Janus-faced influence of Hund's rule coupling in strongly correlated materials

Non-Fermi liquid to charge-transfer Mott insulator in flat bands of copper-doped lead apatite

Copper-doped lead apatite, called LK-99, was initially claimed to be a room temperature superconductor driven by flat electron bands, but was later found to be a wide gap insulator. Despite the lack of room temperature superconductivity, there is growing evidence that LK-99 and related compounds host various strong electron correlation phenomena arising from their flat electron bands. Depending on the copper doping site and crystal structure, LK-99 can exhibit two distinct flat bands crossing the Fermi level in the non-interacting limit: either a single or two entangled flat bands. We explore potential correlated metallic and insulating phases in the flat bands of LK-99 compounds by constructing their correlation phase diagrams, and find both non-Fermi liquid and Mott insulating states. We demonstrate that LK-99 is a charge-transfer Mott insulator driven by strong electron correlations, regardless of the flat band type. We also find that the non-Fermi liquid state in the multi-flat band system exhibits strange metal behaviour, while the corresponding state in the single flat band system exhibits pseudogap behaviour. Our findings align with available experimental observations and provide crucial insights into the correlation phenomenology of LK-99 and related compounds that could arise independently of superconductivity. Overall, our research highlights that LK-99 and related compounds offer a compelling platform for investigating correlation physics in flat band systems.

Map of Crystal-Field Effects in Correlated Layered t_{2g}^{n} Perovskites

Correlated metallic layered t_{2g}^{n} perovskites are intensively studied and yet their low-energy electronic properties remain hotly debated. Important elements of the puzzle, beside the on-site Coulomb repulsion, are the tetragonal crystal-field splitting and the spin-orbit interaction. Here, we show that they control the electronic properties principally via form and occupations of natural orbitals. We discuss consequences for shape and topology of the Fermi surface, effective masses, and metal-insulator transition, building a map of crystal-field effects. The emerging picture captures electronic-structure trends in this family of systems within a single framework.

Exotic Magnetism in Perovskite KOsO_{3}

A new perovskite KOsO_{3} has been stabilized under high-pressure and high-temperature conditions. It is cubic at 500 K (Pm-3m) and undergoes subsequent phase transitions to tetragonal at 320 K (P4/mmm) and rhombohedral (R-3m) at 230 K as shown from refining synchrotron x-ray powder diffraction (SXRD) data. The larger orbital overlap integral and the extended wave function of 5d electrons in the perovskite KOsO_{3} allow to explore physics from the regime where Mott and Hund's rule couplings dominate to the state where the multiple interactions are on equal footing. We demonstrate an exotic magnetic ordering phase found by neutron powder diffraction along with physical properties via a suite of measurements including magnetic and transport properties, differential scanning calorimetry, and specific heat, which provide comprehensive information for a system at the crossover from localized to itinerant electronic behavior.

Orbital-Selectivity-Induced Robust Quantum Anomalous Hall Effect in Hund's Metals MgFeP

Ferromagnetic (FM) states with high Curie temperatures (Tc) and strong spin-orbit coupling (SOC) are indispensable for the long-sought room-temperature quantum anomalous Hall (QAH) effects. Here, we propose a two-dimensional (2D) iron-based monolayer MgFeP that exhibits a notably high FM Tc (about 1525 K) along with exceptional structural stabilities. The unique multiorbital nature in MgFeP, where localized d x 2 - y 2 and dxz/yz orbitals coexist with itinerant dxy and dz2 orbitals, renders the monolayer a Hund's metal and in an orbital-selective Mott phase (OSMP). This OSMP triggers an FM double exchange mechanism, rationalizing the high Tc in the Hund's metal. This material transitions to a QAH insulator upon consideration of the SOC effect. By leveraging orbital selectivity, the QAH band gap can be enlarged by more than two times (to 137 meV). Our findings showcase Hund's metals as a promising material platform for realizing high-performance quantum topological electronic devices.

Transition to the Haldane phase driven by electron-electron correlations

One of the most famous quantum systems with topological properties, the spin [Formula: see text] antiferromagnetic Heisenberg chain, is well-known to display exotic [Formula: see text] edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons - the two-orbital Hubbard model-with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

