Session U6: Strong Electronic Correlation in Solids: Applications of the LDA+U method

LDA+U Based Studies of Electronic, Vibrational and Spectroscopic Properties of Solids

The LDA+U method is a physically motivated approach that attempts to incorporate the effects of important orbital-specific local Coulomb interactions in strongly correlated electron systems while retaining the simplicity of local density approximation (LDA) calculations for real materials. In this talk, we discuss several applications of this method within the ab initio pseudopotential planewave framework. For transition metal oxides, the appropriate inclusion of the effects of onsite Coulomb U significantly alters their electronic structure leading to better agreement with experiment for quantities such as the nature of the electronic state, structural parameters, magnetic moments, phonon frequencies, etc. We have also studied the effects of doping on the electronic, magnetic, and structural properties of NaxCoO2. Undoped CoO2 is a metal with a high density of states at the Fermi level within LSDA, but a charge transfer insulator within LSDA+U. It is found that, due to a strong interaction between the doped electrons and the other Co d electrons, the calculated electronic structure is sensitively depended on the doping level. Finally, we discuss the use of LDA+U results as a starting mean-field solution for calculation of the electron self energy and quasiparticle excitations within the GW approximation.   

LDA+$U$ applied to oxide and nitride wide-band-gap semiconductors

Nitride and oxide semiconductors have important technological applications, but the theoretical understanding of their properties is hampered by the shortcomings of density functional theory (DFT) in the local density approximation (LDA). In particular, DFT-LDA underestimates the binding energy of the semicore $d$ states, leading to poor descriptions of quantities such as band offsets and deformation potentials. In this work we calculate the electronic and structural properties of wurtzite MgO, ZnO, and CdO, and discuss their similarities and dissimilarities with the corresponding nitrides AlN, GaN, and InN. We treat the semicore $d$ states of Zn, Cd, Ga, and In explicitly as valence states in a pseudopotential framework, and improve the description of electron-electron interactions in these narrow bands by including an on-site Coulomb interaction through the LDA+$U$ method. We propose a novel approach to calculate the parameter $U$, based on first-principles calculations for atoms. The approach is general and could be extended to other semiconductors and insulators where semicore $d$ states play a fundamental role in the description of electronic and structural properties. The LDA+$U$ approach systematically improves the LDA band gap by indirectly acting on both the valence-band maximum and conduction-band minimum. We investigate the effects of the on-site Coulomb interaction on lattice parameters, band structure, absolute deformation potentials, and band lineups. Finally we discuss how results based on LDA and LDA+$U$ can be used to calculate defect transition levels and formation energies that can be directly compared with experiment.   

First-principles calculations of electronic structure and spectra of strongly correlated systems: the LDA+U method

Realistic approach to the electronic structure of complex materials which contains correlated d- or f- electrons will be discussed. The density functional theory within the local spin density approximation have been highly successful for electronic structure calculations and zero temperature magnetic properties of non-correlated systems. We investigate some failures of the LDA-scheme for the charge, spin and orbital ordering in transition metal compounds. General formulation of the LDA+U method which takes into account local Coulomb correlations for the d-shell of transition metals ions in the crystal within the mean-field approximation will be presented. The LDA+U scheme describe well the antiferromagnetic Mott insulators, rare-earth and actinide systems. Electronic structure, spin and orbital moments and lattice distortions of transition-metal compounds are investigated in the framework of rotationally invariant LDA+U method. Starting from conventional LDA+U scheme the different ways to go beyond the mean-field approximation which includes in effects of the spin- and charge-fluctuations will be analyzed. Dynamical mean field theory (DMFT) in combination with the first-principle LDA scheme (LDA+DMFT) is a good starting point for calculation of the quasiparticle spectrum for metallic transition metal systems. Recent progress in analysis of the metal-insulator transition for complex transition metal oxides and calculations of the spectral function for itinerant magnetic systems will be discussed.   

Disproportionation, Metal-Insulator Transition, and Critical Interaction Strength in Na$_{1/2}$CoO$_2$

Spontaneous breaking of symmetry is one of the key concepts of solid state physics related to phase transitions. Charge/spin density wave, or charge/spin ordering if the propagation vector is commensurate, are notorious examples of broken symmetry. The charge disproportionation in Na$_{0.5}$CoO$_2$ is the main theme of the present work. The results of LDA+U calculations will be presented, exhibiting a charge disproportionation transition at U$\approx$3eV. Na$_x$CoO$_2$ attracted considerable attention mainly due to superconductivity of its hydrated form Na$_{0.3}$CoO$_2$.1.3H$_2$O [1]. Besides the superconductivity Na$_x$CoO$_2$ exhibits several intriguing properties throughout its phase diagram, such crossover from Pauli-like to Curie-Weiss susceptibility at x=0.5, spin-density wave around x=0.7 or several phase transitions for x=0.5 including metal-insulator transition, charge ordering and magnetic ordering [2]. The Na$_x$CoO$_2$ lattice consists of triangular CoO$_2$ layers separated by Na layer. The mobility of Na ions and fractional occupation of Na sublattice provides an additional complication. Using LDA+U functional within FPLO [3] bandstructure method we have performed series of supercell calculations allowing for breaking of the symmetry between different Co sites. We have found that for large enough, but physically realistic, values of the on-site Coulomb interaction U the Co sublattice disproportionates into sites with formal valencies Co$^{4+}$ and Co$^{3+}$. We have found that at the same time a gap opens in the excitation spectrum. Details of the bandstructure across the transition as well as the driving forces of the transition in the LDA+U mean field picture will be discussed. \newline \newline [1] K. Takada {\it et al.}, Nature (London) {\bf 422}, 53 (2003).\newline [2] M. L. Foo {\it et al.}, Phys. Rev. Lett. {\bf 92}, 247001 (2004).\newline [3] K. Koepernik and H. Eschrig, Phys. Rev. B {\bf 59}, 1743 (1999).   

A consistent, linear-response approach to LDA+U

Hubbard U-correction to LDA or GGA has proven very effective in describing several strongly-correlated systems for which these approximations to DFT otherwise fail. \newline Constrained DFT or semiempirical approaches have been often used to compute the Hubbard U. I introduce here an alternative scheme to evaluate the effective electronic interaction in a fully consistent way. \newline This approach is based on the linear response of the system under consideration to a potential shift acting on the localized orbitals of the correlated sites. Using the occupations of these orbitals as the relevant electronic degrees of freedom we compute the on-site electronic coupling as the difference between the inverse of the bare and of the fully-interacting response matrices. The U computed in this way thus corresponds to the effective, atomically-averaged kernel of the Hartree-exchange-correlation interaction, in agreement with the second quantization expression of the "+U" energy functional. In this way the strength of the "+U" correction is evaluated from the same DFT scheme we aim to correct so that LDA+U becomes a consistent non-parametric method, with no need for semiempirical evaluations of the effective coupling. \newline \newline With this approach we successfully studied the structural, electronic, chemical and electrochemical properties of several transition-metal compounds. Examples will include minerals in the Earth's interior$^{1}$, cathode materials for next-generation lithium batteries$^{2}$ and metal-organic complexes $^{3}$. \newline \newline 1) M. Cococcioni and S. de Gironcoli, PRB (2005). \newline \newline 2) F. Zhou, M. Cococcioni, A. C. Marianetti, D. Morgan and G. Ceder, PRB (2004). \newline \newline 3) H. J. Kulik, M. Cococcioni, D. Scherlis and N. Marzari, submitted to PRL.