Fermi surface and van Hove singularities in the itinerant Metamagnet Sr3Ru2O7

Hierarchy of Lifshitz Transitions in the Surface Electronic Structure of Sr_{2}RuO_{4} under Uniaxial Compression

We report the evolution of the electronic structure at the surface of the layered perovskite Sr_{2}RuO_{4} under large in-plane uniaxial compression, leading to anisotropic B_{1g} strains of ϵ_{xx}-ϵ_{yy}=-0.9±0.1%. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of Sr_{2}RuO_{4} hosts. From comparison to tight-binding modeling, we find that the strain is accommodated predominantly by bond-length changes rather than modifications of octahedral tilt and rotation angles. Our study sheds new light on the nature of structural distortions at oxide surfaces, and how targeted control of these can be used to tune density of state singularities to the Fermi level, in turn paving the way to the possible realization of rich collective states at the Sr_{2}RuO_{4} surface.

Atomic-scale imaging of emergent order at a magnetic field-induced Lifshitz transition

The phenomenology and radical changes seen in material properties traversing a quantum phase transition have captivated condensed matter research over the past decades. Strong electronic correlations lead to exotic electronic ground states, including magnetic order, nematicity, and unconventional superconductivity. Providing a microscopic model for these requires detailed knowledge of the electronic structure in the vicinity of the Fermi energy, promising a complete understanding of the physics of the quantum critical point. Here, we demonstrate such a measurement at the surface of Sr₃Ru₂O₇. Our results show that, even in zero field, the electronic structure is strongly C₂ symmetric and that a magnetic field drives a Lifshitz transition and induces a charge-stripe order. We track the changes of the electronic structure as a function of field via quasiparticle interference imaging at ultralow temperatures. Our results provide a complete microscopic picture of the field-induced changes of the electronic structure across the Lifshitz transition.

Differentiated roles of Lifshitz transition on thermodynamics and superconductivity in La2-xSrxCuO4

The effect of Lifshitz transition on thermodynamics and superconductivity in hole-doped cuprates has been heavily debated but remains an open question. In particular, an observed peak of electronic specific heat is proposed to originate from fluctuations of a putative quantum critical point p* (e.g., the termination of pseudogap at zero temperature), which is close to but distinguishable from the Lifshitz transition in overdoped La-based cuprates where the Fermi surface transforms from hole-like to electron-like. Here we report an in situ angle-resolved photoemission spectroscopy study of three-dimensional Fermi surfaces in La_2-xSr_xCuO₄ thin films (x = 0.06 to 0.35). With accurate k_z dispersion quantification, the said Lifshitz transition is determined to happen within a finite range around x = 0.21. Normal state electronic specific heat, calculated from spectroscopy-derived band parameters, reveals a doping-dependent profile with a maximum at x = 0.21 that agrees with previous thermodynamic microcalorimetry measurements. The account of the specific heat maximum by underlying band structures excludes the need for additionally dominant contribution from the quantum fluctuations at p*. A d-wave superconducting gap smoothly across the Lifshitz transition demonstrates the insensitivity of superconductivity to the dramatic density of states enhancement.

Magnetic-Field Tunable Intertwined Checkerboard Charge Order and Nematicity in the Surface Layer of Sr2 RuO4

In strongly correlated electron materials, the electronic, spin, and charge degrees of freedom are closely intertwined. This often leads to the stabilization of emergent orders that are highly sensitive to external physical stimuli promising opportunities for technological applications. In perovskite ruthenates, this sensitivity manifests in dramatic changes of the physical properties with subtle structural details of the RuO₆ octahedra, stabilizing enigmatic correlated ground states, from a hotly debated superconducting state via electronic nematicity and metamagnetic quantum criticality to ferromagnetism. Here, it is demonstrated that the rotation of the RuO₆ octahedra in the surface layer of Sr₂ RuO₄ generates new emergent orders not observed in the bulk material. Through atomic-scale spectroscopic characterization of the low-energy electronic states, four van Hove singularities are identified in the vicinity of the Fermi energy. The singularities can be directly linked to intertwined nematic and checkerboard charge order. Tuning of one of these van Hove singularities by magnetic field is demonstrated, suggesting that the surface layer undergoes a Lifshitz transition at a magnetic field of ≈32T. The results establish the surface layer of Sr₂ RuO₄ as an exciting 2D correlated electron system and highlight the opportunities for engineering the low-energy electronic states in these systems.

