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 roles of the long spatial range and the frequency dependence of the xc kernel fxc 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 (1D) Kronig-Penney model and simple approximate xc kernels, providing an easily accessible model system for studying excitonic effects in TDDFT. For the 1D model system, it is found that adiabatic xc kernels can produce at most two bound excitons, confirming that the long spatial range of fxc 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.
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Research Article| July 06 2012
A minimal model for excitons within time-dependent density-functional theory
Zeng-hui Yang, Yonghui Li, Carsten A. Ullrich; A minimal model for excitons within time-dependent density-functional theory. J. Chem. Phys. 7 July 2012; 137 (1): 014513. https://doi.org/10.1063/1.4730031
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