Multiorbital System Research Articles

Multiorbital Nature of Doped Sr_{2}IrO_{4}.

The low-energy j_{eff}=1/2 band of Sr_{2}IrO_{4} bears stark resemblances with the x^{2}-y^{2} band of La_{2}CuO_{4}, and yet no superconductivity has been found so far by doping Sr_{2}IrO_{4}. Behind such a behavior could be inherent failures of the j_{eff}=1/2 picture, in particular when electrons or holes are introduced in the IrO_{2} planes. In view of this, here we reanalyze the j_{eff}=1/2 scenario. By using the local-density approximation plus dynamical mean-field theory approach, we show that the form of the effective j_{eff}=1/2 state is surprisingly stable upon doping. This supports the j_{eff}=1/2 picture. We show that, nevertheless, Sr_{2}IrO_{4} remains in essence a multiorbital system: The hybridization with the j_{eff}=3/2 orbitals sizably reduces the Mott gap by enhancing orbital degeneracy, and part of the holes go into the j_{eff}=3/2 channels. These effects cannot be reproduced by a simple effective screened Coulomb repulsion. In the optical conductivity spectra, multiorbital processes involving the j_{eff}=3/2 states contribute both to the Drude peak and to relatively low-energy features.

Topological flat bands in a kagome lattice multiorbital system

Flat bands and dispersive Dirac bands are known to coexist in the electronic bands in a two-dimensional kagome lattice. Including the relativistic spin-orbit coupling, such systems often exhibit nontrivial band topology, allowing for gapless edge modes between flat bands at several locations in the band structure, and dispersive bands or at the Dirac band crossing. Here, we theoretically demonstrate that a multiorbital system on a kagome lattice is a versatile platform to explore the interplay between nontrivial band topology and electronic interaction. Specifically, here we report that the multiorbital kagome model with the atomic spin–orbit coupling naturally supports topological bands characterized by nonzero Chern numbers {{{{{{{mathcal{C}}}}}}}}, including a flat band with | {{{{{{{mathcal{C}}}}}}}}| =1. When such a flat band is 1/3 filled, the non-local repulsive interactions induce a fractional Chern insulating state. We also discuss the possible realization of our findings in real kagome materials.

Light-induced hidden odd-frequency order in a model for A3C60

Laser driving in systems with competing or coupled electronic orders can lead to the enhancement of orders, or even to the appearance of hidden phases without an equilibrium analogue. Here we consider a model for A$_3$C$_{60}$ which exhibits a unique interplay between conventional and odd-frequency (or composite) orders. In particular, we show that photo-doping of the antiferromagnetic Mott insulating phase, as realized in Cs$_3$C$_{60}$, results in a paramagnetic gapped state with broken orbital symmetry. This hidden phase, which does not exist under equilibrium conditions, can be interpreted as an odd-frequency orbital-ordered state, and is conceptually related to the equilibrium Jahn-Teller metal in more weakly correlated compounds. Our study demonstrates the appearance of pure odd-frequency order via the nonthermal melting of magnetic order, and provides an interesting example of nonequilibrium control of electronic orders in a multi-orbital system.

Ferromagnetic percolation transition in a multiorbital flat band assisted by Hund's coupling

By connecting Hund's physics with flat band physics, we establish an exact result for studying ferromagnetism in a multiorbital system. We consider a two-layer model consisting of a ${p}_{x}, {p}_{y}$-orbital honeycomb lattice layer and an $f$-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. The system features a flat band that admits a percolation representation for an appropriate chemical potential difference between the two layers. In this representation, the ground-state space is spanned by maximum-spin clusters of localized single-particle states, and averaging over the ground states yields a correlated percolation problem with weights due to the spin degeneracy of the clusters. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large maximum-spin cluster, as shown by Monte Carlo simulation.

Floquet engineering of Mott insulators with strong spin-orbit coupling

We propose a method for controlling the exchange interactions of Mott insulators with strong spin-orbit coupling. We consider a multiorbital system with strong spin-orbit coupling and a circularly polarized light field and derive its effective Hamiltonian in the strong-interaction limit. Applying this theory to a minimal model of $\alpha$-RuCl$_{3}$, we show that the magnitudes and signs of three exchange interactions, $J$, $K$, and $\Gamma$, can be changed simultaneously. Then, considering another case in which one of the hopping integrals has a different value and the other parameters are the same as those for $\alpha$-RuCl$_{3}$, we show that the Heisenberg interaction $J$ can be made much smaller than the anisotropic exchange interactions $K$ and $\Gamma$.

