Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems.

We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and spin susceptibility in the magnetic phase are expressed in terms of single-particle quantities. This fact not only can be used for realistic calculations of multiband systems but also allows us to reconsider a general description of many-body effects in the most interesting physical regimes, where the physical properties of the system are dominated by collective (bosonic) fluctuations. In the strongly spin-polarized limit, when the local magnetic moment is well defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.

Excitonic Instability and Pseudogap Formation in Nodal Line Semimetal ZrSiS.

Electron correlation effects are studied in ZrSiS using a combination of first-principles and model approaches. We show that basic electronic properties of ZrSiS can be described within a two-dimensional lattice model of two nested square lattices. A high degree of electron-hole symmetry characteristic for ZrSiS is one of the key features of this model. Having determined model parameters from first-principles calculations, we then explicitly take electron-electron interactions into account and show that, at moderately low temperatures, ZrSiS exhibits excitonic instability, leading to the formation of a pseudogap in the electronic spectrum. The results can be understood in terms of Coulomb-interaction-assisted pairing of electrons and holes reminiscent of that of an excitonic insulator. Our finding allows us to provide a physical interpretation of the unusual mass enhancement of charge carriers in ZrSiS recently observed experimentally.

Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators.

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.

By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.

Correlation-Driven Charge and Spin Fluctuations in LaCoO_{3}.

The spin transition in LaCoO_{3} has been investigated using density-functional theory in combination with dynamical mean-field theory employing continuous time quantum Monte Carlo and exact diagonalization impurity solvers. Calculations on the experimental rhombohedral atomic structure with two Co sites per unit cell show that an independent treatment of the Co atoms results in a ground state with strong charge fluctuations induced by electronic correlations. Each atom shows a contribution from either a d^{5} or a d^{7} state in addition to the main d^{6} state. These states play a relevant role in the spin transition which can be understood as a low spin-high spin (LS-HS) transition with significant contributions (~10%) to the LS and HS states of d^{5} and d^{7} states, respectively. We report spectra as well as optical conductivity data for all cases. A thermodynamic analysis reveals a significant kinetic energy gain through introduction of charge fluctuations, which in addition to the potential energy reduction lowers the total energy of the system.

Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion.

We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include nonlocal dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical √q behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.

Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene, and benzene.

To understand how nonlocal Coulomb interactions affect the phase diagram of correlated electron materials, we report on a method to approximate a correlated lattice model with nonlocal interactions by an effective Hubbard model with on-site interactions U(*) only. The effective model is defined by the Peierls-Feynman-Bogoliubov variational principle. We find that the local part of the interaction U is reduced according to U(*)=U-V[over ¯], where V[over ¯] is a weighted average of nonlocal interactions. For graphene, silicene, and benzene we show that the nonlocal Coulomb interaction can decrease the effective local interaction by more than a factor of 2 in a wide doping range.

Adatoms and clusters of 3d transition metals on graphene: electronic and magnetic configurations.

We investigate the electronic and magnetic properties of single Fe, Co, and Ni atoms and clusters on monolayer graphene (MLG) on SiC(0001) by means of scanning tunneling microscopy (STM), x-ray absorption spectroscopy, x-ray magnetic circular dichroism (XMCD), and ab initio calculations. STM reveals different adsorption sites for Ni and Co adatoms. XMCD proves Fe and Co adatoms to be paramagnetic and to exhibit an out-of-plane easy axis in agreement with theory. In contrast, we experimentally find a nonmagnetic ground state for Ni monomers while an increasing cluster size leads to sizeable magnetic moments. These observations are well reproduced by our calculations and reveal the importance of hybridization effects and intra-atomic charge transfer for the properties of adatoms and clusters on MLG.

Excitation spectra of transition-metal atoms on the Ag (100) surface controlled by Hund's exchange.

We report photoemission experiments revealing the valence electron spectral function of Mn, Fe, Co, and Ni atoms on the Ag (100) surface. The series of spectra shows splittings of higher energy features which decrease with the filling of the 3d shell and a highly nonmonotonic evolution of spectral weight near the Fermi edge. First principles calculations demonstrate that two manifestations of Hund's exchange J are responsible for this evolution. First, there is a monotonic reduction of the effective exchange splittings with increasing filling of the 3d shell. Second, the amount of charge fluctuations and, thus, the weight of quasiparticle peaks at the Fermi level varies nonmonotonically through this 3d series due to a distinct occupancy dependence of effective charging energies U(eff).

Enhanced screening in chemically functionalized graphene.

Resonant scatterers such as hydrogen adatoms can strongly enhance the low-energy density of states in graphene. Here, we study the impact of these impurities on electronic screening. We find a two-faced behavior: Kubo formula calculations reveal an increased dielectric function ε upon creation of midgap states but no metallic divergence of the static ε at small momentum transfer q→0. This bad metal behavior manifests also in the dynamic polarization function and can be directly measured by means of electron energy loss spectroscopy. A new length scale l(c) beyond which screening is suppressed emerges, which we identify with the Anderson localization length.

Local gating of an Ir(111) surface resonance by graphene islands.

The influence of graphene islands on the electronic structure of the Ir(111) surface is investigated. Scanning tunneling spectroscopy (STS) indicates the presence of a two-dimensional electron gas with a binding energy of -160 meV and an effective mass of -0.18me underneath single-layer graphene on the Ir(111) surface. Density functional calculations reveal that the STS features are predominantly due to a holelike surface resonance of the Ir(111) substrate. Nanometer-sized graphene islands act as local gates, which shift and confine the surface resonance.

In-plane magnetic anisotropy of Fe atoms on Bi2Se3(111).

