Using a semiclassical approach, we derive a fully analytical expression for the ionization rate of excitons in two-dimensional materials due to an external static electric field, which eliminates the need for complicated numerical calculations. Our formula shows quantitative agreement with more sophisticated numerical methods based on the exterior complex scaling approach, which solves a non-Hermitian eigenvalue problem yielding complex energy eigenvalues, where the imaginary part describes the ionization rate. Results for excitons in hexagonal boron nitride and the $A$ exciton in transition metal dichalcogenides are given as simple examples. The extension of the theory to include spin-orbit-split excitons in transition metal dichalcogenides is trivial.

中文翻译：

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二维激子中Lo Surdo–Stark效应和电离的定量分析半经典方法

使用半经典方法，由于外部静电场，我们导出了二维材料中激子电离速率的完全解析表达式，从而无需进行复杂的数值计算。我们的公式显示了与基于外部复比例缩放方法的更复杂的数值方法之间的定量一致性，该方法解决了非赫米特特征值问题，产生了复杂的能量特征值，其中虚部描述了电离率。六方氮化硼中激子的结果$\mathrm{一种}$作为简单的例子，给出了过渡金属二卤化物中的激子。该理论的扩展很简单，将自旋轨道分裂激子包括在过渡金属二卤化物中。