Three-orbital Model Research Articles

Non-Fermi-liquid behavior of the scattering rate in the three-orbital Emery model

Non-Fermi-liquid behavior of the scattering rate in the three-orbital Emery model

Charge density wave ordering in NdNiO2: effects of multiorbital nonlocal correlations

In this work, we investigate collective electronic fluctuations and, in particular, the possibility of the charge density wave ordering in an infinite-layer NdNiO2. We perform advanced many-body calculations for the ab-initio three-orbital model by taking into account local correlation effects, nonlocal charge and magnetic fluctuations, and the electron-phonon coupling. We find that in the considered material, electronic correlations are strongly orbital- and momentum-dependent. Notably, the charge density wave and magnetic instabilities originate from distinct orbitals. In particular, we show that the correlation effects lead to the momentum-dependent hybridization between different orbitals, resulting in the splitting and shifting of the flat part of the Ni-dz2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{z}^{2}}$$\\end{document} band. This strong renormalization of the electronic spectral function drives the charge density wave instability that is related to the intraband Ni-dz2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{z}^{2}}$$\\end{document} correlations. Instead, the magnetic instability stems from the Ni-dx2−y2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{x}^{2}-{y}^{2}}$$\\end{document} orbital, which remains half-filled through the redistribution of the electronic density between different bands even upon hole doping. Consequently, the strength of the magnetic fluctuations remains nearly unchanged for the considered doping levels. We argue that this renormalization is not inherent to the stoichiometric case but can be induced by hole doping.

Nb3Cl8: a prototypical layered Mott-Hubbard insulator

Despite its simplicity and relevance for the description of electronic correlations in solids, the Hubbard model is seldom inarguably realized in real materials. Here, we show that monolayer Nb3Cl8 is an ideal candidate to be described within a single-orbital Hubbard model, constructed within a “molecular” rather than atomic basis set using ab initio constrained random phase approximation calculations. We provide the necessary ingredients to connect experimental reality with ab initio material descriptions and correlated electron theory, which clarifies that monolayer Nb3Cl8 is a Mott insulator with a gap of about 1.4 to 2.0 eV depending on its dielectric environment. Comparisons to an atomistic three-orbital model show that the single-molecular-orbital description is adequate and reliable. We further comment on the electronic and magnetic structure of the compound and show that the Mott insulating state survives in the low-temperature bulk phases of the material featuring distinct experimentally verifiable characteristics.

Effects of carrier density and interactions on pairing symmetry in a t2g model

By utilizing the fluctuation exchange approximation method, we perform a study on the superconducting pairing symmetry in a t2g three-orbital model on the square lattice. Although the tight-binding parameters of the model are based on Sr2RuO4, we have systematically studied the evolution of superconducting pairing symmetry with the carrier density and interactions, making our findings relevant to a broader range of material systems. Under a moderate Hund’s coupling, we find that spin fluctuations dominate the superconducting pairing, leading to a prevalent spin-singlet pairing with a d x 2–y 2 -wave symmetry for the carrier density within the range of n = 1.5–4 per site. By reducing the Hund’s coupling, the charge fluctuations are enhanced and play a crucial role in determining the pairing symmetry, leading to a transition of the pairing symmetry from the spin-singlet d x 2–y 2 -wave to the spin-triplet p-wave. Furthermore, we find that the superconducting pairings are orbital dependent. As the carrier density changes from n = 4 to n = 1.5, the active orbitals for superconducting pairing shift from the quasi-two-dimensional orbital d xy to the quasi-one-dimensional orbitals d xz and d yz .

Quasiparticle approach to the transport in infinite-layer nickelates

The normal-state transport properties of superconducting infinite-layer nickelates are investigated within an interacting three-orbital model. It includes effective Ni-${d}_{{z}^{2}}$ and Ni-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ bands as well as the self-doping band degree of freedom. The thermopower, Hall coefficient, and optical conductivity are modeled within a quasiparticle approximation to the electronic states. Qualitative agreement in comparison to experimentally available Hall data is achieved, with notably a temperature-dependent sign change of the Hall coefficient for larger hole doping $x$. The Seebeck coefficient changes from negative to positive in a nontrivial way with $x$, but generally shows only a modest temperature dependence. The optical conductivity shows a pronounced Drude response and a prominent peak structure at higher frequencies due to interband transitions. While the quasiparticle picture is surely approximative to low-valence nickelates, it provides enlightening insights into the multiorbital nature of these challenging systems.

