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

Zeng-hui Yang1, Yonghui Li, Carsten A Ullrich

  • 1Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, Missouri 65211, USA.

The Journal of Chemical Physics
|July 12, 2012
PubMed
Summary
This summary is machine-generated.

Time-dependent density-functional theory (TDDFT) accurately describes optical spectra using a minimal model. This study explores the role of exchange-correlation kernels in excitonic binding for insulators and semiconductors.

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Area of Science:

  • Condensed matter physics
  • Quantum chemistry
  • Computational materials science

Background:

  • Accurate description of optical spectra in insulators and semiconductors is a key challenge for time-dependent density-functional theory (TDDFT).
  • Previous studies suggest TDDFT can model bound and continuum excitons, but the influence of dynamical exchange-correlation (xc) effects remains unclear.
  • The specific roles of the xc kernel's spatial range and frequency dependence in excitonic binding require further investigation.

Purpose of the Study:

  • To investigate the role of dynamical exchange-correlation (xc) effects on excitonic binding within TDDFT.
  • To explore the impact of the xc kernel's spatial range and frequency dependence on exciton properties.
  • To develop a simplified model for studying excitonic phenomena in TDDFT.

Main Methods:

  • Development of a minimal model using a one-dimensional (1D) Kronig-Penney model with two bands.
  • Implementation of simple approximate exchange-correlation (xc) kernels within the TDDFT framework.
  • Analysis of the emergence of the Wannier model and collective exciton behavior from the TDDFT formulation.

Main Results:

  • Adiabatic xc kernels in the 1D model system were found to yield a maximum of two bound excitons.
  • The study confirmed that a long spatial range of the xc kernel is not essential for excitonic binding.
  • The research demonstrated the emergence of the Wannier model, highlighting effective electron-hole interactions.
  • The collective, many-body nature of excitons was explicitly shown.

Conclusions:

  • A minimal TDDFT model provides insights into excitonic effects in 1D systems.
  • The spatial range of the xc kernel is not the sole determinant of excitonic binding.
  • TDDFT naturally incorporates the collective behavior of excitons and the effective electron-hole interaction described by the Wannier model.