A First‐Principles Scheme for Calculating the Electronic Structure of Strongly Correlated Materials: GW+DMFT

Abstract

Strongly correlated systems are characterized by partially occupied localized orbitals such as found in transition metal oxides or 4f metals. Here the problem is often more of qualitative rather than quantitative nature. It is often found that the LDA predicts a transition metal oxide to be a metal whereas experimentally it is an antiferromagnetic insulator. To cite some examples, LaMnO 3 , famous for its colossal magnetoresistance, and La 2 CuO 4 , a well-known parent compound of high-temperature superconductors, are antiferromagnetic insulators but predicted to be metals by the LDA [39]. In cases where the LDA does predict the correct structure, it is legitimate to ask if the one-particle spectrum is also reproduced correctly. According to the currently accepted interpretation, transition metal oxides may be classified as charge-transfer insulators [18,42], which are characterized by the presence of occupied and unoccupied 3d bands with the oxygen 2p band in between. The gap is then formed by the oxygen 2p and unoccupied 3d bands, unlike the gap in LDA, which is formed by the 3d states (Mott-Hubbard gap). A more appropriate interpretation is to say that the highest valence state is a charge-transfer state: During photoemission a hole is created in the transition metal site but due to the strong 3d Coulomb repulsion it is energetically more favourable for the hole to hop to the oxygen site despite the cost in energy transfer. A number of experimental data, notably 2p core photoemission resonance, suggest that the charge-transfer picture is more appropriate to describe the electronic structure of transition metal oxides. And of course in the case of 4f metals, the LDA, being a one-particle theory, is totally incapable of yielding the incoherent part of the spectral function or satellite structures.The difficulties encountered by the LDA discussed above have prompted a number of attempts at improving the LDA. Notable among these is the GW approximation (GWA), developed systematically by Hedin in the early sixties [20]. He showed that the self-energy can be formally expanded in powers of the screened interaction W , the lowest term being iGW, where G is the Green function. Due to computational difficulties, for a long time the applications of the GWA were restricted to the electron gas. With the rapid progress in computer power, applications to realistic materials eventually became possible about two decades ago. Numerous applications to semiconductors and insulators reveal that in most cases the GWA [10,12] removes a large fraction of the LDA band-gap error. Applications to alkalis show band narrowing from the LDA values and account for more than half of the LDA error (although controversy about this issue still remains [29]).The success of the GWA in sp materials has prompted further applications to more strongly correlated systems. For this type of materials the GWA has been found to be less successful. For example, GW calculation on nickel [8] does reproduce the photoemission quasiparticle band structure rather...

Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure

“…However, going beyond this framework and being able to treat the electron-electron interaction entirely from first-principles is a tempting and challenging project. Work in this direction have appeared recently [152,125,153,154,155,156,6].…”

“…This is described in more details in Refs. [152,155,156]. Concrete implementations of this scheme to electronic structure (and to model hamiltonians as well) is currently being pursued by several groups.…”

“…Concrete implementations of this scheme to electronic structure (and to model hamiltonians as well) is currently being pursued by several groups. For early results, see [152,153,154,155,156,6]. …”

“…Recently, it has been suggested to improve on the GWA for the local contributions by using the DMFT framework [152,153] (see also [125,154,155,156]). One can think of different approximations to the Ψ-functional in this context, depending on whether the DMFT approach is used for all the valence orbitals L = s, p, d, · · ·, or for a subset (corresponding to the index a, b, ...) of correlated orbitals only.…”

Electronic polarons, cumulants and doubly dynamical mean field theory: Theoretical spectroscopy for correlated and less correlated materials

“…This implies not only addressing the question of how to relate effective local Hubbard interactions to the full Coulomb interactions in the continuum (while taking care to avoid double-counting of screening), that is the ab initio calculation of the infamous effective local "Hubbard U"; since at the DFT level no rigorous distinction between contributions of "correlated degrees of freedom" and "uncorrelated" ones can be made, a truly double-counting free theory can only be achieved by eliminating the reference to the DFT Kohn-Sham Hamiltonian altogether. A successful route is the combination of Hedin's GW approximation with DMFT, the so-called GW+DMFT method [14,15,16,17]. A summary of recent progress along these lines can be found in [13]; for most recent applications both, in the model and realistic electronic structure context we refer the reader to Refs.…”