Pines' demon observed as a 3D acoustic plasmon in Sr2RuO4

The characteristic excitation of a metal is its plasmon, which is a quantized collective oscillation of its electron density. In 1956, David Pines predicted that a distinct type of plasmon, dubbed a 'demon', could exist in three-dimensional (3D) metals containing more than one species of charge carrier1. Consisting of out-of-phase movement of electrons in different bands, demons are acoustic, electrically neutral and do not couple to light, so have never been detected in an equilibrium, 3D metal. Nevertheless, demons are believed to be critical for diverse phenomena including phase transitions in mixed-valence semimetals2, optical properties of metal nanoparticles3, soundarons in Weyl semimetals4 and high-temperature superconductivity in, for example, metal hydrides3,5-7. Here, we present evidence for a demon in Sr2RuO4 from momentum-resolved electron energy-loss spectroscopy. Formed of electrons in the β and γ bands, the demon is gapless with critical momentum qc = 0.08 reciprocal lattice units and room-temperature velocity v = (1.065 ± 0.12) × 105 m s-1 that undergoes a 31% renormalization upon cooling to 30 K because of coupling to the particle-hole continuum. The momentum dependence of the intensity of the demon confirms its neutral character. Our study confirms a 67-year old prediction and indicates that demons may be a pervasive feature of multiband metals.

Tuning orbital-selective phase transitions in a two-dimensional Hund's correlated system

Hund's rule coupling (J) has attracted much attention recently for its role in the description of the novel quantum phases of multi-orbital materials. Depending on the orbital occupancy, J can lead to various intriguing phases. However, experimental confirmation of the orbital occupancy dependency has been difficult as controlling the orbital degrees of freedom normally accompanies chemical inhomogeneities. Here, we demonstrate a method to investigate the role of orbital occupancy in J related phenomena without inducing inhomogeneities. By growing SrRuO₃ monolayers on various substrates with symmetry-preserving interlayers, we gradually tune the crystal field splitting and thus the orbital degeneracy of the Ru t_2g orbitals. It effectively varies the orbital occupancies of two-dimensional (2D) ruthenates. Via in-situ angle-resolved photoemission spectroscopy, we observe a progressive metal-insulator transition (MIT). It is found that the MIT occurs with orbital differentiation: concurrent opening of a band insulating gap in the d_xy band and a Mott gap in the d_xz/yz bands. Our study provides an effective experimental method for investigation of orbital-selective phenomena in multi-orbital materials.

Mimicking Multiorbital Systems with SU(N) Atoms: Hund’s Physics and Beyond

The physics of many interesting correlated materials can be captured by multiorbital Hubbard models, where conduction electrons feature an additional orbital degree of freedom. The multiorbital characteristic is not a mere complication, but it leads to an immensely richer landscape of physical regimes. One of the key features is the interplay between Hubbard repulsion and Hund’s exchange coupling, which has been shown to lead to orbital-selective correlations and to the existence of correlation-resilient metals (usually called Hund’s metals) defying Mott localization. Here, we show that experimentally available platforms of SU(N)-symmetric ultracold atoms can indeed mimic the rich physics disclosed by multiorbital materials, by exploiting the internal degrees of freedom of multicomponent atoms. We discuss in detail the SU(N) version of interaction-resilient Hund’s metal and some other interesting regimes.

Mott transition, magnetic and orbital orders in the ground state of the two-band Hubbard model using variational slave-spin mean field formalism

We study the ground state phase diagram of the degenerate two-band Hubbard model at integer fillings as a function of onsite Hubbard interactionUand Hund's exchange couplingJ. We use a variational slave-spin mean field method which allows symmetry broken states to be studied within the computationally less intensive slave-spin mean field formalism. The results show that at half-filling, the ground state at smallerUis a Slater antiferromagnet with substantial local charge fluctuations. AsUis increased, the antiferromagnetic (AF) state develops a Heisenberg behavior, finally undergoing a first-order transition to a Mott insulating AF state at a critical interactionU_cwhich is of the order of the bandwidth. Introducing the Hund's couplingJcorrelates the system more and reducesU_cdrastically. At quarter-filling with one electron per site, the ground state at smallerUis paramagnetic metallic. At finiteJ, as interaction is increased beyond a lower critical valueU_c1, it goes to a fully spin polarized ferromagnetic state coexisting with an antiferro-orbital order. Further increase inUbeyond a higher critical valueU_c2results in the Mott insulating state where local charge fluctuation vanishes.

Moving Dirac nodes by chemical substitution

Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, [Formula: see text], through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of [Formula: see text] across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the [Formula: see text] symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making [Formula: see text] a model system to functionalize Dirac materials by varying the strength of electron correlations.

Ground state of a three-band Hubbard model with Hund's coupling: Janus-faced behavior in presence of magnetic order

We study the ground state of the three-band degenerate Hubbard model on a square lattice at integer fillings using the variational slave-spin mean field method. At half-filling, the method reproduces the well known result that the ground state is antiferromagnetic (AF) insulating at smaller values of Hubbard onsite repulsionU, while it becomes Mott insulating with Néel AF order at higherU. Away from half-filling, for two particles per site, we show that the model supports a ferromagnetic (FM) metallic state with fully polarized spins at sufficiently largeU. The FM state occurs irrespective of the value of Hund's couplingJ. The ferromagnetism atJ= 0 can be explained by the Stoner mechanism while that forJ> 0 is shown to arise from the superexchange process. At this band filling, the Hund's couplingJis known to have the Janus-faced effect on electronic correlations where it enhances correlations at smallerUwhile reducing it at higherU. We show that these two effects are separated by the paramagnetic (PM) to FM transition point. The former effect is obtained at the PM state while the latter occurs in the FM state. The FM phase also occurs for one particle per site but here Hund's couplingJreduces the effect of electronic correlations at allU.