Spin–orbit coupling, orbitally entangled antiferromagnetic order, and collective spin–orbital excitations in

With electron filling n = 1 in the compound, the octahedrally coordinated orbitals are strongly active when the tetragonal distortion induced crystal field is tuned by external agent such as pressure. Considering the full range of crystal field induced tetragonal splitting in a realistic three-orbital model, collective spin–orbital excitations are investigated using the generalized self-consistent plus fluctuation approach. At ambient pressure, an entangled orbital + antiferromagnetic order is found to be stabilized beyond a critical value (∼30 meV) of spin–orbit coupling which is in the realistic range for 3d ions. The behavior of the calculated energy scales of collective excitations with crystal field is consistent with that of the transition temperatures with pressure as obtained from susceptibility and resistivity anomalies in high-pressure studies.

Spin-triplet superconducting pairing in doped MoS2

Searching for triplet superconductivity has been pursued intensively in a broad field of material science and quantum information for decades. Nevertheless, these novel states remain rare. Within a simplified effective three-orbital model, we reveal a spin triplet pairing in doped MoS$_2$ by employing both the finite temperature determinant quantum Monte Carlo approach and the ground state constrained-phase quantum Monte Carlo method. In a wide filling region of $\avg{n}=0.60-0.80$ around charge neutrality $\avg{n}=2/3$, the $f$-wave pairing dominates over other symmetries. The pairing susceptibility strongly increases as the on-site Coulomb interaction increases, and it is insensitive to spin-orbit coupling.

Antisymmetric thermopolarization by electric toroidicity

We investigate electric polarizations that emerge perpendicular to an applied thermal gradient in insulating systems. The thermally induced electric polarization, known as thermopolarization, has been studied conventionally in the case where an electric polarization appears along the thermal gradient. Here, we focus on the antisymmetric component of the thermopolarization tensor, and we reveal that it becomes nonzero due to the ferrotype order for electric-toroidal dipole moments. To describe local electric polarizations originating from the disproportionation of localized electronic clouds, we introduce a two-dimensional three-orbital model with localized $s$ and two $p$ orbitals, where the electric polarization at each site interacts with the neighboring one as dipole-dipole interactions. We find that a vortex-type configuration of local electric polarizations appears as a mean-field ground state, corresponding to a ferrotype electric-toroidal dipole order. By taking account of collective modes from this ordered state, we calculate the coefficient of the thermopolarization based on the linear-response theory. The antisymmetric component is nonzero in the presence of the electric-toroidal dipole order. We clarify that fluctuations in the $p$ orbitals are crucial in enhancing the antisymmetric thermopolarization. We discuss the appearance conditions based on the symmetry argument and the relevance to real materials.

Phase diagram of the three-orbital Hubbard-Holstein model simulating Superconducting Tungsten Bronze AxWO3

The superconductivity in tungsten bronze Ax WO3 (A═alkali metal) is studied based on first-principles calculations and orbital fluctuation theory. We discuss the effects of the electron-Jahn-Teller phonon interaction and the on-site Coulomb interaction in the random phase approximation, and obtain a phase diagram on the U — g plane in the low-doped regime at x~0.05, where high-temperature superconductivity has been experimentally observed.

Ab Initio Downfolding Based on the GW Approximation for Infinite-Layer Nickelates

We derive an effective three-orbital model for the infinite-layer nickelates based on the band structure obtained by the GW approximation (GWA), where we consider the Ni 3dx2−y2 and O 2p orbitals forming the σ-bond. In the GWA, the self-energy correction to the local density approximation (LDA) increases the energy difference between Ni 3dx2−y2 and O 2p, which reduces the bandwidth of the antibonding 3dx2−y2 orbitals. The isolation of the Ni 3dx2−y2 around the Fermi level suppresses the screening effect. As a result, the correlation effect becomes more significant than that in the model constructed by the LDA-based downfolding. Furthermore, the Mott-Hubbard type character is enhanced in the GWA-based effective model, because the charge-transfer energy increases more rapidly compared to the increase in the interaction parameters.

Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr2RuO4 superconductor

We study the spin susceptibility of the orbital-singlet pairings, including the spin-triplet/orbital-singlet/$s$-wave $E_g$ representation proposed by Suh \textit{et al}., [H.\ G.\ Suh \textit{et al}., Phys.\ Rev.\ Research \textbf{2}, 032023 (2020)], for a three-orbital model of superconducting Sr$_2$RuO$_4$ in three dimensions. For the pseudospin-singlet states represented in the band basis, the spin susceptibility decreases when reducing the temperature, irrespective of the direction of the applied magnetic fields, even if they are spin-triplet/orbital-singlet pairings in the spin-orbital space. However, because the pseudospin-triplet \textbf{d}-vector in the band basis is not completely aligned in the $xy$-plane (along $z$-axis) owing to the strong atomic spin-orbit coupling, the spin susceptibility for spin-singlet/orbital-singlet/odd-parity pairings is reduced around $5$-$10$ percent with the decrease of the temperature along the $z$ ($x$) axis. We can determine the symmetry of the pseudospin structure of the Cooper pair by the temperature dependence of the spin susceptibility measured by nuclear magnetic resonance experiments. Our obtained results serve as a guide to determine the pairing symmetry of Sr$_2$RuO$_4$.

