We investigate the dynamical properties of Sr$_2$RuO$_4$ at zero and very low temperature using density functional theory plus dynamical mean-field theory with an exact diagonalization solver. By considering rotationally invariant local interaction, we examine how Hund's coupling and spin-orbit coupling affect the correlated nature of the system. In the absence of Hund's coupling, the system shows a Fermi liquid behavior over the entire range of temperatures we consider. We confirm that the Fermi liquid persists at zero temperature even with nonzero Hund's coupling; however, at sufficient temperatures Hund's coupling significantly reduces the Fermi liquid regime and the system evolves into a typical Hund's metal. At the bare electronic occupancy of Sr$_2$RuO$_4$ ($t_{2g}^4$), a stronger Hund's metallicity accompanies a larger long-time correlator. Remarkably, electron doping further destabilizes the Fermi liquid even though the long-time correlator and magnetic fluctuations decrease upon doping. This suppression of the Fermi liquid is driven by the van Hove singularity above the Fermi level in Sr$_2$RuO$_4$, combined with an enhanced Van Vleck susceptibility by spin-orbit coupling. Such findings point to the important role that electronic structure plays in the behavior of Hund's metals, in addition to magnetic fluctuations.
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 …
We report the results of a combined study of the normal state resistivity and superconducting transition temperature $T_c$ of the unconventional superconductor Sr$_2$RuO$_4$ under uniaxial pressure. There is strong evidence that as well as driving $T_c$ through a maximum at $\sim$3.5 K, compressive strains $\varepsilon$ of nearly 1 % along the crystallographic [100] axis drive the $γ$ Fermi surface sheet through a Van Hove singularity, changing the temperature dependence of the resistivity from $T^2$ above and below the transition region to $T^{1.5}$ within it. This occurs in extremely pure si…
The single-layered ruthenate Sr$_2$RuO$_4$ is one of the most enigmatic unconventional superconductors. While for many years it was thought to be the best candidate for a chiral $p$-wave superconducting ground state, desirable for topological quantum computations, recent experiments suggest a singlet state, ruling out the original $p$-wave scenario. The superconductivity as well as the properties of the multi-layered compounds of the ruthenate perovskites are strongly influenced by a van Hove singularity in proximity of the Fermi energy. Tiny structural distortions move the van Hove singularit…
Multi-band quasi-particle calculations based on perturbation theory and dynamical mean field methods show that the creation of a photoemission hole state in Sr$_2$RuO$_4$ is associated with a highly anisotropic self-energy. Since the narrow Ru-derived $d_{xz,yz}$ bands are more strongly distorted by Coulomb correlations than the wide $d_{xy}$ band, charge is partially transferred from $d_{xz,yz}$ to $d_{xy}$, thereby shifting the $d_{xy}$ van Hove singularity close to the Fermi level.
We study the magnetic susceptibility in the normal state of Sr$_2$RuO$_4$ using dynamical mean-field theory including dynamical vertex corrections. Besides the well known incommensurate response, our calculations yield quasi-local spin fluctuations which are broad in momentum and centered around the $Γ$ point, in agreement with recent inelastic neutron scattering experiments [P. Steffens, et al., Phys. Rev. Lett. 122, 047004 (2019)]. We show that these quasi-local fluctuations are controlled by the Hund's coupling and account for the dominant contribution to the momentum-integrated response. W…
A paradigmatic case of multi-band Mott physics including spin-orbit and Hund's coupling is realised in Ca$_2$RuO$_4$. Progress in understanding the nature of this Mott insulating phase has been impeded by the lack of knowledge about the low-energy electronic structure. Here we provide -- using angle-resolved photoemission electron spectroscopy -- the band structure of the paramagnetic insulating phase of Ca$_2$RuO$_4$ and show how it features several distinct energy scales. Comparison to a simple analysis of atomic multiplets provides a quantitative estimate of the Hund's coupling $J=0.4$ eV. …
Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr$_2$RuO$_4$
Bu-Ali Sina University（布阿利·西纳大学）；University of Toronto（多伦多大学）；DelQuanTech Inc.（DelQuanTech公司）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京应用数学与物理研究所）