Hund Physics Landscape of Two-Orbital Systems

Motivated by the recent discovery of superconductivity in infinite-layer nickelates RE_{1-δ}Sr_{δ}NiO_{2} (RE=Nd, Pr), we study the role of Hund coupling J in a quarter-filled two-orbital Hubbard model, which has been on the periphery of the attention. A region of negative effective Coulomb interaction of this model is revealed to be differentiated from three- and five-orbital models in their typical Hund metal active fillings. We identify distinctive regimes including four different correlated metals, one of which stems from the proximity to a Mott insulator, while the other three, which we call "intermediate" metal, weak Hund metal, and valence-skipping metal, from the effect of J being away from Mottness. Defining criteria characterizing these metals is suggested, establishing the existence of Hund metallicity in two-orbital systems.

Optical Properties of the Infinite-Layer La_{1-x}Sr_{x}NiO_{2} and Hidden Hund's Physics

We investigate the optical properties of the normal state of the infinite-layer La_{1-x}Sr_{x}NiO_{2} using density functional theory plus dynamical mean-field theory. We find a correlated metal which exhibits substantial transfer of spectral weight to high energies relative to the density functional theory. The correlations are not due to Mott physics, which would suppress the charge fluctuations and the integrated optical spectral weight as we approach a putative insulating state. Instead, we find the unusual situation, that the integrated optical spectral weight decreases with doping and increases with increasing temperature. We contrast this with the coherent component of the optical conductivity, which decreases with increasing temperature as a result of a coherence-incoherence crossover. Our studies reveal that the effective crystal field splitting is dynamical and increases strongly at low frequency. This leads to a picture of a Hund's metallic state, where dynamical orbital fluctuations are visible at intermediate energies, while at low energies a Fermi surface with primarily d_{x^{2}-y^{2}} character emerges. The infinite-layer nickelates are thus in an intermediate position between the iron based high temperature superconductors where multiorbital Hund's physics dominates and a one-band system such as the cuprates. To capture this physics we propose a low-energy two-band model with atom centered e_{g} states.

Direct observation of kink evolution due to Hund's coupling on approach to metal-insulator transition in NiS2-xSex

Understanding characteristic energy scales is a fundamentally important issue in the study of strongly correlated systems. In multiband systems, an energy scale is affected not only by the effective Coulomb interaction but also by the Hund’s coupling. Direct observation of such energy scale has been elusive so far in spite of extensive studies. Here, we report the observation of a kink structure in the low energy dispersion of NiS_2−xSe_x and its characteristic evolution with x, by using angle resolved photoemission spectroscopy. Dynamical mean field theory calculation combined with density functional theory confirms that this kink originates from Hund’s coupling. We find that the abrupt deviation from the Fermi liquid behavior in the electron self-energy results in the kink feature at low energy scale and that the kink is directly related to the coherence-incoherence crossover temperature scale. Our results mark the direct observation of the evolution of the characteristic temperature scale via kink features in the spectral function, which is the hallmark of Hund’s physics in the multiorbital system.

A decisive spectroscopic evidence of the Hund’s coupling energy scale in multi-orbital correlated systems has been lacking. Here, the authors identify a kink feature due to Hund´s coupling in the spectral function of NiS_2xSe_x as they track its evolution across the Mott-insulator transition.

Fingerprints of the Local Moment Formation and its Kondo Screening in the Generalized Susceptibilities of Many-Electron Problems

We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches for correlated systems.

Evolution of Structure and Electronic Correlations in a Series of BaT2As2 (T = Cr-Cu) Single Crystals

We present a systematic study of the evolution of structural parameters and electronic correlations as a function of 3d band filling in a single crystal series of BaT₂As₂ (T = Cr-Cu). The structure trends are discussed in relation to the orbital occupation of the corresponding d elements supported by calculations of the charge density and electron localization function. Analysis of our specific heat data yields the mass enhancement (m*/m_b) throughout the series. By combining the structural data with the mass enhancement values, we find that the decrease in m*/m_b for n > 5 follows an increase of the crystal field splitting, determined by the progressive distortion of the As-T-As angle from the ideal tetrahedral environment. This study finds a strong interplay between crystal structure, bonding behavior, band filling, and electronic properties.

