We investigate the theoretical band structure of organic-inorganic perovskites APbX3 with tetragonal crystal structure. Using D4h point group symmetry properties, we derive a general 16-band Hamiltonian describing the electronic band diagram in the vicinity of the wave-vector point corresponding to the direct band gap. For bulk crystals, a very good agreement between our predictions and experimental physical parameters, as band gap energies and effective carrier masses, is obtained. Extending this description to three-dimensional confined hybrid halide perovskite, we calculate the size dependence of the excitonic radiative lifetime and fine structure. We describe the exciton fine structure of cube-shaped nanocrystals by an interplay of crystal-field and electron-hole exchange interaction (short- and long-range parts) enhanced by confinement. Using very recent experimental results on FAPbBr3 nanocrystals, we extract the bulk short-range exchange interaction in this material and predict its value in other hybrid compounds. Finally, we also predict the bright-bright and bright-dark splittings as a function of nanocrystal size.

中文翻译：

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四方晶体的多频带k·p模型：在混合卤化物钙钛矿纳米晶体中的应用。

我们研究了具有四方晶体结构的有机-无机钙钛矿APbX3的理论能带结构。使用D4h点组对称性，我们推导了描述与直接带隙相对应的波矢点附近的电子能带图的通用16能带哈密顿量。对于块状晶体，在带隙能和有效载流子质量方面，我们的预测与实验物理参数之间取得了很好的一致性。将此描述扩展到三维受限杂化卤化物钙钛矿中，我们计算了激子辐射寿命和精细结构的尺寸依赖性。我们通过限制作用增强的晶体场和电子-空穴交换相互作用（短程和长程部分）的相互作用描述了立方状纳米晶体的激子精细结构。使用关于FAPbBr3纳米晶体的最新实验结果，我们提取了这种材料中的大量短程交换相互作用，并预测了其在其他杂化化合物中的价值。最后，我们还预测了明亮-明亮和黑暗-黑暗的分裂与纳米晶体尺寸的关系。