Recent experiments revealed non-Fermi-liquid resistivity in the unconventional superconductor Sr$_{2}$RuO$_{4}$ when strain pushes one of the Fermi surfaces close to a van Hove singularity. The origin of this behavior and whether it can be understood from a picture of well defined quasiparticles is unclear. We employ a Boltzmann transport analysis beyond the single relaxation-time approximation based on a single band which undergoes a Lifshitz transition, where the Fermi surface crosses a van Hove singularity, either due to uni-axial or epitaxial strain. First analytically investigating impuri…
We study the superconducting gap function of Sr$_2$RuO$_4$. By solving the linearized Eliashberg equation with a correlated pairing vertex extracted from a dynamical mean-field calculation we identify the dominant pairing channels. An analysis of the candidate gap functions in orbital and quasiparticle band basis reveals that an inter-orbital singlet pairing of even parity is in agreement with experimental observations. It reconciles in particular the occurrence of a two-component order parameter with the presence of line-nodes of quasiparticles along the c-axis in the superconducting phase. T…
Strain tuning Sr$_{2}$RuO$_{4}$ through the Lifshitz point, where the Van Hove singularity of the electronic spectrum crosses the Fermi energy, is expected to cause a change in the temperature dependence of the electrical resistivity from its Fermi liquid behavior $ρ\sim T^{2}$ to $ρ\sim T^{2}{\rm log}\left(1/T\right)$, a behavior consistent with experiments by Barber et al. [Phys. Rev. Lett. 120, 076601 (2018)]. This expectation originates from the same multi-band scattering processes with large momentum transfer that were recently shown to account for the linear in $T$ resistivity of the str…
The Hall coefficient $R_H$ of Sr$_2$RuO$_4$ exhibits a non-monotonic temperature dependence with two sign reversals. We show that this puzzling behavior is the signature of two crossovers which are key to the physics of this material. The increase of $R_H$ and the first sign change upon cooling are associated with a crossover into a regime of coherent quasiparticles with strong orbital differentiation of the inelastic scattering rates. The eventual decrease and the second sign change at lower temperature is driven by the crossover from inelastic to impurity-dominated scattering. This qualitati…
We propose an explanation for the temperature dependence of the resistivity of Cd$_2$Re$_2$O$_7$, including the regime above the structural phase transition at $T$=200 $^o$K. The mechanism involved relies on the existence of a strong van Hove singularity close to the Fermi surface, which is evidenced by relevant band structure calculations. The same mechanism has successfully described the $T$-linear resistivity of the cuprates and Sr$_2$RuO$_4$, and the one-particle scattering rate in the former materials, as corroborated by recent experiments. We describe a few predictions for Cd$_2$Re$_2$O$…
We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr$_2$RuO$_4$, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasi-particle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi liquid coherence scale is shown to be tunable by …
A van Hove singularity (VHS) often significantly amplifies the electronic instability of a crystalline solid, including correlation-induced phenomena such as Hund's metallicity. We perform a systematic study on the interplay between Hund's coupling and electronic structures with a VHS focusing on Hund's metallicity. We construct a simplified tight-binding model targeting cubic perovskite materials and test the effects of the VHS utilizing dynamical mean-field theory with an exact diagonalization solver. The quasiparticle weight and the low-frequency power exponent of the self-energy provide a …
The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clearly reveals the emergence of the Fermi-liquid state of Sr$_2$RuO$_4$. We find a two-stage screening process, where orbital fluctuations are screened at much higher energies than spin fluctuations, and…
We use Ru $L_3$-edge (2838.5 eV) resonant inelastic x-ray scattering (RIXS) to quantify the electronic structure of Ca$_2$RuO$_4$, a layered $4d$-electron compound that exhibits a correlation-driven metal-insulator transition and unconventional antiferromagnetism. We observe a series of Ru intra-ionic transitions whose energies and intensities are well described by model calculations. In particular, we find a $\rm{J}=0\rightarrow 2$ spin-orbit excitation at 320 meV, as well as Hund's-rule driven $\rm{S}=1\rightarrow 0$ spin-state transitions at 750 and 1000 meV. The energy of these three featu…
