Combining the hybrid functional method with dynamical mean-field theory

We present a new method to compute the electronic structure of correlated materials combining the hybrid functional method with the dynamical mean-field theory. As a test example of the method we study cerium sesquioxide, a strongly correlated Mott band insulator. The hybrid functional part improves the magnitude of the pd-band gap which is underestimated in the standard approximations to density functional theory while the dynamical mean-field theory part splits the 4f -electron spectra into a lower and an upper Hubbard band. Copyright c © EPLA, 2008 Introduction. – Recently, there has been considerable progress in the realistic description of strongly correlated materials by combining the density functional theory [1] (DFT) with the dynamical mean-field theory (DMFT) [2–5]. In this DFT+DMFT approach [6,7], DFT is employed to obtain an effective mean-field description of the weakly correlated bands while the local correlations in the more strongly correlated bands (i.e. the d -bands of transition metals and the f -bands of lanthanides and actinides) are treated exactly. The DFT+DMFT method allows to predict spectra and energies of strongly correlated materials. The DFT+DMFT method has been successfully applied to a variety of interesting materials that the conventional band structure theory is unable to deal with. For example, using the DFT+DMFT method the 25% of volume increase in the transition from the αto the δ-phase of Pu could be explained by the presence of strong correlations in δ-Pu [8]. However, by construction the DFT+DMFT approach, does not work so well in situations where the one-electron spectra of the weakly correlated bands are not well approximated by the Kohn-Sham (KS) spectra of DFT. For example, the local density approximation (LDA) and the generalized gradient approximation (GGA) notoriously underestimate the magnitudes of band gaps of insulating materials. On the other hand, within the chemistry community, very accurate functionals called hybrid functionals [9], have been constructed by mixing LDA/GGA functionals with (a)E-mail: [email protected] Hartree-Fock. The hybrid functional (HYF) approach has been tremendously successful in providing very accurate energies for molecules. Moreover, one-electron spectra computed with HYFs give fairly accurate gaps for semiconducting materials [10]. In this work we propose a new method that combines the HYF approach with DMFT (HYF+DMFT) to yield a quantitatively and qualitatively correct description of combined band and Mott-Hubbard insulators. The HYF part improves the effective static mean-field description of the uncorrelated electrons while the DMFT part describes the dynamical local electronic correlations of the strongly localized electrons that can lead to Mott insulating behaviour. Although the HYF approach introduces a new parameter, α, that determines the amount of Hartree-Fock exchange, we show that this α can actually be linked to the Coulomb repulsion parameter U of the DMFT calculation. An important example which illustrates the need for the HYF+DMFT method is provided by the rare-earth sesquioxides [11] series which are insulators. In addition to the Mott-Hubbard gap between the occupied and the unoccupied 4f -bands, a band gap between the uncorrelated O 2pand 5d-bands opens. One thus has to deal with the two-fold problem of finding an accurate description for the pd-band gap and the 4f Hubbard bands in the same material. DFT and related static mean-field methods fail to describe the splitting of the 4f Hubbard band, without invoking some form of magnetic long-range order. For example, HYFs give the correct magnitude for the band