Synergy between Hund-Driven Correlations and Boson-Mediated Superconductivity

Multiorbital systems such as the iron-based superconductors provide a new avenue to attack the long-standing problem of superconductivity in strongly correlated systems. In this work we study the superconductivity driven by a generic bosonic mechanism in a multiorbital model including the full dynamical electronic correlations induced by the Hubbard U and the Hund's coupling. We show that superconductivity survives much more in a Hund's metal than in an ordinary correlated metal with the same degree of correlation. The redistribution of spectral weight characteristic of the Hund's metal reflects also in the enhancement of the orbital-selective character of the superconducting gaps, in agreement with experiments in iron-based superconductors.

Osmates on the Verge of a Hund's-Mott Transition: The Different Fates of NaOsO_{3} and LiOsO_{3}

We clarify the origin of the strikingly different spectroscopic properties of the chemically similar compounds NaOsO_{3} and LiOsO_{3}. Our first-principle, many-body analysis demonstrates that the highly sensitive physics of these two materials is controlled by their proximity to an adjacent Hund's-Mott insulating phase. Although 5d oxides are mildly correlated, we show that the cooperative action of intraorbital repulsion and Hund's exchange becomes the dominant physical mechanism in these materials if their t_{2g} shell is half filled. Small material specific details hence result in an extremely sharp change of the electronic mobility, explaining the surprisingly different properties of the paramagnetic high-temperature phases of the two compounds.

Sr_{2}MoO_{4} and Sr_{2}RuO_{4}: Disentangling the Roles of Hund's and van Hove Physics

Sr_{2}MoO_{4} is isostructural to the unconventional superconductor Sr_{2}RuO_{4} but with two electrons instead of two holes in the Mo/Ru-t_{2g} orbitals. Both materials are Hund's metals, but while Sr_{2}RuO_{4} has a van Hove singularity in close proximity to the Fermi surface, the van Hove singularity of Sr_{2}MoO_{4} is far from the Fermi surface. By using density functional plus dynamical mean-field theory, we determine the relative influence of van Hove and Hund's metal physics on the correlation properties. We show that theoretically predicted signatures of Hund's metal physics occur on the occupied side of the electronic spectrum of Sr_{2}MoO_{4}, identifying Sr_{2}MoO_{4} as an ideal candidate system for a direct experimental confirmation of the theoretical concept of Hund's metals via photoemission spectroscopy.

Bethe-Salpeter Equation at the Critical End Point of the Mott Transition

Strong repulsive interactions between electrons can lead to a Mott metal-insulator transition. The dynamical mean-field theory (DMFT) explains the critical end point and the hysteresis region usually in terms of single-particle concepts, such as the spectral function and the quasiparticle weight. In this Letter, we reconsider the critical end point of the metal-insulator transition on the DMFT's two-particle level. We show that the relevant eigenvalue and eigenvector of the nonlocal Bethe-Salpeter kernel in the charge channel provide a unified picture of the hysteresis region and of the critical end point of the Mott transition. In particular, they simultaneously explain the thermodynamics of the hysteresis region and the iterative stability of the DMFT equations. This analysis paves the way for a deeper understanding of phase transitions in correlated materials.

Characteristic Timescales of the Local Moment Dynamics in Hund's Metals

We study the characteristic timescales of the fluctuating local moments in Hund's metal systems for different degrees of correlation. By analyzing the dynamical spin susceptibility in the real-time domain, we determine the timescales controlling oscillation and damping of on-site fluctuations-a crucial factor for the detection of local moments with different experimental probes. We apply this procedure to different families of iron pnictides or chalcogenides, explaining the material trend in the discrepancies reported between experimental and theoretical estimates of their magnetic moments.

Electronic correlation effects and local magnetic moments in L10phase of FeNi

We study the electronic and magnetic properties of L10phase of FeNi, a perspective rare-earth-free permanent magnet, by using a combination of density functional and dynamical mean-field theory. Although L10FeNi has a slightly tetragonally distorted fcc lattice, we find that magnetic properties of its constituent Fe atoms resemble those in pure bcc Fe. In particular, our results indicate the presence of well-localized magnetic moments on Fe sites, which are formed due to Hund's exchange. At the same time, magnetism of Ni sites is much more itinerant. Similarly to pure bcc Fe, the self-energy of Fe 3d states is found to show the non-Fermi-liquid behavior. This can be explained by peculiarities of density of Fe 3d states, which has pronounced peaks near the Fermi level. Our study of local spin correlation function and momentum dependence of particle-hole bubble suggests that the magnetic exchange in this substance is expected to be of RKKY-type, with iron states providing local-moment contribution, and the states corresponding to nickel sites (including virtual hopping to iron sites) providing itinerant contribution.

