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arXiv 1202.4779cond-mat.mtrl-scicond-mat.other
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含时密度泛函理论中激子的极小模型

A minimal model for excitons within time-dependent density-functional theory

Zeng-hui Yang, Yonghui Li, Carsten A. Ullrich

摘要:

绝缘体和半导体光谱的精确描述一直是含时密度泛函理论(TDDFT)面临的一个重要挑战。在文献中已经给出的证据表明,TDDFT可以产生绑定以及连续激子的特定系统,但仍有许多未解决的基本问题,动力学交换和相关(xc)的作用。特别是,xc内核$f_{\rm xc}$的激子结合的长空间范围和频率依赖性的作用仍然没有很好地探索。我们提出了一个极小模型激子在TDDFT,由两个带从一维Kronig-Penney模型和简单的近似xc内核,这使我们能够解决这些问题,在一个透明的方式。根据不同的系统,它被发现,绝热xc内核可以产生一个单一的束缚激子,有时两个束缚激子,其中长的空间范围的$f_{\rm xc}$是不是一个必要条件。它示出了如何Wannier模型,具有有效的电子-空穴相互作用,出现从TDDFT。激子的集体性、多体性得到了明确的证明。

英文摘要:

The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the role of the long spatial range and the frequency dependence of the xc kernel $f_{\rm xc}$ for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional Kronig-Penney model and simple approximate xc kernels, which allows us to address these questions in a transparent manner. Depending on the system, it is found that adiabatic xc kernels can produce a single bound exciton, and sometimes two bound excitons, where the long spatial range of $f_{\rm xc}$ is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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