We calculate the in-plane Seebeck coefficient of Sr$_2$RuO$_4$ within a framework combining electronic structure and dynamical mean-field theory. We show that its temperature-dependence is consistent with entropic considerations embodied in the Kelvin formula, and that it provides a meaningful probe of the crossover out of the Fermi liquid regime into an incoherent metal. This crossover proceeds in two stages: the entropy of spin degrees of freedom is released around room-temperature while orbital degrees of freedom remain quenched up to much higher temperatures. This is confirmed by a direct …
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 "resi…
We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diag…
We study the static susceptibilities for charge and spin sectors in paramagnetic states for Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ in $0.5\leq x \leq 2$ within random phase approximation on the basis of an effective Ru $t_{2g}$ orbital Hubbard model. We find that several modes of spin fluctuation around $\boldq=(0,0)$ and $\boldq\sim(0.797π,0)$ are strongly enhanced for the model of $x=0.5$. This enhancement arises from the increase of the corresponding susceptibilities for the $d_{xy}$ orbital due to the rotation-induced modifications of the electronic structure for this orbital (i.e., the flattening of…
The strongly correlated insulator Ca$_{2}$RuO$_4$ is considered as a paradigmatic realization of both spin-orbital physics and a band-Mott insulating phase, characterized by orbitally selective coexistence of a band and a Mott gap. We present a high-resolution oxygen $K$-edge resonant inelastic X-ray scattering study of the antiferromagnetic Mott insulating state of Ca$_{2}$RuO$_4$. A set of low-energy ($\sim$80 and 400 meV) and high-energy ($\sim$1.3 and 2.2 eV) excitations are reported that show strong incident light polarization dependence. Our results strongly support a spin-orbit coupled …
The iso-electronic $d^{4}$ compounds of the $4d$ series show rich phase diagrams due to competing spin, charge and orbital degrees of freedom in presence of strong correlations and structural distortions. One such iso-electronic series, $Ca_{2-x}Sr_{x}RuO_{4}$, is studied within the GGA (and spin-orbit coupled GGA) plus DMFT formalism using the hybridization expansion of continuous time Quantum Monte Carlo solver. While the local dynamical correlations make $Sr_{2}RuO_{4}$ a Hund's metal, they drive $Ca_{2}RuO_{4}$ to a Mott insulating ground state. We study the dynamic and static single-parti…
We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate ($\mathrm{Sr}_2\mathrm{RuO}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. Nature 574, 72 (2019)]. The chir…
We investigate the magnetic instabilities of the nondegenerate (s-band) and a degenerate (d-band) Hubbard model in two dimensions using many-body effects due to the particle-particle diagrams and Hund's rule local correlations. The density of states and the position of Van Hove singularity change depending on the value of next-nearest neighbor hopping t'. The Stoner parameter is strongly reduced in the s-band case, and ferromagnetism survives only if electron density is small, and the band is almost flat at small momenta due to next-nearest neighbor hopping. In contrast, for the d-band case th…
We report a polarization-resolved Raman spectroscopy study of the orbital dependence of the quasiparticles properties in the prototypical multi-band Fermi liquid Sr\textsubscript{2}RuO\textsubscript{4}. We show that the quasiparticle scattering rate displays $ω^{2}$ dependence as expected for a Fermi liquid. Besides, we observe a clear polarization-dependence in the energy and temperature dependence of the quasiparticle scattering rate and mass, with the $d_{xz/yz}$ orbital derived quasiparticles showing significantly more robust Fermi liquid properties than the $d_{xy}$ orbital derived ones. …