Lifshitz transition underlying the metamagnetic transition of UPt3

Comparing quantum oscillation measurements, dc magnetoresistance measurements, and Fermi surfaces obtained from LDA calculations, we argue that the metamagnetic transition of UPt₃, which occurs at an applied field μ _◦ H _M ∼ 20 T, coincides with a Lifshitz transition at which an open orbit on the band 2 hole-like Fermi surface becomes closed for one spin direction. At low field, proximity of the Fermi energy to this particular van Hove singularity may have implications for the superconducting pairing potential of UPt₃. In our picture the magnetization comes from non-linear spin-splitting of the heavy fermion bands. In support of this, we show that the non-linear field dependence of a particular quantum oscillation frequency can be fitted by assuming that the corresponding extremal Fermi surface area is proportional to the magnetization. In addition, below H _M , we find in our LDA calculations a new, non-central orbit on band 1, whose non-linear behaviour explains a field-dependent frequency recently observed in magnetoacoustic quantum oscillation measurements.

Fermi surface and kink structures in [Formula: see text] revealed by synchrotron-based ARPES

The low-energy electronic structure, including the Fermi surface topology, of the itinerant metamagnet [Formula: see text] is investigated for the first time by synchrotron-based angle-resolved photoemission. Well-defined quasiparticle band dispersions with matrix element dependencies on photon energy or photon polarization are presented. Four bands crossing the Fermi-level, giving rise to four Fermi surface sheets are resolved; and their complete topography, effective mass as well as their electron and hole character are determined. These data reveal the presence of kink structures in the near-Fermi-level band dispersion, with energies ranging from 30 to 69 meV. Together with previously reported Raman spectroscopy and lattice dynamic calculation studies, the data suggest that these kinks originate from strong electron-phonon coupling present in [Formula: see text]. Considering that the kink structures of [Formula: see text] are similar to those of the other three members of the Ruddlesden Popper structured ruthenates, the possible universality of strong coupling of electrons to oxygen-related phonons in [Formula: see text] compounds is proposed.

Theory of the strange metal Sr3Ru2O7

The bilayer perovskite Sr3Ru2O7 has been widely studied as a canonical strange metal. It exhibits T-linear resistivity and a T log(1/T) electronic specific heat in a field-tuned quantum critical fan. Criticality is known to occur in "hot" Fermi pockets with a high density of states close to the Fermi energy. We show that while these hot pockets occupy a small fraction of the Brillouin zone, they are responsible for the anomalous transport and thermodynamics of the material. Specifically, a scattering process in which two electrons from the large, "cold" Fermi surfaces scatter into one hot and one cold electron renders the ostensibly noncritical cold fermions a marginal Fermi liquid. From this fact the transport and thermodynamic phase diagram is reproduced in detail. Finally, we show that the same scattering mechanism into hot electrons that are instead localized near a 2D van Hove singularity explains the anomalous transport observed in strained Sr2RuO4.

Magic of high-order van Hove singularity

The van Hove singularity in density of states generally exists in periodic systems due to the presence of saddle points of energy dispersion in momentum space. We introduce a new type of van Hove singularity in two dimensions, resulting from high-order saddle points and exhibiting power-law divergent density of states. We show that high-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field. Correlation effects from high-order van Hove singularity near Fermi level are also discussed.

