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

Abstract

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 $f_{\mathrm{xc}}$ 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 $f_{\mathrm{xc}}$ 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.

12 pages, 11 figures

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• Direct calculation of exciton binding energies with time-dependent density-functional theory
• Pump driven normal-to-excitonic insulator transition: Josephson oscillations and signatures of BEC-BCS crossover in time-resolved ARPES
• Assessment of long-range-corrected exchange-correlation kernels for solids: accurate exciton binding energies via an empirically scaled Bootstrap kernel
• A Snapshot of Time-Dependent Density-Functional Theory
• Coherence and de-coherence in the Time-Resolved ARPES of realistic materials: an ab-initio perspective