We investigate superconducting pairing driven by electron-electron interactions in a theoretical model for monolayer MoS$_2$ with the temperature-flow functional renormalization group(fRG). At low doping, the dominant instability is toward odd-parity pairing with $f$-wave Mo-nearest-neighbor structure. We compute the fRG phase diagram versus electron doping below the van Hove filling of the conduction band. In the superconducting regime, the critical temperature grows with doping, comparable to the experiments. Near van Hove filling the system favors a ferromagnetic state. We demonstrate that …
The effects of uniaxial compressive stress on the normal state $^{17}$O nuclear magnetic resonance properties of the unconventional superconductor Sr$_{2}$RuO$_{4}$ are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal $\mathbf{a}$-axis strain $\varepsilon_{aa}\equiv\varepsilon_v$, that maximizes the superconducting transition temperature, $T_{c}$. The spin susceptibility weakly increases on lowering the temperature below $T$$\simeq$10 K, consistent with an enhanced density of states associated with passing the Fermi energy thro…
Van Hove singularity-induced multiple magnetic transitions in multi-orbital systems
School of Physics and Hangzhou Key Laboratory of Quantum Matter, Hangzhou Normal University（杭州师范大学物理学院与杭州量子物质重点实验室）；Center for Correlated Matter and School of Physics, Zhejiang University（浙江大学关联物质中心与物理学院）
Strontium ruthenate (Sr$_2$RuO$_4$) has long been thought to host a spin-triplet chiral $p$-wave superconducting state. However, the singletlike response observed in recent spin-susceptibility measurements casts serious doubts on this pairing state. Together with the evidence for broken time-reversal symmetry and a jump in the shear modulus $c_{66}$ at the superconducting transition temperature, the available experiments point towards an even-parity chiral superconductor with $k_z(k_x\pm ik_y)$-like $E_g$ symmetry, which has consistently been dismissed based on the quasi-two-dimensional electr…
The ruthenate family of layered perovskites has been a topic of intense interest with much work dedicated to understanding the superconducting state of the single layer, Sr$_2$RuO$_4$. Another longstanding puzzle is the lack of superconductivity in its sister compound, Sr$_3$Ru$_2$O$_7$, which constrains the possible superconducting mechanisms of Sr$_2$RuO$_4$. Here we address a microscopic mechanism that unifies superconducting and spin-density wave order in this family of materials. Beginning from a model of Sr$_2$RuO$_4$ featuring intraband pseudospin-singlet superconductivity originating f…
Layered perovskite ruthenium oxides exhibit a striking series of metal-insulator and magnetic-nonmagnetic phase transitions easily tuned by temperature, pressure, epitaxy, and nonlinear drive. In this work, we combine results from two complementary state of the art many-body methods, Auxiliary Field Quantum Monte Carlo and Dynamical Mean Field Theory, to determine the low-temperature phase diagram of Ca$_2$RuO$_4$. Both methods predict a low temperature, pressure-driven metal-insulator transition accompanied by a ferromagnetic-antiferromagnetic transition. The properties of the ferromagnetic s…
The anomalous charge transport observed in some strongly correlated metals raises questions as to the universal applicability of Landau Fermi liquid theory. The coherence temperature $T_{FL}$ for normal metals is usually taken to be the temperature below which $T^2$ is observed in the resistivity. Below this temperature, a Fermi liquid with well-defined quasiparticles is expected. However, metallic ruthenates in the Ruddlesden-Popper family, frequently show non-Drude low-energy optical conductivity and unusual $ω/T$ scaling, despite the frequent observation of $T^2$ dc resistivity. Herein we r…
We propose to combine the Trotter decomposition and a series expansion of the partition function for Hund's exchange coupling in a quantum Monte Carlo (QMC) algorithm for multiorbital systems that preserves spin and orbital rotational symmetries. This enables us to treat the Hund's (spin-flip and pair-hopping) terms, which is difficult in the conventional QMC method. To demonstrate this, we first apply the algorithm to study ferromagnetism in the two-orbital Hubbard model within the dynamical mean-field theory (DMFT). The result reveals that the preservation of the SU(2) symmetry in Hund's exc…
