Quantum critical phase of FeO spans conditions of Earth's lower mantle.

Seismic and mineralogical studies have suggested regions at Earth's core-mantle boundary may be highly enriched in FeO, reported to exhibit metallic behavior at extreme pressure-temperature (P-T) conditions. However, underlying electronic processes in FeO remain poorly understood. Here we explore the electronic structure of B1-FeO at extreme conditions with large-scale theoretical modeling using state-of-the-art embedded dynamical mean field theory (eDMFT). Fine sampling of the phase diagram reveals that, instead of sharp metallization, compression of FeO at high temperatures induces a gradual orbitally selective insulator-metal transition. Specifically, at P-T conditions of the lower mantle, FeO exists in an intermediate quantum critical state, characteristic of strongly correlated electronic matter. Transport in this regime, distinct from insulating or metallic behavior, is marked by incoherent diffusion of electrons in the conducting t2g orbital and a band gap in the eg orbital, resulting in moderate electrical conductivity (~105 S/m) with modest P-T dependence as observed in experiments. Enrichment of solid FeO can thus provide a unifying explanation for independent observations of low seismic velocities and elevated electrical conductivities in heterogeneities at Earth's mantle base.

Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel.

Precise calculations of dynamics in the homogeneous electron gas (jellium model) are of fundamental importance for design and characterization of new materials. We introduce a diagrammatic Monte Carlo technique based on algorithmic Matsubara integration that allows us to compute frequency and momentum resolved finite temperature response directly in the real frequency domain using a series of connected Feynman diagrams. The data for charge response at moderate electron density are used to extract the frequency dependence of the exchange-correlation kernel at finite momenta and temperature. These results are as important for development of the time-dependent density functional theory for materials dynamics as ground state energies are for the density functional theory.

Single-particle excitations in the uniform electron gas by diagrammatic Monte Carlo.

We calculate the single-particle excitation spectrum and the Landau liquid parameters for the archetypal model of solids, the three-dimensional uniform electron gas, with the variational diagrammatic Monte Carlo method, which gives numerically controlled results without systematic error. In the metallic range of density, we establish benchmark values for the wave-function renormalization factor Z, the effective mass [Formula: see text], and the Landau parameters [Formula: see text] and [Formula: see text] with unprecedented accuracy, and we resolve the long-standing puzzle of non-monotonic dependence of mass on density. We also exclude the possibility that experimentally measured large reduction of bandwidth in Na metal can originate from the charge and spin fluctuations contained in the model of the uniform electron gas.

Author Correction: Signatures of Mottness and Hundness in archetypal correlated metals.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Mott Metal-Insulator Transitions in Pressurized Layered Trichalcogenides.

Transition metal phosphorous trichalcogenides, MPX_{3} (M and X being transition metal and chalcogen elements, respectively), have been the focus of substantial interest recently because they are unusual candidates undergoing Mott transition in the two-dimensional limit. Here we investigate material properties of the compounds with M=Mn and Ni employing ab initio density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e., t_{2g} or e_{g}. Under pressure, MnPS_{3} can undergo an isosymmetric structural transition within monoclinic space group by forming Mn-Mn dimers due to the strong direct overlap between the neighboring t_{2g} orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS_{3} and NiPSe_{3}, with their active e_{g} orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase within the monoclinic symmetry. Hence NiPS_{3} and NiPSe_{3} become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior.

Interfacial charge-transfer Mott state in iridate-nickelate superlattices.

We investigate [Formula: see text]/[Formula: see text] superlattices in which we observe a full electron transfer at the interface from Ir to Ni, triggering a massive structural and electronic reconstruction. Through experimental characterization and first-principles calculations, we determine that a large crystal field splitting from the distorted interfacial [Formula: see text] octahedra surprisingly dominates over the spin-orbit coupling and together with the Hund's coupling results in the high-spin (S = 1) configurations on both the Ir and Ni sites. This demonstrates the power of interfacial charge transfer in coupling lattice, charge, orbital, and spin degrees of freedom, opening fresh avenues of investigation of quantum states in oxide superlattices.

A combined variational and diagrammatic quantum Monte Carlo approach to the many-electron problem.

Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. Here we show that combining both, and introducing a diagrammatic quantum Monte Carlo method, results in a powerful and accurate solver to the generic solid state problem, in which a macroscopic number of electrons interact by the long range Coulomb repulsion. We apply it to the quintessential problem of solid state, the uniform electron gas, which is at the heart of the density functional theory success in describing real materials, yet it has not been adequately solved for over 90 years. Our method allows us to calculate numerically exact momentum and frequency resolved spin and charge response functions. This method can be applied to a number of moderately interacting electron systems, including models of realistic metallic and semiconducting solids.

Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene.

Bilayer graphene can be modified by rotating (twisting) one layer with respect to the other. The interlayer twist gives rise to a moiré superlattice that affects the electronic motion and alters the band structure1-4. Near a 'magic angle' of twist2,4, where the emergence of a flat band causes the charge carriers to slow down3, correlated electronic phases including Mott-like insulators and superconductors were recently discovered5-8 by using electronic transport. These measurements revealed an intriguing similarity between magic-angle twisted bilayer graphene and high-temperature superconductors, which spurred intensive research into the underlying physical mechanism9-14. Essential clues to this puzzle, such as the symmetry and spatial distribution of the spectral function, can be accessed through scanning tunnelling spectroscopy. Here we use scanning tunnelling microscopy and spectroscopy to visualize the local density of states and charge distribution in magic-angle twisted bilayer graphene. Doping the sample to partially fill the flat band, we observe a pseudogap phase accompanied by a global stripe charge order that breaks the rotational symmetry of the moiré superlattice. Both the pseudogap and the stripe charge order disappear when the band is either empty or full. The close resemblance to similar observations in high-temperature superconductors15-21 provides new evidence of a deeper link underlying the phenomenology of these systems.

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.

Phonon Softening due to Melting of the Ferromagnetic Order in Elemental Iron.

We study the fundamental question of the lattice dynamics of a metallic ferromagnet in the regime where the static long-range magnetic order is replaced by the fluctuating local moments embedded in a metallic host. We use the ab initio density functional theory + embedded dynamical mean-field theory functional approach to address the dynamic stability of iron polymorphs and the phonon softening with an increased temperature. We show that the nonharmonic and inhomogeneous phonon softening measured in iron is a result of the melting of the long-range ferromagnetic order and is unrelated to the first-order structural transition from the bcc to the fcc phase, as is usually assumed. We predict that the bcc structure is dynamically stable at all temperatures at normal pressure and is thermodynamically unstable only between the bcc-α and the bcc-δ phases of iron.

Two-Dimensional Massless Dirac Fermions in Antiferromagnetic AFe_{2}As_{2} (A=Ba,Sr).

We report infrared studies of AFe_{2}As_{2} (A=Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a sqrt[B] dependence of the LL transition energies, the zero-energy intercepts at B=0 T under the linear extrapolations of the transition energies and the energy ratio (∼2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in the antiferromagnet BaFe_{2}As_{2}. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction k_{z} indicate that massless Dirac fermions in BaFe_{2}As_{2} are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe_{2}As_{2} by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.

Mott Transition and Magnetism in Rare Earth Nickelates and its Fingerprint on the X-ray Scattering.

The metal-insulator transition (MIT) remains among the most thoroughly studied phenomena in solid state physics, but the complexity of the phenomena, which usually involves cooperation of many degrees of freedom including orbitals, fluctuating local moments, magnetism, and the crystal structure, have resisted predictive ab-initio treatment. Here we develop ab-initio theoretical method for correlated electron materials, based on Dynamical Mean Field Theory, which can predict the change of the crystal structure across the MIT at finite temperature. This allows us to study the coupling between electronic, magnetic and orbital degrees of freedom with the crystal structure across the MIT in rare-earth nickelates. We predict the electronic free energy profile of the competing states, and the theoretical magnetic ground state configuration, which is in agreement with neutron scattering data, but is different from the magnetic models proposed before. The resonant elastic X-ray response at the K-edge, which was argued to be a probe of the charge order, is theoretically modelled within the Dynamical Mean Field Theory, including the core-hole interaction. We show that the line-shape of the measured resonant elastic X-ray response can be explained with the "site-selective" Mott scenario without real charge order on Ni sites.

Metal-Insulator Transition and Topological Properties of Pyrochlore Iridates.

Combining density functional theory (DFT) and embedded dynamical mean-field theory (DMFT) methods, we study the metal-insulator transition in R_{2}Ir_{2}O_{7} (R=Y, Eu, Sm, Nd, Pr, and Bi) and the topological nature of the insulating compounds. Accurate free energies evaluated using the charge self-consistent DFT+DMFT method reveal that the metal-insulator transition occurs for an A-cation radius between that of Nd and Pr, in agreement with experiments. The all-in-all-out magnetic phase, which is stable in the Nd compound but not the Pr one, gives rise to a small Ir^{4+} magnetic moment of ≈0.4 µ_{B} and opens a sizable correlated gap. We demonstrate that within this state-of-the-art theoretical method, the insulating bulk pyrochlore iridates are topologically trivial.