Direct observation of kink evolution due to Hund\u2019s coupling on approach to metal-insulator transition in NiS2\u2212xSex

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 NiS2−xSex 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.

Hund's metal physics: From SrNiO2 to LaNiO2

We study the normal state electronic structure of the recently discovered infinite-layer nickelate superconductor, Nd$_{1-x}$Sr$_x$NiO$_2$. Using SrNiO$_2$ as a reference, we find that Nd$_{1-x}$Sr$_x$NiO$_2$ is a multi-orbital electronic system with characteristic Hund's metal behaviors, such as metallicity, the importance of high-spin configurations, tendency towards orbital differentiation, and the absence of magnetism in regimes which are ordered according to static mean-field theories. In addition, our DFT+DMFT calculations with exact double counting scheme show that despite large charge carrier doping from SrNiO$_2$ to LaNiO$_2$, the Ni-$3d$ total occupancy is barely changed due to the decreased hybridization with the occupied oxygen-2$p$ states, and increased hybridization with the unoccupied La-5$d$ states. Our results are in good agreement with the existing resonant inelastic x-ray scattering measurements and pave the way to understand the pairing mechanism of Nd$_{1-x}$Sr$_x$NiO$_2$.

Multiorbital antiferromagnetic metal induced by intramolecular self-doping

The authors examine the spin and charge states in a multiorbital system through orbital selective NMR spectroscopy combined with fine-structure-resolvable synchrotron X-ray diffractometry. The results show an intramolecular electron redistribution leading to interorbital self-doping

Nickelate superconductors\u2014a renaissance of the one-band Hubbard model

The recently discovered nickelate superconductors appear, at first glance, to be even more complicated multi-orbital systems than cuprates. To identify the simplest model describing the nickelates, we analyse the multi-orbital system and find that it is instead the nickelates which can be described by a one-band Hubbard model, albeit with an additional electron reservoir and only around the superconducting regime. Our calculations of the critical temperature TC are in good agreement with experiment, and show that optimal doping is slightly below 20% Sr-doping. Even more promising than 3d nickelates are 4d palladates.

Topological d+s wave superconductors in a multiorbital quadratic band touching system

Realization of topological superconductors is one of the most important goals in studies of topological phases in quantum materials. In this work, we theoretically propose a novel way to attain topological superconductors with non-trivial Fermi surfaces of Bogoliubov quasiparticles. Considering the interacting Luttinger model with $j\!=\!3/2$ electrons, we investigate the dominant superconducting channels for a multi-orbital quadratic band-touching system with finite chemical potential, which breaks the particle-hole symmetry in the normal state. Notably, while the system generally favors d-wave pairing, the absence of the particle-hole symmetry necessarily induces parasitic s-wave pairing. Based on the Landau theory with $SO(3)$ symmetry, we demonstrate that two kinds of topological superconductors are energetically favored; uniaxial nematic phase with parasitic $s$ wave pairing ($d_{(3z^2-r^2)}\!+\!s$) and time-reversal-symmetry broken phase with parasitic $s$ wave pairing ($d_{(3z^2-r^2,xy)}\!+\!id_{x^2-y^2}\!+\!s$). These superconductors contain either nodal lines or Fermi pockets of gapless Bogoliubov quasiparticles and moreover exhibit topological winding numbers $\pm2$, leading to non-trivial surface states such as drumhead-like surface states or Fermi arcs. We discuss applications of our theory to relevant families of materials, especially half-heusler compound YPtBi, and suggest possible future experiments.

Spin-freezing and the Sachdev-Ye model

Spin-freezing is the origin of bad-metal physics and non-Fermi liquid (non-FL) properties in a broad range of correlated compounds. In a multi-orbital lattice system with Hund coupling, doping of the half-filled Mott insulator results in a highly incoherent metal with frozen magnetic moments. These moments fluctuate and collapse in a crossover region that is characterized by unusual non-Fermi liquid properties such as a self-energy whose imaginary part varies over a significant energy range. At low enough temperature, the local moment fluctuations induce electron pairing, which may be a generic mechanism for unconventional superconductivity. While this physics has been discovered in numerical studies of multi-orbital Hubbard systems, it exhibits a striking similarity to the analytically solvable Sachdev-Ye (SY) model, and its recent fermionic extensions. Here, we explore the relation between spin-freezing and SY physics, and thus shed light on fundamental properties of Hund metals.