Unconventional Hund metal in a weak itinerant ferromagnet

The physics of weak itinerant ferromagnets is challenging due to their small magnetic moments and the ambiguous role of local interactions governing their electronic properties, many of which violate Fermi-liquid theory. While magnetic fluctuations play an important role in the materials' unusual electronic states, the nature of these fluctuations and the paradigms through which they arise remain debated. Here we use inelastic neutron scattering to study magnetic fluctuations in the canonical weak itinerant ferromagnet MnSi. Data reveal that short-wavelength magnons continue to propagate until a mode crossing predicted for strongly interacting quasiparticles is reached, and the local susceptibility peaks at a coherence energy predicted for a correlated Hund metal by first-principles many-body theory. Scattering between electrons and orbital and spin fluctuations in MnSi can be understood at the local level to generate its non-Fermi liquid character. These results provide crucial insight into the role of interorbital Hund's exchange within the broader class of enigmatic multiband itinerant, weak ferromagnets.

Charge and spin degrees of freedom in strongly correlated systems: Mott states opposite Hund's metals

A correlated metallic state can arise as a result of the presence either strong charge or strong spin fluctuations. In the first case, as was shown first in (2004 Phys. Today 57 53) for the Hubbard model on the Bethe lattice, the system is a correlated metallic state close to the Mott-insulator state if the ratio of the value of the Coulomb interaction parameter U and the band width W is [Formula: see text]. The later case exist if [Formula: see text] and Hund's exchange parameter [Formula: see text]. In both cases narrowing of the bands near the Fermi level and renormalization of the effective electron mass is observed, although the mechanism for realizing this state will be fundamentally different. We performed the electronic structure calculations of the paramagnetic phase [Formula: see text]-iron which is a typical Hund's metal. We showed that the statistical distribution of charge between possible electronic d-configurations has a very weak dependence on the exchange interaction and is specific for metals. At the same time, the distribution of statistical weights between different spin configurations fundamentally changes with the inclusion of J. If we neglect Hund's interaction by setting J  =  0, the contributions from the low-spin configurations for all possible charge states dominate. The exchange interaction causes a redistribution of probability in favor of high-spin multiplets, leading to the formation of a larger local moment. We also performed calculations for the two-bands half-filled model. By varying the values of the Coulomb and Hund's exchange interaction parameters, we reproduced the region of the phase diagram of the model in which the system undergoes a transition from the Mott-insulator state to the Hund's metal. This transition is accompanied by a change in the statistical probability distribution of possible multiple configurations. In the region corresponding to the Hund's metal state, a change of J leads to the effect of weights redistribution similar that we observe in [Formula: see text]-iron.

Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations

We present a numerically exact inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems.

Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^{-1/5}), orbital (ω^{1/5}) and spin-orbital (ω^{1}) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Strongly Correlated Materials from a Numerical Renormalization Group Perspective: How the Fermi-Liquid State of Sr_{2}RuO_{4} Emerges

The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clearly reveals the emergence of the Fermi-liquid state of Sr_{2}RuO_{4}. We find a two-stage screening process, where orbital fluctuations are screened at much higher energies than spin fluctuations, and Fermi-liquid behavior, concomitant with spin coherence, below a temperature of 25 K. By computing real-frequency correlation functions, we directly observe this spin-orbital scale separation and show that the van Hove singularity drives strong orbital differentiation. We extract quasiparticle interaction parameters from the low-energy spectrum and find an effective attraction in the spin-triplet sector.

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.

Signatures of Mottness and Hundness in archetypal correlated metals

Physical properties of multi-orbital materials depend not only on the strength of the effective interactions among the valence electrons but also on their type. Strong correlations are caused by either Mott physics that captures the Coulomb repulsion among charges, or Hund physics that aligns the spins in different orbitals. We identify four energy scales marking the onset and the completion of screening in orbital and spin channels. The differences in these scales, which are manifest in the temperature dependence of the local spectrum and of the charge, spin and orbital susceptibilities, provide clear signatures distinguishing Mott and Hund physics. We illustrate these concepts with realistic studies of two archetypal strongly correlated materials, and corroborate the generality of our conclusions with a model Hamiltonian study.

