Hidden Bose–Einstein Singularities of Correlated Electron Systems: III. Thermodynamic Signals

Femtosecond real-time spectroscopy is an emerging new tool for studying low energyelectronic structure in correlated electron systems. Motivated by recent advances inunderstanding the nature of relaxation phenomena in various correlated electron systems(superconductors, density wave systems) the technique has been applied to heavy electroncompounds in comparison with their non-magnetic counterparts. While the dynamics intheir non-magnetic analogues are similar to the dynamics observed in noble metals (onlyweak temperature dependences are observed) and can be treated with a simpletwo-temperature model, the photoexcited carrier dynamics in heavy electron systems showdramatic changes as a function of temperature and excitation level. In particular, belowsome characteristic temperature the relaxation rate starts to decrease, dropping by morethan two orders of magnitude upon cooling down to liquid He temperatures. Thisbehaviour has been consistently observed in various heavy fermion metals as well as Kondoinsulators, and is believed to be quite general. In order to account for the experimentalobservations, two theoretical models have been proposed. The first treats theheavy electron systems as simple metals with very flat electron dispersion near theFermi level. An electron–phonon thermalization scenario can account for theobserved slowing down of the relaxation provided that there exists a mechanism forsuppression of electron–phonon scattering when both the initial and final electronicstates lie in the region of flat dispersion. An alternative scenario argues that therelaxation dynamics in heavy electron systems are governed by the Rothwarf–Taylorbottleneck, where the dynamics are governed by the presence of a narrow gapin the density of states near the Fermi level. The so-called hybridization gapresults from hybridization between localized moments and the conduction electronbackground. Remarkable agreement with the model suggests that carrier relaxation in abroad class of heavy electron systems (both metals and insulators) is governed bythe presence of a (weakly temperature dependent) indirect hybridization gap.Here we review the experimental results on a variety of heavy electron compounds, pointout the common features as well as the peculiarities observed in some compounds, andcompare the data with existing theoretical models.

Mechanism of resonant X-ray scattering to observe the orbital ordering

The emergence of novel quantum ground states in correlated electron systems with strong spin–orbit coupling has been a recent subject of intensive studies. While it has been realized that spin–orbit coupling can provide non-trivial band topology in weakly interacting electron systems, as in topological insulators and semi-metals, the role of electron–electron interaction in strongly spin–orbit coupled systems has not been fully understood. The availability of new materials with significant electron correlation and strong spin–orbit coupling now makes such investigations possible. Many of these materials contain 5d or 4d transition metal elements; the prominent examples are iridium oxides or iridates. In this review, we succinctly discuss recent theoretical and experimental progress on this subject. After providing a brief overview, we focus on pyrochlore iridates and three-dimensional honeycomb iridates. In pyrochlore iridates, we discuss the quantum criticality of the bulk and surface states, and the relevance of the surface/boundary states in a number of topological and magnetic ground states, both in the bulk and thin film configurations. Experimental signatures of these boundary and bulk states are discussed. Domain wall formation and strongly-direction-dependent magneto-transport are also discussed. In regard to the three-dimensional honeycomb iridates, we consider possible quantum spin liquid phases and unusual magnetic orders in theoretical models with strongly bond-dependent interactions. These theoretical ideas and results are discussed in light of recent resonant x-ray scattering experiments on three-dimensional honeycomb iridates. We also contrast these results with the situation in two-dimensional honeycomb iridates. We conclude with the outlook on other related systems.

Critical properties of one-dimensional (1D) correlated electron systems with a mobile impurity are investigated. By applying the finite-size scaling method to a Bethe-ansatz solvable model, we derive the conformal dimensions related to the orthogonality catastrophe. We then apply the results to the Fermi-edge singularity in quantum wires, and clarify how the critical exponent for X-ray absorption depends on the mass of the core-hole created. A generalization to SU(\(\)) electron systems is outlined based on the g-on description of 1D electron systems.

Half-filled electron systems, even with the maximized spin angular moment, have been given little attention because of their zero-orbital angular moment according to Hund's rule. Nevertheless, there are several measurements that show evidence of a nonzero orbital moment as well as spin-orbit coupling. Here we report for the first time the orbital order in a half-filled 4f-electron system GdB_{4}, using the resonant soft x-ray scattering at Gd M_{4,5}-edges. Furthermore, we discovered that the development of this orbital order is strongly coupled with the antiferromagnetic spin order. These results clearly demonstrate that even in half-filled electron systems the orbital angular moment can be an important parameter to describe material properties, and may provide significant opportunities for tailoring new correlated electron systems.

