Long-range Coulomb interactions in surface systems: a first-principles description within self-consistently combined GW and dynamical mean-field theory

Coulomb engineering of two-dimensional Mott materials

Two-dimensional materials can be strongly influenced by their surroundings. A dielectric environment screens and reduces the Coulomb interaction between electrons in the two-dimensional material. Since in Mott materials the Coulomb interaction is responsible for the insulating state, manipulating the dielectric screening provides direct control over Mottness. Our many-body calculations reveal the spectroscopic fingerprints of such Coulomb engineering: we demonstrate eV-scale changes to the position of the Hubbard bands and show a Coulomb engineered insulator-to-metal transition. Based on our proof-of-principle calculations, we discuss the (feasible) conditions under which our scenario of Coulomb engineering of Mott materials can be realized experimentally.

Lattice dynamical properties of antiferromagnetic oxides calculated using self-consistent extended Hubbard functional method

We study the lattice dynamics of antiferromagnetic transition-metal oxides by using self-consistent Hubbard functionals. We calculate the ground states of the oxides with the on-site and intersite Hubbard interactions determined self-consistently within the framework of density functional theory. The on-site and intersite Hubbard terms fix the errors associated with the electron self-interaction in the local and semilocal functionals. Inclusion of the intersite Hubbard terms in addition to the on-site Hubbard terms produces accurate phonon dispersion of the transition-metal oxides. Calculated Born effective charges and high-frequency dielectric constants are in good agreement with experiment. Our study provides a computationally inexpensive and accurate set of first-principles calculations for strongly-correlated materials and related phenomena.

Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate

Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the on-site term is paramount. Recently, the onset of superconductivity at 4.7 K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.

Electronic correlations in dense iron: from moderate pressure to Earth's core conditions

We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). We review in detail two particularly interesting regimes: first, a moderate pressure range up to 60 GPa and, second, the ultra-high pressure of about 360 GPa expected inside the solid inner core of Earth. Electronic correlations in iron under the moderate pressure of several tens GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced body-centered cubic α to hexagonal close-packed [Formula: see text] phase transition. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the [Formula: see text]-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in [Formula: see text]-Fe by many-electron effects; its experimental signatures are analyzed. The next section focuses on the geophysically relevant pressure-temperature regime of the Earth's inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes ([Formula: see text], [Formula: see text] and face-centered-cubic [Formula: see text]) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of [Formula: see text]-Fe and an almost perfect Fermi liquid in the case of [Formula: see text]-Fe. A recent active discussion on the electronic state and transport properties of [Formula: see text]-Fe at the EIC conditions is reviewed in details. Estimations for the dynamical many-electron contribution to the relative phase stability are presented. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework relevant for studies of iron-base systems as well as perspective directions for further development.

Correlation-Driven Charge Order in a Frustrated Two-Dimensional Atom Lattice

We thoroughly examine the ground state of the triangular lattice of Pb on Si(111) using scanning tunneling microscopy and spectroscopy. We detect electronic charge order, and disentangle this contribution from the atomic configuration which we find to be 1-down-2-up, contrary to previous predictions from density functional theory. Applying an extended variational cluster approach we map out the phase diagram as a function of local and nonlocal Coulomb interactions. Comparing the experimental data with the theoretical modeling leads us to conclude that electron correlations are the driving force of the charge-ordered state in Pb/Si(111). These results resolve the discussion about the origin of the well-known 3×3 reconstruction. By exploiting the tunability of correlation strength, hopping parameters, and band filling, this material class represents a promising platform to search for exotic states of matter, in particular, for chiral topological superconductivity.

Chiral Spin Texture in the Charge-Density-Wave Phase of the Correlated Metallic Pb/Si(111) Monolayer

We investigate the 1/3 monolayer α-Pb/Si(111) surface by scanning tunneling spectroscopy (STS) and fully relativistic first-principles calculations. We study both the high-temperature sqrt[3]×sqrt[3] and low-temperature 3×3 reconstructions and show that, in both phases, the spin-orbit interaction leads to an energy splitting as large as 25% of the valence-band bandwidth. Relativistic effects, electronic correlations, and Pb-substrate interaction cooperate to stabilize a correlated low-temperature paramagnetic phase with well-developed lower and upper Hubbard bands coexisting with 3×3 periodicity. By comparing the Fourier transform of STS conductance maps at the Fermi level with calculated quasiparticle interference from nonmagnetic impurities, we demonstrate the occurrence of two large hexagonal Fermi sheets with in-plane spin polarizations and opposite helicities.