Multicritical Fermi Surface Topological Transitions

A wide variety of complex phases in quantum materials are driven by electron-electron interactions, which are enhanced through density of states peaks. A well-known example occurs at van Hove singularities where the Fermi surface undergoes a topological transition. Here we show that higher order singularities, where multiple disconnected leaves of Fermi surface touch all at once, naturally occur at points of high symmetry in the Brillouin zone. Such multicritical singularities can lead to stronger divergences in the density of states than canonical van Hove singularities, and critically boost the formation of complex quantum phases via interactions. As a concrete example of the power of these Fermi surface topological transitions, we demonstrate how they can be used in the analysis of experimental data on Sr_{3}Ru_{2}O_{7}. Understanding the related mechanisms opens up new avenues in material design of complex quantum phases.

Coulomb correlations in 4d and 5d oxides from first principles-or how spin-orbit materials choose their effective orbital degeneracies

The interplay of spin-orbit coupling and Coulomb correlations has become a hot topic in condensed matter theory and is especially important in 4d and 5d transition metal oxides, like iridates or rhodates. Here, we review recent advances in dynamical mean-field theory (DMFT)-based electronic structure calculations for treating such compounds, introducing all necessary implementation details. We also discuss the evaluation of Hubbard interactions in spin-orbit materials. As an example, we perform DMFT calculations on insulating strontium iridate (Sr₂IrO₄) and its 4d metallic counterpart, strontium rhodate (Sr₂RhO₄). While a Mott-insulating state is obtained for Sr₂IrO₄ in its paramagnetic phase, the spectral properties and Fermi surfaces obtained for Sr₂RhO₄ show excellent agreement with available experimental data. Finally, we discuss the electronic structure of these two compounds by introducing the notion of effective spin-orbital degeneracy as the key quantity that determines the correlation strength. We stress that effective spin-orbital degeneracy introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth, analogous to the degeneracy-controlled Mott transition in d¹ perovskites.

Strain and vector magnetic field tuning of the anomalous phase in Sr3Ru2O7

A major area of interest in condensed matter physics is the way electrons in correlated electron materials can self-organize into ordered states, and a particularly intriguing possibility is that they spontaneously choose a preferred direction of conduction. The correlated electron metal Sr₃Ru₂O₇ has an anomalous phase at low temperatures that features strong susceptibility toward anisotropic transport. This susceptibility has been thought to indicate a spontaneous anisotropy, that is, electronic order that spontaneously breaks the point-group symmetry of the lattice, allowing weak external stimuli to select the orientation of the anisotropy. We investigate further by studying the response of Sr₃Ru₂O₇ in the region of phase formation to two fields that lift the native tetragonal symmetry of the lattice: in-plane magnetic field and orthorhombic lattice distortion through uniaxial pressure. The response to uniaxial pressure is surprisingly strong: Compressing the lattice by ~0.1% induces an approximately 100% transport anisotropy. However, neither the in-plane field nor the pressure phase diagrams are qualitatively consistent with spontaneous symmetry reduction. Instead, both are consistent with a multicomponent order parameter that is likely to preserve the point-group symmetry of the lattice, but is highly susceptible to perturbation.

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.

Multiple Metamagnetic Quantum Criticality in Sr_{3}Ru_{2}O_{7}

Bilayer strontium ruthenate Sr_{3}Ru_{2}O_{7} displays pronounced non-Fermi liquid behavior at magnetic fields around 8 T, applied perpendicular to the ruthenate planes, which previously has been associated with an itinerant metamagnetic quantum critical end point (QCEP). We focus on the magnetic Grüneisen parameter Γ_{H}, which is the most direct probe to characterize field-induced quantum criticality. We confirm quantum critical scaling due to a putative two-dimensional QCEP near 7.845(5) T, which is masked by two ordered phases A and B, identified previously by neutron scattering. In addition, we find evidence for a QCEP at 7.53(2) T and determine the quantum critical regimes of both instabilities and the effect of their superposition.