We report a study of magnetic, thermal, and transport properties of La(3+) substituted Sr2RuO4, performed in order to investigate the effects of additional electron doping in this correlated metal. A gradual enhancement of the electronic part of specific heat and a more drastic increase of the static magnetic susceptibility were observed in Sr(2-y)La(y)RuO(4) with increasing y. Furthermore, the quasi-two-dimensional Fermi-liquid behavior seen in pure Sr2RuO4 breaks down near the critical concentration y ~ 0.20. Combined with a realistic tight-binding model with rigid-band shift of Fermi level,…
Quantum Oscillations of $\mathrm{Sr}_2\mathrm{RuO}_4$ under c-Axis Uniaxial Stress
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学学院苏格兰大学物理联盟）；National Institute for Materials Science（国立材料研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）
Hund's pairing refers to Cooper pairing generated by onsite interactions that become attractive due to large Hund's exchange $J$. This is possible in multiorbital systems even when all local bare interactions are repulsive, since attraction in specific channels are given by certain linear combinations of interaction parameters. On the other hand, pairing processes such as the exchange of spin fluctuations, are also present. We compare these two mechanisms on an equal footing using electronic bands appropriate for different classes of multiorbital systems over a wide range of interaction parame…
We study the quantum many-body instabilities of interacting electrons with SU(2)$\times$SU(2) symmetry in spin and orbital degrees of freedom on the triangular lattice near van-Hove filling. Our work is motivated by effective models for the flat bands in hexagonal moiré heterostructures like twisted bilayer boron nitride and trilayer graphene-boron nitride systems. We consider an extended Hubbard model including onsite Hubbard and Hund's couplings, as well as nearest-neighbor exchange interactions and analyze the different ordering tendencies with the help of an unbiased functional renormaliza…
Hund's coupling in multiorbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing, which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears in the band basis as a pseudospin-singlet, with the momentum dependence determined by the SOC and the underlying triplet character remaining in the form of interband pairing active away from the Fermi energy. Here, we examine the role of momentum-dependent SOC in generating nontrivial pairing symmetries, as well as the hidden tr…
The interplay between multiple bands, sizable multi-band electronic correlations and strong spin-orbit coupling may conspire in selecting a rather unusual unconventional pairing symmetry in layered Sr$_{2}$RuO$_{4}$. This mandates a detailed revisit of the normal state and, in particular, the $T$-dependent incoherence-coherence crossover. Using a modern first-principles correlated view, we study this issue in the actual structure of Sr$_{2}$RuO$_{4}$ and present a unified and quantitative description of a range of unusual physical responses in the normal state. Armed with these, we propose tha…
Incoherent Spectral Weight Emerging from a Van Hove Singularity in a Kagome Metal
Donostia International Physics Center (DIPC)（多诺斯蒂亚国际物理中心）；University of the Basque Country (UPV/EHU)（巴斯克大学）；Aalto University School of Science（阿尔托大学理学院）；Department of Physics, University of Science and Technology of China（中国科学技术大学物理系）；CIC nanoGUNE（nanoGUNE创新中心）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Diamond Light Source Ltd（钻石光源有限公司）
We investigate the 5d transition metal oxide BaOsO$_3$ within a combination of density functional theory (DFT) and dynamical mean-field theory (DMFT), using a matrix-product-state impurity solver. BaOsO$_3$ has 4 electrons in the t$_{2g}$ shell akin to ruthenates but stronger spin-orbit coupling (SOC) and is thus expected to reveal an interplay of Hund's metal behavior with SOC. We explore the paramagnetic phase diagram as a function of SOC and Hubbard interaction strengths, identifying metallic, band (van-Vleck) insulating and Mott insulating regions. At the physical values of the two couplin…
Motivated by recent experiments on ABC-stacked rhombohedral trilayer graphene (RTG) which observed spin-valley symmetry-breaking and superconductivity, we study instabilities of the RTG metallic state to symmetry breaking orders. We find that interactions select the inter-valley coherent order (IVC) as the preferred ordering channel over a wide range, whose theoretically determined phase boundaries agree well with experiments on both the hole and electron doped sides. The Fermi surfaces near van Hove singularities admit partial nesting between valleys, which promotes both inter-valley supercon…