The robustness of the gapless topological surface state hosted by a 3D topological insulator against perturbations of magnetic origin has been the focus of recent investigations. We present a comprehensive study of the magnetic properties of Fe impurities on the prototypical 3D topological insulator Bi(2)Se(3) using local low-temperature scanning tunneling spectroscopy and integral x-ray magnetic circular dichroism techniques. Single Fe adatoms on the Bi(2)Se(3) surface, in the coverage range ≈ 1% of a monolayer, are heavily relaxed into the surface and exhibit a magnetic easy axis within the surface plane, contrary to what was assumed in recent investigations on the supposed opening of a gap. Using ab initio approaches, we demonstrate that an in-plane easy axis arises from the combination of the crystal field and dynamic hybridization effects.

Orbital Kondo effect in cobalt-benzene sandwich molecules.

We study a Co-benzene sandwich molecule bridging the tips of a Cu nanocontact as a realistic model of correlated molecular transport. To this end we employ a recently developed method for calculating the correlated electronic structure and transport properties of nanoscopic conductors. When the molecule is slightly compressed by the tips of the nanocontact the dynamic correlations originating from the strongly interacting Co 3d shell give rise to an orbital Kondo effect while the usual spin Kondo effect is suppressed due to Hund's rule coupling. This nontrivial Kondo effect produces a sharp and temperature-dependent Abrikosov-Suhl resonance in the spectral function at the Fermi level and a corresponding Fano line shape in the low bias conductance.

Strength of effective Coulomb interactions in graphene and graphite.

To obtain an effective many-body model of graphene and related materials from first principles we calculate the partially screened frequency dependent Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction is U(00)=9.3 eV in close vicinity to the critical value separating conducting graphene from an insulating phase emphasizing the importance of nonlocal Coulomb terms. The nearest-neighbor Coulomb interaction strength is computed to U(01)=5.5 eV. In the long-wavelength limit, we find the effective background dielectric constant of graphite to be ϵ=2.5 in very good agreement with experiment.

Two-site Kondo effect in atomic chains.

Linear CoCu(n)Co clusters on Cu(111) fabricated by atomic manipulation represent a two-site Kondo system with tunable interaction. Scanning tunneling spectroscopy reveals oscillations of the Kondo temperature T(K) with the number n of Cu atoms for n≥3. Density functional calculations show that the Ruderman-Kittel-Kasuya-Yosida interaction mediated by the Cu chains causes the oscillations. Calculations find ferromagnetic and antiferromagnetic interaction for n=1 and 2, respectively. Both interactions lead to a decrease of T(K) as experimentally observed.

Spectral functions of isolated Ce adatoms on paramagnetic surfaces.

We report photoemission experiments revealing the full valence electron spectral function of Ce adatoms on Ag(111), W(110), and Rh(111) surfaces. A transfer of Ce 4f spectral weight from the ionization peak towards the Fermi level is demonstrated upon changing the substrate from Ag(111) to Rh(111). In the intermediate case of Ce on W(110) the ionization peak is found to be split. This evolution of the spectra is explained by means of first-principles theory, which clearly demonstrates that a reliable understanding of magnetic adatoms on metal surfaces requires simultaneous low and high energy spectroscopic information.

Nature of the Mott transition in Ca2RuO4.

We study the origin of the temperature-induced Mott transition in Ca2RuO4. As a method we use the local-density approximation+dynamical mean-field theory. We show the following. (i) The Mott transition is driven by the change in structure from long to short c-axis layered perovskite (L-Pbca→S-Pbca); it occurs together with orbital order, which follows, rather than produces, the structural transition. (ii) In the metallic L-Pbca phase the orbital polarization is ∼0. (iii) In the insulating S-Pbca phase the lower energy orbital, ∼xy, is full. (iv) The spin-flip and pair-hopping Coulomb terms reduce the effective masses in the metallic phase. Our results indicate that a similar scenario applies to Ca2-xSrxRuO4 (x≤0.2). In the metallic x≤0.5 structures electrons are progressively transferred to the xz/yz bands with increasing x; however, we find no orbital-selective Mott transition down to ∼300 K.

Resonant scattering by realistic impurities in graphene.

We develop a first-principles theory of resonant impurities in graphene and show that a broad range of typical realistic impurities leads to the characteristic sublinear dependence of the conductivity on the carrier concentration. By means of density functional calculations various organic groups as well as adatoms such as H absorbed to graphene are shown to create midgap states within ±0.03 eV around the neutrality point. A low energy tight-binding description is mapped out. Boltzmann transport theory as well as a numerically exact Kubo formula approach yield the conductivity of graphene contaminated with these realistic impurities in accordance with recent experiments.

Correlated electrons step by step: itinerant-to-localized transition of fe impurities in free-electron metal hosts.

High-resolution photoemission spectroscopy and ab initio calculations have been employed to analyze the onset and progression of d-sp hybridization in Fe impurities deposited on alkali metal films. The interplay between delocalization, mediated by the free-electron environment, and Coulomb interaction among d electrons gives rise to complex electronic configurations. The multiplet structure of a single Fe atom evolves and gradually dissolves into a quasiparticle peak near the Fermi level with increasing host electron density. The effective multiorbital impurity problem within the exact diagonalization scheme describes the whole range of hybridizations.

Strength of correlation effects in the electronic structure of iron.

The strength of electronic correlation effects in the spin-dependent electronic structure of ferromagnetic bcc Fe(110) has been investigated by means of spin and angle-resolved photoemission spectroscopy. The experimental results are compared to theoretical calculations within the three-body scattering approximation and within the dynamical mean-field theory, together with one-step model calculations of the photoemission process. This comparison indicates that the present state of the art many-body calculations, although improving the description of correlation effects in Fe, give too small mass renormalizations and scattering rates thus demanding more refined many-body theories including nonlocal fluctuations.