Field-tunable spin-density-wave phases in Sr3Ru2O7

The conduction electrons in a metal experience competing interactions with each other and the atomic nuclei. This competition can lead to many types of magnetic order in metals. For example, in chromium the electrons order to form a spin-density-wave (SDW) antiferromagnetic state. A magnetic field may be used to perturb or tune materials with delicately balanced electronic interactions. Here, we show that the application of a magnetic field can induce SDW magnetic order in a quasi-2D metamagnetic metal, where none exists in the absence of the field. We use magnetic neutron scattering to show that the application of a large (B ≈ 8 T) magnetic field to the perovskite metal Sr3Ru2O7 (refs 3-7) can be used to tune the material through two magnetically ordered SDW states. The ordered states exist over relatively small ranges in field (≲0.4 T), suggesting that their origin is due to a new mechanism related to the electronic fine structure near the Fermi energy, possibly combined with the stabilizing effect of magnetic fluctuations. The magnetic field direction is shown to control the SDW domain populations, which naturally explains the strong resistivity anisotropy or 'electronic nematic' behaviour observed in this material.

Carrier localization and electronic phase separation in a doped spin-orbit-driven Mott phase in Sr₃(Ir(1-x)Ru(x))₂O₇

Interest in many strongly spin-orbit-coupled 5d-transition metal oxide insulators stems from mapping their electronic structures to a J(eff)=1/2 Mott phase. One of the hopes is to establish their Mott parent states and explore these systems' potential of realizing novel electronic states upon carrier doping. However, once doped, little is understood regarding the role of their reduced Coulomb interaction U relative to their strongly correlated 3d-electron cousins. Here we show that, upon hole-doping a candidate J(eff)=1/2 Mott insulator, carriers remain localized within a nanoscale phase-separated ground state. A percolative metal-insulator transition occurs with interplay between localized and itinerant regions, stabilizing an antiferromagnetic metallic phase beyond the critical region. Our results demonstrate a surprising parallel between doped 5d- and 3d-electron Mott systems and suggest either through the near-degeneracy of nearby electronic phases or direct carrier localization that U is essential to the carrier response of this doped spin-orbit Mott insulator.

Similarity of scattering rates in metals showing T-linear resistivity

Many exotic compounds, such as cuprate superconductors and heavy fermion materials, exhibit a linear in temperature (T) resistivity, the origin of which is not well understood. We found that the resistivity of the quantum critical metal Sr(3)Ru(2)O(7) is also T-linear at the critical magnetic field of 7.9 T. Using the precise existing data for the Fermi surface topography and quasiparticle velocities of Sr(3)Ru(2)O(7), we show that in the region of the T-linear resistivity, the scattering rate per kelvin is well approximated by the ratio of the Boltzmann constant to the Planck constant divided by 2π. Extending the analysis to a number of other materials reveals similar results in the T-linear region, in spite of large differences in the microscopic origins of the scattering.

Thermodynamics of phase formation in the quantum critical metal Sr3Ru2O7

The behavior of matter near zero temperature continuous phase transitions, or "quantum critical points" is a central topic of study in condensed matter physics. In fermionic systems, fundamental questions remain unanswered: the nature of the quantum critical regime is unclear because of the apparent breakdown of the concept of the quasiparticle, a cornerstone of existing theories of strongly interacting metals. Even less is known experimentally about the formation of ordered phases from such a quantum critical "soup." Here, we report a study of the specific heat across the phase diagram of the model system Sr(3)Ru(2)O(7), which features an anomalous phase whose transport properties are consistent with those of an electronic nematic. We show that this phase, which exists at low temperatures in a narrow range of magnetic fields, forms directly from a quantum critical state, and contains more entropy than mean-field calculations predict. Our results suggest that this extra entropy is due to remnant degrees of freedom from the highly entropic state above T(c). The associated quantum critical point, which is "concealed" by the nematic phase, separates two Fermi liquids, neither of which has an identifiable spontaneously broken symmetry, but which likely differ in the topology of their Fermi surfaces.

