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Direct calculation of exciton binding energies with time-dependent density-functional theory

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 Added by Zenghui Yang
 Publication date 2013
  fields Physics
and research's language is English




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Excitons are electron-hole pairs appearing below the band gap in insulators and semiconductors. They are vital to photovoltaics, but are hard to obtain with time-dependent density-functional theory (TDDFT), since most standard exchange-correlation (xc) functionals lack the proper long-range behavior. Furthermore, optical spectra of bulk solids calculated with TDDFT often lack the required resolution to distinguish discrete, weakly bound excitons from the continuum. We adapt the Casida equation formalism for molecular excitations to periodic solids, which allows us to obtain exciton binding energies directly. We calculate exciton binding energies for both small- and large-gap semiconductors and insulators, study the recently proposed bootstrap xc kernel [S. Sharma et al., Phys. Rev. Lett. 107, 186401 (2011)], and extend the formalism to triplet excitons.



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We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose, we derive the nonlinear (third-order) TDDFT equation for the excitonic polarization. In this equation, the nonlinear time-dependent effects are described by the time-dependent (non-adiabatic) part of the effective exciton-exciton interaction, which depends on the exchange-correlation (XC) kernel. We apply the approach to study the nonlinear optical response of a GaAs quantum well. In particular, we calculate the 2D Fourier spectra of the system and compare it with experimental data. We find that it is necessary to use a non-adiabatic XC kernel to describe excitonic bound states - biexcitons, which are formed due to the retarded TDDFT exciton-exciton interaction.
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