Optical spectroscopy study of Ca3(Ru0.91Mn0.09)2O7 single crystal in high magnetic fields

The magneto-optical spectrum, with magnetic fields up to 42 T, of double layered ruthenates Ca3(Ru0.91Mn0.09)2O7 (CRMO) single crystal is studied. Both the temperature and magnetic field induced insulator-to-metal transitions (IMTs) are observed via magneto-optical properties of the crystal. The critical magnetic field (H // c) of IMT for CRMO is found to be as large as 35 T at 5 K. The fine structure of optical spectra identified the antiferromagnetic/ferro-orbital-ordering configurations of Ru 4d orbitals at low temperatures. Meanwhile, the configuration of orbital polarization of such double-layer CRMO single crystal is discussed. These results suggest that the orbital degree of freedom plays an important role in the field induced IMT of multi-orbital system.

Orbital-selective metal-insulator transition lifting the t2g band hybridization in the Hund metal Sr3(Ru1−xMnx)2O7

We reveal the orbital-selective metal-insulator transition in a $4d$ multiorbital system, ${\mathrm{Sr}}_{3}{({\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x})}_{2}{\mathrm{O}}_{7}\phantom{\rule{4pt}{0ex}}(x=0\ensuremath{-}0.2)$, by means of angle-resolved photoemission spectroscopy. With a small substitution $(x=0.05)$ of Mn with localized $3d$ orbitals, the spectra for the $4{d}_{xy}$ band become incoherent with a large gap, while the $4{d}_{xz/yz}$ bands stay metallic with sharp quasiparticle peaks. Intriguingly, this lifts band hybridization among $4d$ orbitals, and causes a two- to one-dimensional crossover in the remaining Fermi surface. Significant nesting in the remaining Fermi surface is implied to induce the reported magnetic ordering, and yields the insulating bulk state at higher Mn substitution, where all bands are gapped and totally incoherent. The availability of orbital-selective tuning of the pseudogap by a small impurity will prompt further theoretical studies of Hund's metals, which were recognized only recently in condensed matter physics.

Dynamic signature of orbital selective Mott transition in the metallic phase of VO2

An orbital-selective technique, nuclear magnetic resonance (NMR) spectroscopy, which could simultaneously probe the atomic structure and electronic properties, was employed to address the ‘bad metal’ behaviors, i.e., negligible electron thermal conductivity in the metallic phase of VO2. The measured electric field gradients at V sites by 51V NMR were found to evolve significantly in the pure metallic phase within the vicinity of structural phase transition temperatures, unexpected in a simple metal within this temperature region according to structural analysis by diffraction. This abnormal temperature-dependent local symmetry evolution can be well explained by a simple phenomenological model of orbital selective Mott transition in this multiorbital system.

Mott Transition in the A15 Phase of Cs_{3}C_{60}: Absence of a Pseudogap and Charge Order.

We present a detailed NMR study of the insulator-to-metal transition induced by an applied pressure p in the A15 phase of Cs_{3}C_{60}. We evidence that the insulating antiferromagnetic (AFM) and superconducting (SC) phases coexist only in a narrow p range. At fixed p, in the metallic state above the SC transition T_{c}, the ^{133}Cs and ^{13}C NMR spin-lattice relaxation data are seemingly governed by a pseudogaplike feature. We prove that this feature, also seen in the ^{133}Cs NMR shift data, is rather a signature of the Mott transition which broadens and smears out progressively for increasing (p,T). The analysis of the variation of the quadrupole splitting ν_{Q} of the ^{133}Cs NMR spectrum precludes any cell symmetry change at the Mott transition and only monitors a weak variation of the lattice parameter. These results open an opportunity to consider theoretically the Mott transition in a multiorbital three-dimensional system well beyond its critical point.

Spin-freezing perspective on cuprates

The high-temperature superconducting state in cuprates appears if charge carriers are doped into a Mott insulating parent compound. An unresolved puzzle is the unconventional nature of the normal state above the superconducting dome, and its connection to the superconducting instability. At weak hole-doping, a "pseudo-gap" metal state with signatures of time-reversal symmetry breaking is observed, which near optimal doping changes into a "strange metal" with non-Fermi liquid properties. Qualitatively similar phase diagrams are found in multi-orbital systems, such as pnictides, where the unconventional metal states arise from a Hund coupling induced spin-freezing. Here, we show that the relevant model for cuprates, the single-orbital Hubbard model on the square lattice, can be mapped onto an effective multi-orbital problem with strong ferromagnetic Hund coupling. The spin-freezing physics of this multi-orbital system explains the phenomenology of cuprates, including the pseudo-gap, the strange metal, and the d-wave superconducting instability. Our analysis suggests that spin-freezing is the universal mechanism which controls the properties of unconventional superconductors.

