后，各向同性的相互作用势被证明是从泊松方程推导的更精确的各向异性相互作用的极好的近似值，这证明磷的各向异性很大程度上是由于有效质量的方向依赖性所致。