Hund's metal regimes and orbital selective Mott transitions in three band systems

We analyze the electronic properties of interacting crystal field split three band systems. Using a rotationally invariant slave boson approach we analyze the behavior of the electronic mass renormalization as a function of the intralevel repulsion U, the Hund's coupling J, the crystal field splitting, and the number of electrons per site n. We first focus on the case in which two of the bands are identical and the levels of the third one are shifted by [Formula: see text] with respect to the former. We find an increasing quasiparticle mass differentiation between the bands, for system away from half-filling (n  =  3), as the Hubbard interaction U is increased. This leads to orbital selective Mott transitions where either the higher energy band (for 4  >  n  >  3) or the lower energy degenerate bands (2  <  n  <  3) become insulating for U larger than a critical interaction [Formula: see text]. Away from the half-filled case [Formula: see text] there is a wide range of parameters for [Formula: see text] where the system presents a Hund's metal phase with the physics dominated by the local high spin multiplets. Finally, we study the fate of the n  =  2 Hund's metal as the energy splitting between orbitals is increased for different possible crystal distortions. We find a strong sensitivity of the Hund's metal regime to crystal fields due to the opposing effects of J and the crystal field splittings on the charge distribution between the bands.

Charge Disproportionation, Mixed Valence, and Janus Effect in Multiorbital Systems: A Tale of Two Insulators

Multiorbital Hubbard models host strongly correlated "Hund's metals" even for interactions much stronger than the bandwidth. We characterize this interaction-resilient metal as a mixed-valence state. In particular, it can be pictured as a bridge between two strongly correlated insulators: a high-spin Mott insulator and a charge-disproportionated insulator which is stabilized by a very large Hund's coupling. This picture is confirmed comparing models with negative and positive Hund's coupling for different fillings. Our results provide a characterization of the Hund's metal state and connect its presence with charge disproportionation, which has indeed been observed in chromates and proposed to play a role in iron-based superconductors.

Imaging orbital-selective quasiparticles in the Hund's metal state of FeSe

Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high-temperature superconductivity. By contrast, the parent phase of an iron-based high-temperature superconductor is never a correlated insulator. However, this distinction may be deceptive because Fe has five actived d orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund's metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations, producing orbitally selective strong correlations. The spectral weights Z_m of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle Z_m appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that [Formula: see text], consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based high-temperature superconductivity in FeSe.

Thermoelectricity in correlated narrow-gap semiconductors

We review many-body effects, their microscopic origin, as well as their impact on thermoelectricity in correlated narrow-gap semiconductors. Members of this class-such as FeSi and FeSb₂-display an unusual temperature dependence in various observables: insulating with large thermopowers at low temperatures, they turn bad metals at temperatures much smaller than the size of their gaps. This insulator-to-metal crossover is accompanied by spectral weight-transfers over large energies in the optical conductivity and by a gradual transition from activated to Curie-Weiss-like behaviour in the magnetic susceptibility. We show a retrospective of the understanding of these phenomena, discuss the relation to heavy-fermion Kondo insulators-such as Ce₃Bi₄Pt₃ for which we present new results-and propose a general classification of paramagnetic insulators. From the latter, FeSi emerges as an orbital-selective Kondo insulator. Focussing on intermetallics such as silicides, antimonides, skutterudites, and Heusler compounds we showcase successes and challenges for the realistic simulation of transport properties in the presence of electronic correlations. Further, we explore new avenues in which electronic correlations may contribute to the improvement of thermoelectric performance.

Spin-Orbit Coupling and Interband Transitions in the Optical Conductivity of Sr_{2}RhO_{4}

The prototypical correlated metal Sr_{2}RhO_{4} was studied using optical and photoemission spectroscopy. At low energies and temperatures, the optical data reveal a complex, multicomponent response that on the surface points to an unconventional metallic state in this material. Via a comparison with photoemission, the anomalous optical response may be attributed to an unexpectedly strong interband transition near 180 meV between spin-orbit coupled bands that are nearly parallel along ΓX. This spin-orbit coupling effect is shown to occur in a number of related metallic ruthenates and explains the previously puzzling optical properties reported for these materials.

Observation of a remarkable reduction of correlation effects in BaCr2As2 by ARPES

The superconducting phase in iron-based high-[Formula: see text] superconductors (FeSC), as in other unconventional superconductors such as the cuprates, neighbors a magnetically ordered one in the phase diagram. This proximity hints at the importance of electron correlation effects in these materials, and Hund's exchange interaction has been suggested to be the dominant correlation effect in FeSCs because of their multiband nature. By this reasoning, correlation should be strongest for materials closest to a half-filled [Formula: see text] electron shell (Mn compounds, hole-doped FeSCs) and decrease for systems with both higher (electron-doped FeSCs) and lower (Cr-pnictides) [Formula: see text] counts. Here we address the strength of correlation effects in nonsuperconducting antiferromagnetic BaCr₂As₂ by means of angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations. This combination provides us with two handles on the strength of correlation: First, a comparison of the experimental and calculated effective masses yields the correlation-induced mass renormalization. In addition, the lifetime broadening of the experimentally observed dispersions provides another measure of the correlation strength. Both approaches reveal a reduction of electron correlation in BaCr₂As₂ with respect to systems with a [Formula: see text] count closer to five. Our results thereby support the theoretical predictions that Hund's exchange interaction is important in these materials.