Microscopic theory on charge transports of a correlated multiorbital system

Current vertex correction (CVC), the back-flow-like correction to the current, comes from conservation laws, and the CVC due to electron correlation contains information about many-body effects. However, it has been little understood how the CVC due to electron correlation affects the charge transports of a correlated multiorbital system. To improve this situation, I studied the inplane resistivity, $\rho_{ab}$, and the Hall coefficient in the weak-field limit, $R_{\textrm{H}}$, in addition to the magnetic properties and the electronic structure, for a $t_{2g}$-orbital Hubbard model on a square lattice in a paramagnetic state away from or near an antiferromagnetic (AF) quantum-critical point (QCP) in the fluctuation-exchange (FLEX) approximation with the CVCs arising from the self-energy ($\Sigma$), the Maki-Thompson (MT) irreducible four-point vertex function, and the main terms of the Aslamasov-Larkin (AL) one. Then, I found three main results about the CVCs. First, the main terms of the AL CVC does not qualitatively change the results obtained in the FLEX approximation with the $\Sigma$ CVC and the MT CVC. Second, $\rho_{ab}$ and $R_{\textrm{H}}$ near the AF QCP have high-temperature region, governed mainly by the $\Sigma$ CVC, and low-temperature region, governed mainly by the $\Sigma$ CVC and the MT CVC. Third, in case away from the AF QCP, the MT CVC leads to a considerable effect on only $R_{\textrm{H}}$ at low temperatures, although $R_{\textrm{H}}$ at high temperatures and $\rho_{ab}$ at all temperatures considered are sufficiently described by including only the $\Sigma$ CVC. I also achieved the qualitative agreement with several experiments of Sr$_{2}$RuO$_{4}$ or Sr$_{2}$Ru$_{0.975}$Ti$_{0.025}$O$_{4}$. Moreover, I showed several better points of this theory than other theories.

Accuracy of downfolding based on the constrained random-phase approximation

We study the reliability of the constrained random phase approximation (cRPA) method for the calculation of low-energy effective Hamiltonians by considering multi-orbital lattice models with one strongly correlated "target" band and two weakly correlated "screening" bands. The full multi-orbital system and the effective model are solved within dynamical mean field theory (DMFT) in a consistent way. By comparing the quasi-particle weights for the correlated bands, we examine how accurately the effective model describes the low-energy properties of the multi-band system. We show that the violation of the Pauli principle in the cRPA method leads to overscreening effects when the inter-orbital interaction is small. This problem can be overcome by using a variant of the cRPA method which restores the Pauli principle.

Many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid theory

I review many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point (QCP). These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multi-orbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multi-orbital systems. To improve this situation, I formulate the resistivity of a multi-orbital Hubbard model using the extended Éliashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki–Thompson term. The results away from and near the antiferromagnetic QCP reproduce the temperature dependence observed in Sr 2 RuO 4 and Sr 2 Ru 0.075 Ti 0.025 O 4, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems.

Exact results for itinerant ferromagnetism in at2g-orbital system on cubic and square lattices

We study itinerant ferromagnetism in a ${t}_{2g}$ multiorbital Hubbard system in the cubic lattice, which consists of three planar oriented orbital bands of ${d}_{xy},\phantom{\rule{0.16em}{0ex}}{d}_{yz}$, and ${d}_{zx}$. Electrons in each orbital band can only move within a two-dimensional plane in the three-dimensional lattice parallel to the corresponding orbital orientation. Electrons of different orbitals interact through the on-site multiorbital interactions including Hund's coupling. The strong-coupling limit is considered in which there are no doubly occupied orbitals but multiple on-site occupations are allowed. We show that in the case in which there is one and only one hole for each orbital band in each layer parallel to the orbital orientation, the ground state is a fully spin-polarized itinerant ferromagnetic state, which is unique apart from the trivial spin degeneracy. When the lattice is reduced into a single two-dimensional layer, the ${d}_{zx}$ and ${d}_{yz}$ bands become quasi-one-dimensional while the ${d}_{xy}$ band remains two-dimensional. The ground-state ferromagnetism also appears in the strong-coupling limit as a generalization of the double-exchange mechanism. Possible applications to the systems of ${\mathrm{SrRuO}}_{3}$ and ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ interface are discussed.