Realization of a Hole-Doped Mott Insulator on a Triangular Silicon Lattice

The physics of doped Mott insulators is at the heart of some of the most exotic physical phenomena in materials research including insulator-metal transitions, colossal magnetoresistance, and high-temperature superconductivity in layered perovskite compounds. Advances in this field would greatly benefit from the availability of new material systems with a similar richness of physical phenomena but with fewer chemical and structural complications in comparison to oxides. Using scanning tunneling microscopy and spectroscopy, we show that such a system can be realized on a silicon platform. The adsorption of one-third monolayer of Sn atoms on a Si(111) surface produces a triangular surface lattice with half filled dangling bond orbitals. Modulation hole doping of these dangling bonds unveils clear hallmarks of Mott physics, such as spectral weight transfer and the formation of quasiparticle states at the Fermi level, well-defined Fermi contour segments, and a sharp singularity in the density of states. These observations are remarkably similar to those made in complex oxide materials, including high-temperature superconductors, but highly extraordinary within the realm of conventional sp-bonded semiconductor materials. It suggests that exotic quantum matter phases can be realized and engineered on silicon-based materials platforms.

Coulomb correlations in 4d and 5d oxides from first principles-or how spin-orbit materials choose their effective orbital degeneracies

The interplay of spin-orbit coupling and Coulomb correlations has become a hot topic in condensed matter theory and is especially important in 4d and 5d transition metal oxides, like iridates or rhodates. Here, we review recent advances in dynamical mean-field theory (DMFT)-based electronic structure calculations for treating such compounds, introducing all necessary implementation details. We also discuss the evaluation of Hubbard interactions in spin-orbit materials. As an example, we perform DMFT calculations on insulating strontium iridate (Sr₂IrO₄) and its 4d metallic counterpart, strontium rhodate (Sr₂RhO₄). While a Mott-insulating state is obtained for Sr₂IrO₄ in its paramagnetic phase, the spectral properties and Fermi surfaces obtained for Sr₂RhO₄ show excellent agreement with available experimental data. Finally, we discuss the electronic structure of these two compounds by introducing the notion of effective spin-orbital degeneracy as the key quantity that determines the correlation strength. We stress that effective spin-orbital degeneracy introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth, analogous to the degeneracy-controlled Mott transition in d¹ perovskites.

Dynamical screening in correlated electron systems-from lattice models to realistic materials

Recent progress in treating the dynamical nature of the screened Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We discuss approximate and exact methods for the solution of impurity models with retarded interactions, and explain how these models appear as auxiliary problems in various extensions of the dynamical mean field formalism. The current state of the field is illustrated with results from recent applications of these schemes to U-V Hubbard models and correlated materials.

Nature of the Insulating Ground State of the Two-Dimensional Sn Atom Lattice on SiC(0001)

Semiconductor surfaces with narrow surface bands provide unique playgrounds to search for Mott-insulating state. Recently, a combined experimental and theoretical study of the two-dimensional (2D) Sn atom lattice on a wide-gap SiC(0001) substrate proposed a Mott-type insulator driven by strong on-site Coulomb repulsion U within a single-band Hubbard model. However, our systematic density-functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals shows that the Sn dangling-bond state largely hybridizes with the substrate Si 3p and C 2p states to split into three surface bands due to the crystal field. Such a hybridization gives rise to the stabilization of the antiferromagnetic order via superexchange interactions. The band gap and the density of states predicted by the hybrid DFT calculation agree well with photoemission data. Our findings not only suggest that the Sn/SiC(0001) system can be represented as a Slater-type insulator driven by long-range magnetism, but also have an implication that taking into account long-range interactions beyond the on-site interaction would be of importance for properly describing the insulating nature of Sn/SiC(0001).

Uncertainty principle for experimental measurements: Fast versus slow probes

The result of a physical measurement depends on the time scale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to charge, spin or orbital instabilities combined with the disparity of the time scales associated to their fluctuations can lead to seemingly contradictory experimental findings. A particularly striking example is provided by systems of adatoms adsorbed on semiconductor surfaces where different experiments--angle-resolved photoemission, scanning tunneling microscopy and core-level spectroscopy--suggest different ordering phenomena. Using most recent first principles many-body techniques, we resolve this puzzle by invoking the time scales of fluctuations when approaching the different instabilities. These findings suggest a re-interpretation of ordering phenomena and their fluctuations in a wide class of solid-state systems ranging from organic materials to high-temperature superconducting cuprates.