Orbital Selective Spin Excitations and their Impact on Superconductivity of LiFe_{1-x}Co_{x}As.

We use neutron scattering to study spin excitations in single crystals of LiFe_{0.88}Co_{0.12}As, which is located near the boundary of the superconducting phase of LiFe_{1-x}Co_{x}As and exhibits non-Fermi-liquid behavior indicative of a quantum critical point. By comparing spin excitations of LiFe_{0.88}Co_{0.12}As with a combined density functional theory and dynamical mean field theory calculation, we conclude that wave-vector correlated low energy spin excitations are mostly from the d_{xy} orbitals, while high-energy spin excitations arise from the d_{yz} and d_{xz} orbitals. Unlike most iron pnictides, the strong orbital selective spin excitations in the LiFeAs family cannot be described by an anisotropic Heisenberg Hamiltonian. While the evolution of low-energy spin excitations of LiFe_{1-x}Co_{x}As is consistent with the electron-hole Fermi surface nesting conditions for the d_{xy} orbital, the reduced superconductivity in LiFe_{0.88}Co_{0.12}As suggests that Fermi surface nesting conditions for the d_{yz} and d_{xz} orbitals are also important for superconductivity in iron pnictides.

Transport Properties of Metallic Ruthenates: A DFT+DMFT Investigation.

We present a systematical theoretical study on the transport properties of an archetypal family of Hund's metals, Sr_{2}RuO_{4}, Sr_{3}Ru_{2}O_{7}, SrRuO_{3}, and CaRuO_{3}, within the combination of first principles density functional theory and dynamical mean field theory. The agreement between theory and experiments for optical conductivity and resistivity is good, which indicates that electron-electron scattering dominates the transport of ruthenates. We demonstrate that in the single-site dynamical mean field approach the transport properties of Hund's metals fall into the scenario of "resilient quasiparticles." We explain why the single layered compound Sr_{2}RuO_{4} has a relative weak correlation with respect to its siblings, which corroborates its good metallicity.

The valence-fluctuating ground state of plutonium.

A central issue in material science is to obtain understanding of the electronic correlations that control complex materials. Such electronic correlations frequently arise because of the competition of localized and itinerant electronic degrees of freedom. Although the respective limits of well-localized or entirely itinerant ground states are well understood, the intermediate regime that controls the functional properties of complex materials continues to challenge theoretical understanding. We have used neutron spectroscopy to investigate plutonium, which is a prototypical material at the brink between bonding and nonbonding configurations. Our study reveals that the ground state of plutonium is governed by valence fluctuations, that is, a quantum mechanical superposition of localized and itinerant electronic configurations as recently predicted by dynamical mean field theory. Our results not only resolve the long-standing controversy between experiment and theory on plutonium's magnetism but also suggest an improved understanding of the effects of such electronic dichotomy in complex materials.

Exact Double Counting in Combining the Dynamical Mean Field Theory and the Density Functional Theory.

We propose a continuum representation of the dynamical mean field theory, in which we were able to derive an exact overlap between the dynamical mean field theory and band structure methods, such as the density functional theory; double counting. The implementation of this exact double counting shows improved agreement between the theory and experiment in several correlated solids, such as the transition metal oxides and lanthanides. Previously introduced nominal double counting is in much better agreement with the exact double counting than the most widely used fully localized limit formula.

Unveiling hidden ferrimagnetism and giant magnetoelectricity in polar magnet Fe2Mo3O8.

Magnetoelectric (ME) effect is recognized for its utility for low-power electronic devices. Largest ME coefficients are often associated with phase transitions in which ferroelectricity is induced by magnetic order. Unfortunately, in these systems, large ME response is revealed only upon elaborate poling procedures. These procedures may become unnecessary in single-polar-domain crystals of polar magnets. Here we report giant ME effects in a polar magnet Fe2Mo3O8 at temperatures as high as 60 K. Polarization jumps of 0.3 µC/cm(2), and repeated mutual control of ferroelectric and magnetic moments with differential ME coefficients on the order of 10(4) ps/m are achieved. Importantly, no electric or magnetic poling is needed, as necessary for applications. The sign of the ME coefficients can be switched by changing the applied "bias" magnetic field. The observed effects are associated with a hidden ferrimagnetic order unveiled by application of a magnetic field.