Localized-itinerant dichotomy and unconventional magnetism in SrRu2O6

Electron correlations tend to generate local magnetic moments that usually order if the lattices are not too frustrated. The hexagonal compound SrRu₂O₆ has a relatively high Neel temperature but small local moments, which seem to be at odds with the nominal valence of Ru⁵⁺ in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t}_{2g}^{3}$$\end{document}t2g3 configuration. Here, we investigate the electronic property of SrRu₂O₆ using density functional theory (DFT) combined with dynamical-mean-field theory (DMFT). We find that the strong hybridization between Ru d and O p states results in a Ru valence that is closer to +4, leading to the small ordered moment ~1.2 μ_B. While this is consistent with a DFT prediction, correlation effects are found to play a significant role. The local moment per Ru site remains finite ~2.3 μ_B in the whole temperature range investigated. Due to the lower symmetry, the t_2g manifold is split and the quasiparticle weight is renormalized significantly in the a_1g state, while the renormalization in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${e}_{g}^{{\rm{^{\prime} }}}$$\end{document}eg′ states is about a factor of 2–3 weaker. Our theoretical Neel temperature ~700 K is in reasonable agreement with experimental observations. SrRu₂O₆ is a unique system in which localized and itinerant electrons coexist with the proximity to an orbitally-selective Mott transition within the t_2g sector.

The simplest representative of a complex series: the Hg-rich amalgam Yb11Hg54

Yb11Hg54 is a new member of a series of amalgams with composition close to MHg5. Its crystal structure was solved and refined on the basis of single crystal data. The structure model was confirmed with a Rietveld refinement. Yb11Hg54 has the first crystal structure in this family in which no disorder effects such as mixed occupation, split positions or superstructure formation is observed. It therefore can be regarded as a parent structure for all other amalgams. The crystal structure of Yb11Hg54 can be derived from the Gd14Ag51 structure type, the aristotype of this family. We give a detailed crystal structure description for Yb11Hg54 and discuss it in the context of the further known crystal structures closely related. A ranking within this structure family can be established by calculating features for the structural complexity for all structures, including the individual disorder phenomena.

J Freezing and Hund's Rules in Spin-Orbit-Coupled Multiorbital Hubbard Models

We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We find that the spin-freezing crossover occurring in the metallic phase of the nonrelativistic multiorbital Hubbard model can be generalized to a J-freezing crossover, with J=L+S, in the spin-orbit-coupled case. In the J-frozen regime the correlated electrons exhibit a nontrivial flavor selectivity and energy dependence. Furthermore, in the regions near n=2 and n=4 the metallic states are qualitatively different from each other, which reflects the atomic Hund's third rule. Finally, we explore the appearance of magnetic order from exciton condensation at n=4 and discuss the relevance of our results for real materials.

Hund's Rule-Driven Dzyaloshinskii-Moriya Interaction at 3d-5d Interfaces

Using relativistic first-principles calculations, we show that the chemical trend of the Dzyaloshinskii-Moriya interaction (DMI) in 3d-5d ultrathin films follows Hund's first rule with a tendency similar to their magnetic moments in either the unsupported 3d monolayers or 3d-5d interfaces. We demonstrate that, besides the spin-orbit coupling (SOC) effect in inversion asymmetric noncollinear magnetic systems, the driving force is the 3d orbital occupations and their spin-flip mixing processes with the spin-orbit active 5d states control directly the sign and magnitude of the DMI. The magnetic chirality changes are discussed in the light of the interplay between SOC, Hund's first rule, and the crystal-field splitting of d orbitals.

Orbital-Dependent Band Narrowing Revealed in an Extremely Correlated Hund's Metal Emerging on the Topmost Layer of Sr_{2}RuO_{4}

We use a surface-selective angle-resolved photoemission spectroscopy and unveil the electronic nature on the topmost layer of Sr_{2}RuO_{4} crystal, consisting of slightly rotated RuO_{6} octahedrons. The γ band derived from the 4d_{xy} orbital is found to be about three times narrower than that for the bulk. This strongly contrasts with a subtle variation seen in the α and β bands derived from the one-dimensional 4d_{xz/yz}. This anomaly is reproduced by the dynamical mean-field theory calculations, introducing not only the on-site Hubbard interaction but also the significant Hund's coupling. We detect a coherence-to-incoherence crossover theoretically predicted for Hund's metals, which has been recognized only recently. The crossover temperature in the surface is about half that of the bulk, indicating that the naturally generated monolayer of reconstructed Sr_{2}RuO_{4} is extremely correlated and well isolated from the underlying crystal.