Efficient Slave-Boson Approach for Multiorbital Two-Particle Response Functions and Superconductivity

We develop an efficient approach for computing two-particle response functions and interaction vertices for multiorbital strongly correlated systems based on fluctuation around rotationally-invariant slave-boson saddle-point. The method is applied to the degenerate three-orbital Hubbard-Kanamori model for investigating the origin of the s-wave orbital antisymmetric spin-triplet superconductivity in the Hund's metal regime, previously found in the dynamical mean-field theory studies. By computing the pairing interaction considering the particle-particle and the particle-hole scattering channels, we identify the mechanism leading to the pairing instability around Hund's metal crossover arises from the particle-particle channel, containing the local electron pair fluctuation between different particle-number sectors of the atomic Hilbert space. On the other hand, the particle-hole spin fluctuations induce the s-wave pairing instability before entering the Hund's regime. Our approach paves the way for investigating the pairing mechanism in realistic correlated materials.

Orbital Isotropy of Magnetic Fluctuations in Correlated Electron Materials Induced by Hund's Exchange Coupling.

Characterizing nonlocal magnetic fluctuations in materials with strong electronic Coulomb interactions remains one of the major outstanding challenges of modern condensed matter theory. In this Letter, we address the spatial symmetry and orbital structure of magnetic fluctuations in perovskite materials. To this aim, we develop a consistent multiorbital diagrammatic extension of dynamical mean-field theory, which we apply to an anisotropic three-orbital model of cubic t_{2g} symmetry. We find that the form of spatial spin fluctuations is governed by the local Hund's coupling. For small values of the coupling, magnetic fluctuations are anisotropic in orbital space, which reflects the symmetry of the considered t_{2g} model. Large Hund's coupling enhances collective spin excitations, which mixes orbital and spatial degrees of freedom, and magnetic fluctuations become orbitally isotropic. Remarkably, this effect can be seen only in two-particle quantities; single-particle observables remain anisotropic for any value of the Hund's coupling. Importantly, we find that the orbital isotropy can be induced both at half filling and for the case of four electrons per lattice site, where the magnetic instability is associated with different, antiferromagnetic and ferromagnetic, modes, respectively.

Electrical control of Ruderman–Kittel–Kasuya–Yosida exchange interaction in zigzag edge MoS2 nanoflakes

In this study, we investigate the spin–spin correlation of two magnetic impurities in zigzag edge MoS2 nanoflakes using a three-orbital tight-binding model. In particular, we consider the dependence of the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction on the local electric field strength for providing a degree of tunability in triangular and rectangular nanoflakes. Our results indicate that manipulating the local electric field at the zigzag edges could allow the control of all the different components of the RKKY interaction in MoS2 nanoflakes. Interestingly, the Dzyaloshinskii–Moriya JDM oscillates but does not decay due to strong spin–orbit coupling. Moreover, the electric field induces a sizable JDM interaction as a function of the magnetic separation along zigzag edges for various Fermi energies. Our findings provide a method for enhancing the RKKY exchange interactions with magnetic arrays in these materials.

Coupled spin–orbital fluctuations in a three orbital model for 4d and 5d oxides with electron fillings n = 3, 4, 5—application to NaOsO3, Ca2RuO4 and Sr2IrO4

A unified approach is presented for investigating coupled spin–orbital fluctuations within a realistic three-orbital model for strongly spin–orbit coupled systems with electron fillings n = 3, 4, 5 in the t 2g sector of d yz , d xz , d xy orbitals. A generalized fluctuation propagator is constructed which is consistent with the generalized self-consistent Hartree–Fock approximation where all Coulomb interaction contributions involving orbital diagonal and off-diagonal spin and charge condensates are included. Besides the low-energy magnon, intermediate-energy orbiton and spin–orbiton, and high-energy spin–orbit exciton modes, the generalized spectral function also shows other high-energy excitations such as the Hund’s coupling induced gapped magnon modes. We relate the characteristic features of the coupled spin–orbital excitations to the complex magnetic behavior resulting from the interplay between electronic bands, spin–orbit coupling, Coulomb interactions, and structural distortion effects, as realized in the compounds NaOsO3, Ca2RuO4, and Sr2IrO4.