Surface Effects on the Mott-Hubbard Transition in Archetypal V{2}O{3}

We present an experimental and theoretical study exploring surface effects on the evolution of the metal-insulator transition in the model Mott-Hubbard compound Cr-doped V{2}O{3}. We find a microscopic domain formation that is clearly affected by the surface crystallographic orientation. Using scanning photoelectron microscopy and x-ray diffraction, we find that surface defects act as nucleation centers for the formation of domains at the temperature-induced isostructural transition and favor the formation of microscopic metallic regions. A density-functional theory plus dynamical mean-field theory study of different surface terminations shows that the surface reconstruction with excess vanadyl cations leads to doped, and hence more metallic, surface states, which explains our experimental observations.

Towards a full ab initio theory of strong electronic correlations in nanoscale devices

In this paper I give a detailed account of an ab initio methodology for describing strong electronic correlations in nanoscale devices hosting transition metal atoms with open d- or f-shells. The method combines Kohn-Sham density functional theory for treating the weakly interacting electrons on a static mean-field level with non-perturbative many-body methods for the strongly interacting electrons in the open d- and f-shells. An effective description of the strongly interacting electrons in terms of a multi-orbital Anderson impurity model is obtained by projection onto the strongly correlated subspace properly taking into account the non-orthogonality of the atomic basis set. A special focus lies on the ab initio calculation of the effective screened interaction matrix U for the Anderson model. Solution of the effective Anderson model with the one-crossing approximation or other impurity solver techniques yields the dynamic correlations within the strongly correlated subspace giving rise e.g. to the Kondo effect. As an example the method is applied to the case of a Co adatom on the Cu(0 0 1) surface. The calculated low-bias tunnel spectra show Fano-Kondo lineshapes similar to those measured in experiments. The exact shape of the Fano-Kondo feature as well as its width depend quite strongly on the filling of the Co 3d-shell. Although this somewhat hampers accurate quantitative predictions regarding lineshapes and Kondo temperatures, the overall physical situation can be predicted quite reliably.

Ultrafast Atomic Diffusion Inducing a Reversible (2sqrt[3]×2sqrt[3])R30°↔(sqrt[3]×sqrt[3])R30° Transition on Sn/Si(111)∶B

Dynamical phase transitions are a challenge to identify experimentally and describe theoretically. Here, we study a new reconstruction of Sn on silicon and observe a reversible transition where the surface unit cell divides its area by a factor of 4 at 250 °C. This phase transition is explained by the 24-fold degeneracy of the ground state and a novel diffusive mechanism, where four Sn atoms arranged in a snakelike cluster wiggle at the surface exploring collectively the different quantum mechanical ground states.

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.

Dynamical mean field theory-based electronic structure calculations for correlated materials

We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.

Dynamical screening effects in correlated electron materials-a progress report on combined many-body perturbation and dynamical mean field theory: 'GW + DMFT'

We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed 'LDA + DMFT'. It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(ω) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency dependence leads to effects that cannot be neglected in a truly first principles description. We review the recently introduced extension of LDA + DMFT to dynamical local Coulomb interactions 'LDA + U(ω) + DMFT' (Casula et al 2012 Phys. Rev. B 85 035115, Werner et al 2012 Nature Phys. 1745-2481). A reliable description of dynamical screening effects is also a central ingredient of the 'GW + DMFT' scheme (Biermann et al 2003 Phys. Rev. Lett. 90 086402), a combination of many-body perturbation theory in Hedin's GW approximation and dynamical mean field theory. Recently, the first GW + DMFT calculations including dynamical screening effects for real materials have been achieved, with applications to SrV O3 (Tomczak et al 2012 Europhys. Lett. 100 67001, Tomczak et al Phys. Rev. B submitted (available electronically as arXiv:1312.7546)) and adatom systems on surfaces (Hansmann et al 2013 Phys. Rev. Lett. 110 166401). We review these and comment on further perspectives in the field. This review is an attempt to put elements of the original works into the broad perspective of the development of truly first principles techniques for correlated electron materials.

Ferrimagnetic Slater insulator phase of the Sn/Ge(111) surface

We perform semilocal and hybrid density-functional theory (DFT) studies of the Sn/Ge(111) surface to identify the origin of the observed insulating sqrt[3]×sqrt[3] phase below ∼30  K. In contrast with the semilocal DFT calculation predicting a metallic 3×3 ground state, the hybrid DFT calculation including van der Waals interactions shows that the insulating ferrimagnetic structure with a sqrt[3]×sqrt[3] structural symmetry is energetically favored over the metallic 3×3 structure. It is revealed that the correction of the self-interaction error with a hybrid exchange-correlation functional gives rise to a band gap opening induced by a ferrimagnetic order. The results show that the observed insulating phase is attributed to the Slater mechanism via itinerant magnetic order rather than the hitherto accepted Mott-Hubbard mechanism via electron correlations.

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.