纳米晶体中的激子精细结构：长方体与球体形状的影响

中文摘要 AI 辅助

本文提出了球体和长方体形状纳米晶体（NCs）的带边激子精细结构理论，非微扰地考虑了晶格的立方对称性、NC的立方形状以及NC单轴各向异性对空穴能态和电子-空穴交换相互作用的影响。对称性分析得到了激子精细结构的有效哈密顿量，其参数包括1个空穴能级分裂常数和5个独立的交换相互作用常数。数值计算表明，在具有单轴各向异性的闪锌矿型NCs中，空穴基态分裂的符号取决于材料参数和各向异性轴相对于晶轴的取向。除了源自布洛赫函数对称性、通常可忽略的常规体立方对称交换相互作用贡献外，在纳米晶体中，我们还识别出包络波函数的立方对称性产生的贡献。这种由包络诱导的立方对称短程交换在长方体NCs中不可忽略，会诱导暗激子态发生显著分裂。我们进一步分析了交换常数的单轴各向异性对激子精细结构和振子强度的影响，特别关注交换常数各向异性与较小的空穴能量各向异性分裂相当的NCs。

英文摘要

We present the theory of the band-edge exciton fine structure in nanocrystals (NCs) with spheroidal and cuboidal shapes. The effects of the cubic symmetry of the crystal lattice, the cubic shape of the NC, and NC uniaxial anisotropy on the hole energy states and electron-hole exchange interactions are considered non-perturbatively. Symmetry analysis yields an effective Hamiltonian for the exciton fine structure, parameterized by one constant for hole energy splitting and five independent constants for exchange interaction. Numerical calculations reveal that in uniaxially anisotropic zinc-blende NCs, the sign of the hole ground state splitting depends on the material parameters and on the orientation of the anisotropy axis relative to the crystallographic axes. Beyond the conventional bulk cubically-symmetric contribution to the exchange interaction, which originates from Bloch-function symmetry and is typically negligible, in nanocrystals, we identify the contribution arising from the cubic symmetry of the envelope wavefunction. This cubically symmetric envelope-induced short-range exchange is non-negligible in cuboidal NCs and induces a pronounced splitting of the dark exciton states. We further analyze the influence of uniaxial anisotropy of the exchange constants on both the exciton fine structure and the oscillator strength. Special attention is paid to NCs, where the anisotropy of the exchange constants is comparable to a relatively small hole energy anisotropic splitting.

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35 pages, 9 figures