This research project examined the changes in electronic and magnetic properties of transition metals and oxides under applied pressures, focusing on complex relationship between magnetism and phase stability in these correlated electron systems. As part of this LDRD project, we developed new measurement techniques and adapted synchrotron-based electronic and magnetic measurements for use in the diamond anvil cell. We have performed state-of-the-art X-ray spectroscopy experiments at the dedicated high-pressure beamline HP-CAT (Sector 16 Advanced Photon Source, Argonne National Laboratory), maintained in collaboration with of University of Nevada, Las Vegas and Geophysical Laboratory of The Carnegie Institution of Washington. Using these advanced measurements, we determined the evolution of the magnetic order in the ferromagnetic 3d transition metals (Fe, Co and Ni) under pressure, and found that at high densities, 3d band broadening results in diminished long range magnetic coupling. Our experiments have allowed us to paint a unified picture of the effects of pressure on the evolution of magnetic spin in 3d electron systems. The technical and scientific advances made during this LDRD project have been reported at a number of scientific meetings and conferences, and have been submitted for publication in technical journals. Both the technical advances and the physicalmore » understanding of correlated systems derived from this LDRD are being applied to research on the 4f and 5f electron systems under pressure.« less

Until the mid-1980s, condensed matter physicists were contented with the nearly independent electron model or quasiparticle picture developed out of weakly interacting Fermions. Discoveries of high Tc superconductivity in oxides and other exotic systems, namely heavy Fermion systems, colossal magnetoresistive manganites, metal-insulator transition in two dimensions etc presented a variety of formidable challenges to work within the conventional ideas. Soon it became clear that there is a need to develop microscopic theories of correlated electron systems. There one has to take into account explicit inter-electron Coulomb interactions to understand several remarkable properties of these novel materials. Since last two decades the 'correlated electron systems' remain at the forefront of condensed matter physics. Experimental techniques and fine measurements (angle-resolved photoemission, optical, tunnelling and neutron scattering studies etc.) are far ahead of the theory. Mathematical formalism dwells a lot on the field theoretical techniques. Numerical simulation is undergoing rapid advancement. Charge and spin degrees of electrons, phonons and their interaction with electrons contribute non-trivially to the exotic properties. If we consider the example of high Tc oxides, we start with the parent undoped material as a highly correlated antiferromagnetic Mott insulator. Under hole/electron doping, the system becomes a superconductor with d-wave pairing. Here we encounter several phase changes as doping continues. In particular, the understanding of the normal state (above the superconducting phase) poses enormous difficulties in terms of their anomalous properties. Now a large number of researchers are working on various important aspects of this unresolved issue. However, there is no clear consensus. As well as posing the deepest intellectual challenges on fundamentals, these materials offer new possibilities for technological applications. This special issue presents invited articles from some of the leading exponents of this fascinating field of research.

The Hefei Advanced Light Facility is the fourth-generation diffraction-limited storage ring light source, scheduled to begin operation in 2028. With its high-brightness and highly coherent X-rays, it will break through the current spatiotemporal resolution bottlenecks of X-ray techniques in studying correlated electron systems, providing crucial information for understanding the nature and microscopic origins of novel physical properties in these materials. This article introduces the main scientific goals and technical advantages of the Hefei Advanced Light Facility, focusing on the application perspectives of advanced technologies such as angle-resolved photoemission spectroscopy, magnetic circular dichroism, coherent X-ray scattering, and coherent X-ray imaging in researches of quantum materials and correlated electron systems. These techniques will enable the detailed analysis of the distribution and dynamics of electronic/spin/orbital states, reveal various novel quantum phenomena, and elucidate the fluctuations of order parameters in correlated electron systems. The completion of the Hefei Advanced Light Facility will provide advanced technical supports for decoding complex quantum states and non-equilibrium properties, ultimately promoting the application of quantum materials and correlated electron systems in frontier fields such as energy and information.