Probing bulk electronic structure with hard X-ray angle-resolved photoemission

Traditional ultraviolet/soft X-ray angle-resolved photoemission spectroscopy (ARPES) may in some cases be too strongly influenced by surface effects to be a useful probe of bulk electronic structure. Going to hard X-ray photon energies and thus larger electron inelastic mean-free paths should provide a more accurate picture of bulk electronic structure. We present experimental data for hard X-ray ARPES (HARPES) at energies of 3.2 and 6.0 keV. The systems discussed are W, as a model transition-metal system to illustrate basic principles, and GaAs, as a technologically-relevant material to illustrate the potential broad applicability of this new technique. We have investigated the effects of photon wave vector on wave vector conservation, and assessed methods for the removal of phonon-associated smearing of features and photoelectron diffraction effects. The experimental results are compared to free-electron final-state model calculations and to more precise one-step photoemission theory including matrix element effects.

The Kondo-lattice state and non-Fermi-liquid behavior in the presence of Van Hove singularities

A scaling consideration of the Kondo lattices is performed with account of logarithmic Van Hove singularities (VHS) in the electron density of states. The scaling trajectories are presented for different magnetic phases. It is demonstrated that VHS lead to a considerable increase of the non-Fermi-liquid behavior region owing to softening of magnon branches during the renormalization process. Although the effective coupling constant remains moderate, the renormalized magnetic moment and spin-fluctuation frequency can decrease by several orders of magnitude. A possible application to f-systems and weak itinerant magnets is discussed.

Strong electron correlations in the normal state of the iron-based FeSe0.42Te0.58 superconductor observed by angle-resolved photoemission spectroscopy

We investigate the normal state of the "11" iron-based superconductor FeSe0.42Te0.58 by angle-resolved photoemission. Our data reveal a highly renormalized quasiparticle dispersion characteristic of a strongly correlated metal. We find sheet dependent effective carrier masses between approximately 3 and 16m{e} corresponding to a mass enhancement over band structure values of m{*}/m{band} approximately 6-20. This is nearly an order of magnitude higher than the renormalization reported previously for iron-arsenide superconductors of the "1111" and "122" families but fully consistent with the bulk specific heat.

Spectroscopic imaging scanning tunneling microscopy as a probe of orbital structures and ordering

Unlike charge and spin, the orbital degree of freedom of electrons in transition metal oxides is difficult to detect. We present a theoretical study of a new detection method in metallic orbitally active systems by analyzing the quasiparticle scattering interference (QPI) pattern of the spectroscopic imaging scanning tunneling spectroscopy, which is sensitive to orbital structures and orbital ordering. The QPIs for the d(xz) and d(yz)-orbital bands in the t(2g)-orbital systems show a characteristic stripelike feature as a consequence of their quasi-one-dimensional nature, which is robust against orbital hybridization. With the occurrence of orbital ordering proposed in Sr3Ru2O7 and iron pnictides, the stripelike QPI patterns exhibit nematic distortion breaking the C4 symmetry.

Quantum oscillations in the anomalous phase in Sr3Ru2O7

We report measurements of quantum oscillations detected in the putative nematic phase of Sr3Ru2O7. Improvements in sample purity enabled the resolution of small amplitude de Haas-van Alphen (dHvA) oscillations between two first order metamagnetic transitions delimiting the phase. Two distinct frequencies were observed, whose amplitudes follow the normal Lifshitz-Kosevich profile. Variations of the dHvA frequencies are explained in terms of a chemical potential shift produced by reaching a peak in the density of states, and an anomalous field dependence of the oscillatory amplitude provides information on domains.

Inhomogeneous magnetic phases: a Fulde-Ferrell-Larkin-Ovchinnikov-like phase in Sr3Ru2O7

The phase diagram of Sr3Ru2O7 contains a metamagnetic transition that bifurcates to enclose an anomalous phase with intriguing properties--a large resistivity with anisotropy that breaks the crystal-lattice symmetry. We propose that this is a magnetic analogue of the spatially inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We show-through a Ginzburg-Landau expansion where the magnetization transverse to the applied field can become spatially inhomogeneous-that a Stoner model with electronic band dispersion can reproduce this phase diagram and transport behavior.