Modeling multiorbital effects in Sr2IrO4 under strain and a Zeeman field

We present a comprehensive study of a three-orbital lattice model suitable for the layered iridate Sr2IrO4. Our analysis includes various on-site interactions (including Hubbard and Hund's) as well as compressive strain, and a Zeeman magnetic field. We use a self-consistent mean field approach with multiple order parameters to characterize the resulting phases. While in some parameter regimes the compound is well described by an effective J=1/2 model, in other regimes the full multiorbital description is needed. As a function of the compressive strain, we uncover two quantum phase transitions: first a continuous metal-insulator transition, and subsequently a first order magnetic melting of the antiferromagnetic order. Crucially, bands of both J=1/2 and J=3/2 nature play important roles in these transitions. Our results qualitatively agree with experiments of Sr2IrO4 under strain induced by a substrate, and motivate the study of higher strains.

Polaron and bipolaron tendencies in a semiclassical model for hole-doped bismuthates

Bismuth perovskites ABiO$_3$ (A = Sr, Ba) host a variety of peculiar phenomena including bond-disproportionated insulating phases and high-temperature superconductivity upon hole doping. While the mechanisms underlying these phenomena are still debated, off-diagonal electron-phonon ($e$-ph) coupling originating from the modulation of the orbital overlaps has emerged as a promising candidate. Here, we employ classical Monte Carlo simulations to study a semiclassical three-orbital model with off-diagonal $e$-ph interactions. We demonstrate the existence of a (bi)polaron correlations that persists in the model at high temperatures and for hole doping away from the bond-disproportionated insulating phase. Using a spatiotemporal regression analysis between various local quantities and the lattice degrees of freedom, we also identify the similarity between heating- and doping-induced melting of a bond-disproportionated insulator at a microscopic level. Our results imply that (bi)polaron physics can be a unifying concept that helps us understand the rich bismuth perovskite phase diagram.

Orbital rotations induced by charges of polarons and defects in doped vanadates

We explore the competiton of doped holes and defects that leads to the loss of orbital order in vanadate perovskites. In compounds such as La$_{1-{\sf x}}$Ca$_{\,\sf x}$VO$_3$ spin and orbital order result from super-exchange interactions described by an extended three-orbital degenerate Hubbard-Hund model for the vanadium $t_{2g}$ electrons. Long-range Coulomb potentials of charged Ca$^{2+}$ defects and $e$-$e$ interactions control the emergence of defect states inside the Mott gap. The quadrupolar components of the Coulomb fields of doped holes induce anisotropic orbital rotations of degenerate orbitals. These rotations modify the spin-orbital polaron clouds and compete with orbital rotations induced by defects. Both mechanisms lead to a mixing of orbitals, and cause the suppression of the asymmetry of kinetic energy in the $C$-type magnetic phase. We find that the gradual decline of orbital order with doping, a characteristic feature of the vanadates, however, has its origin not predominantly in the charge carriers, but in the off-diagonal couplings of orbital rotations induced by the charges of the doped ions.

Orbital driven two-dome superconducting phases in multiorbital superconductors

We theoretically study the superconductivity in multiorbital superconductors based on a three-orbital tight-banding model. With appropriate values of the nearest-neighbor exchange J1αβ and the next-nearest-neighbor exchange J2αβ, we find a two-dome structure in the Tc−n phase diagram: one dome in the doping range n<3.9 where the superconducting (SC) state is mainly sx2y2 component contributed by inter-orbital pairing, the other dome in the doping range 3.9<n<4.46 where the SC state is mainly sx2y2+sx2+y2 components contributed by intra-orbital pairing. We find that the competition between different orbital pairing leads to two-dome SC phase diagrams in multiorbital superconductors, and different matrix elements of J1 and J2 considerably affect the boundary of two SC domes.

Ferroelectricity-induced multiorbital odd-frequency superconductivity in SrTiO3

We demonstrate that SrTiO$_3$ can be a platform for observing the bulk odd-frequency superconducting state owing to the multiorbital/multiband nature. We consider a three-orbital tight-binding model for SrTiO$_3$ in the vicinity of a ferroelectric critical point. Assuming an intraorbital spin-singlet $s$-wave superconducting order parameter, it is shown that the odd-frequency pair correlations are generated due to the intrinsic LS coupling which leads to the local orbital mixing. Furthermore, we show the existence of additional odd-frequency pair correlations in the ferroelectric phase, which is induced by an odd-parity orbital hybridization term proportional to the ferroelectric order parameter. We also perform a group theoretical classification of the odd-frequency pair amplitudes based on the fermionic and space group symmetries of the system. The classification table enables us to predict dominant components of the odd-frequency pair correlations based on the symmetry of the normal state Hamiltonian that we take into account. Furthermore, we show that experimental signatures of the odd-parity orbital hybridization, which is an essential ingredient for the ferroelectricity-induced odd-frequency pair correlations, can be observed in the spectral functions and density of states.