Electron-phonon (e-ph) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons, and metal-insulator transitions. First-principles approaches enable accurate calculations of e-ph interactions in a wide range of solids. However, they remain an open challenge in correlated electron systems (CES), where density functional theory often fails to describe the ground state. Therefore reliable e-ph calculations remain out of reach for many transition metal oxides, high-temperature superconductors, Mott insulators, planetary materials, and multiferroics. Here we show first-principles calculations of e-ph interactions in CES, using the framework of Hubbard-corrected density functional theory (DFT+U) and its linear response extension (DFPT+U), which can describe the electronic structure and lattice dynamics of many CES. We showcase the accuracy of this approach for a prototypical Mott system, CoO, carrying out a detailed investigation of its e-ph interactions and electron spectral functions. While standard DFPT gives unphysically divergent and short-ranged e-ph interactions, DFPT+U is shown to remove the divergences and properly account for the long-range Fröhlich interaction, allowing us to model polaron effects in a Mott insulator. Our work establishes a broadly applicable and affordable approach for quantitative studies of e-ph interactions in CES, a novel theoretical tool to interpret experiments in this broad class of materials.

We study a magnetic impurity embedded in a correlated electron system using the density-matrix renormalization group method. The correlated electron system is described by the one-dimensional Hubbard model. At half filling, we confirm that the binding energy of the singlet bound state increases exponentially in the weak-coupling regime and decreases inversely proportional to the correlation in the strong-coupling regime. The spin-spin correlation shows an exponential decay with distance from the impurity site. The correlation length becomes smaller with increasing the correlation strength. We find discontinuous reduction of the binding energy and of spin-spin correlations with hole doping. The binding energy is reduced by hole doping; however, it remains of the same order of magnitude as for the half-filled case.

We report on the direct observation of the thermoelectric transport in a nondegenerate electron system trapped on the surface of liquid helium. The microwave-induced excitation of the vertical transitions of electrons between the surface-bound states results in their lateral flow, which we were able to detect by employing a segmented electrode configuration. We show that this flow of electrons arises due to the Seebeck effect. Our experimental results are in good agreement with the theoretical calculations based on kinetic equations. This demonstrates the importance of the fast electron-electron collisions, which, in particular, leads to the violation of the Wiedemann-Franz law in this system.

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum–space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high [Formula: see text] superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high [Formula: see text] cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.

We propose an efficient method for nonperturbative calculation of Green’s function in acorrelated electron system. The key idea of the method is to project out irrelevantoperators having zero norm in the ground state, which we refer to as effective projectiontheory. We apply the method to a mesoscopic Anderson model and show that for agiven wavefunction ansatz, equations of motion can be closed only by relevantoperators, allowing easy calculation of the zero-temperature Green’s function. Itturns out that the resulting Green’s functions reproduce exact limits of bothweak and strong interactions. The accuracy is also verified for small systems bycomparison with exact diagonalization results, revealing that effective projection theorycaptures the essential correlated features in the entire regime of interactions.

Recent progress in conformai field theory enables us to precisely treat the critical phenomena in (1 + 1)-dimension. We review how conformai field theory applies to correlated electron systems in one dimension and explain the way of exact calculation of the correlation exponents. We demonstrate that conformai field theory provides the microscopic foundation of the Luttinger liquid which describes the universal behavior of 1D correlated electron systems.

We introduce the notion of superstructure Mottness to describe the Mott and Wigner-Mott transition in doped strongly correlated electron systems at commensurate filling fractions away from one electron per site. We show that superstructure Mottness emerges in an inhomogeneous electron system when the superstructure contains an odd number of electrons per supercell. We argue that superstructure Mottness exists even in the absence of translation symmetry breaking by a superlattice, provided that the extended or intersite Coulomb interaction is strong. In the latter case, superstructure Mottness offers a unifying framework for the Mott and Wigner physics and a nonperturbative, strong coupling description of the Wigner-Mott transition. We support our proposal by studying a minimal single-band ionic Hubbard $t$-$U$-$V$-$\Delta$ model with nearest neighbor Coulomb repulsion $V$ and a two-sublattice ionic potential $\Delta$. The model is mapped onto a Hubbard model with two effective ``orbitals'' representing the two sites within the supercell, the intra and interorbital Coulomb repulsion $U$ and $U^\prime \sim V$, and a crystal field splitting $\Delta$. Charge order on the original lattice corresponds to orbital order. Developing a cluster Gutzwiller approximation, we study the effects and the interplay between $V$ and $\Delta$ on the Mott and Wigner-Mott transitions at quarter-filling. We provide the mechanism by which the superlattice potential enhances the correlation effects and the tendency towards local moment formation, construct and elucidate the phase diagram in the unifying framework of superstructure Mottness.