Magnetic Precursor of the Pressure-Induced Superconductivity in Fe-Ladder Compounds

The pressure effects on the antiferromagentic orders in iron-based ladder compounds CsFe_{2}Se_{3} and BaFe_{2}S_{3} have been studied using neutron diffraction. With identical crystal structure and similar magnetic structures, the two compounds exhibit highly contrasting magnetic behaviors under moderate external pressures. In CsFe_{2}Se_{3} the ladders are brought much closer to each other by pressure, but the stripe-type magnetic order shows no observable change. In contrast, the stripe order in BaFe_{2}S_{3} undergoes a quantum phase transition where an abrupt increase of Néel temperature by more than 50% occurs at about 1 GPa, accompanied by a jump in the ordered moment. With its spin structure unchanged, BaFe_{2}S_{3} enters an enhanced magnetic phase that bears the characteristics of an orbital selective Mott phase, which is the true neighbor of superconductivity emerging at higher pressures.

Orbital-selective Mott phases of a one-dimensional three-orbital Hubbard model studied using computational techniques

A recently introduced one-dimensional three-orbital Hubbard model displays orbital-selective Mott phases with exotic spin arrangements such as spin block states [J. Rincón et al., Phys. Rev. Lett. 112, 106405 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.106405]. In this publication we show that the constrained-path quantum Monte Carlo (CPQMC) technique can accurately reproduce the phase diagram of this multiorbital one-dimensional model, paving the way to future CPQMC studies in systems with more challenging geometries, such as ladders and planes. The success of this approach relies on using the Hartree-Fock technique to prepare the trial states needed in CPQMC. We also study a simplified version of the model where the pair-hopping term is neglected and the Hund coupling is restricted to its Ising component. The corresponding phase diagrams are shown to be only mildly affected by the absence of these technically difficult-to-implement terms. This is confirmed by additional density matrix renormalization group and determinant quantum Monte Carlo calculations carried out for the same simplified model, with the latter displaying only mild fermion sign problems. We conclude that these methods are able to capture quantitatively the rich physics of the several orbital-selective Mott phases (OSMP) displayed by this model, thus enabling computational studies of the OSMP regime in higher dimensions, beyond static or dynamic mean-field approximations.

Strain Control of Fermiology and Many-Body Interactions in Two-Dimensional Ruthenates

Here we demonstrate how the Fermi surface topology and quantum many-body interactions can be manipulated via epitaxial strain in the spin-triplet superconductor Sr_{2}RuO_{4} and its isoelectronic counterpart Ba_{2}RuO_{4} using oxide molecular beam epitaxy, in situ angle-resolved photoemission spectroscopy, and transport measurements. Near the topological transition of the γ Fermi surface sheet, we observe clear signatures of critical fluctuations, while the quasiparticle mass enhancement is found to increase rapidly and monotonically with increasing Ru-O bond distance. Our work demonstrates the possibilities for using epitaxial strain as a disorder-free means of manipulating emergent properties, many-body interactions, and potentially the superconductivity in correlated materials.

Assessing the orbital selective Mott transition with variational wave functions

We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.

Fermi Surface of Sr_{2}RuO_{4}: Spin-Orbit and Anisotropic Coulomb Interaction Effects

The topology of the Fermi surface of Sr_{2}RuO_{4} is well described by local-density approximation calculations with spin-orbit interaction, but the relative size of its different sheets is not. By accounting for many-body effects via dynamical mean-field theory, we show that the standard isotropic Coulomb interaction alone worsens or does not correct this discrepancy. In order to reproduce experiments, it is essential to account for the Coulomb anisotropy. The latter is small but has strong effects; it competes with the Coulomb-enhanced spin-orbit coupling and the isotropic Coulomb term in determining the Fermi surface shape. Its effects are likely sizable in other correlated multiorbital systems. In addition, we find that the low-energy self-energy matrix-responsible for the reshaping of the Fermi surface-sizably differs from the static Hartree-Fock limit. Finally, we find a strong spin-orbital entanglement; this supports the view that the conventional description of Cooper pairs via factorized spin and orbital part might not apply to Sr_{2}RuO_{4}.

Superconductivity from Emerging Magnetic Moments

Multiorbital Hubbard models are shown to exhibit a spatially isotropic spin-triplet superconducting phase, where equal-spin electrons in different local orbitals are paired. This superconducting state is stabilized in the spin-freezing crossover regime, where local moments emerge in the metal phase, and the pairing is substantially assisted by spin anisotropy. The phase diagram features a superconducting dome below a non-Fermi-liquid metallic region and next to a magnetically ordered phase. We suggest that this type of fluctuating-moment-induced superconductivity, which is not originating from fluctuations near a quantum critical point, may be realized in spin-triplet superconductors such as strontium ruthenates and uranium compounds.