Entanglement of edge modes in (very) strongly correlated topological insulators

Identifying topological phases for a strongly correlated theory remains a non-trivial task, as defining order parameters, such as Berry phases, is not straightforward. Quantum information theory is capable of identifying topological phases for a theory that exhibits quantum phase transition with a suitable definition of order parameters that are related to different entanglement measures for the system. In this work, we study entanglement entropy for a coupled SSH model, both in the presence and absence of Hubbard interaction and at varying interaction strengths. For the free theory, edge entanglement acts as an order parameter, which is supported by analytic calculations and numerical (DMRG) studies. We calculate the symmetry-resolved entanglement and demonstrate the equipartition of entanglement for this model which itself acts as an order parameter when calculated for the edge modes. As the DMRG calculation allows one to go beyond the free theory, we study the entanglement structure of the edge modes in the presence of on-site Hubbard interaction for the same model. A sudden reduction of edge entanglement is obtained as interaction is switched on. The explanation for this lies in the change in the size of the degenerate subspaces in the presence and absence of interaction. We also study the signature of entanglement when the interaction strength becomes extremely strong and demonstrate that the edge entanglement remains protected. In this limit, the energy eigenstates essentially become a tensor product state, implying zero entanglement. However, a remnant entropy survives in the non-trivial topological phase, which is exactly due to the entanglement of the edge modes.

Realization of Organocerium-Based Fullerene Molecular Materials Showing Mott Insulator-Type Behavior

Electron-rich organocerium complexes (C5Me4H)3Ce and [(C5Me5)2Ce(ortho-oxa)], with redox potentials E1/2 = -0.82 V and E1/2 = -0.86 V versus Fc/Fc+, respectively, were reacted with fullerene (C60) in different stoichiometries to obtain molecular materials. Structurally characterized cocrystals: [(C5Me4H)3Ce]2·C60 (1) and [(C5Me5)2Ce(ortho-oxa)]3·C60 (2) of C60 with cerium-based, molecular rare earth precursors are reported for the first time. The extent of charge transfer in 1 and 2 was evaluated using a series of physical measurements: FT-IR, Raman, solid-state UV-vis-NIR spectroscopy, X-ray absorption near-edge structure (XANES) spectroscopy, and magnetic susceptibility measurements. The physical measurements indicate that 1 and 2 comprise the cerium(III) oxidation state, with formally neutral C60 as a cocrystal in both cases. Pressure-dependent periodic density functional theory calculations were performed to study the electronic structure of 1. Inclusion of a Hubbard-U parameter removes Ce f states from the Fermi level, opens up a band gap, and stabilizes FM/AFM magnetic solutions that are isoenergetic because of the large distances between the Ce(III) cations. The electronic structure of this strongly correlated Mott insulator-type system is reminiscent of the well-studied Ce2O3.

Influence of magnetic field on the electronic ferroelectricity in the extended Falicov-Kimball model

The density-matrix-renormalization-group method is used to study the influence of external magnetic field on the stability of the excitonic phase induced by local hybridization in the one-dimensional spin-1/2 Falicov-Kimball model. It is shown that a fine tuning of external magnetic field through the quantum critical point is able to induce significant changes (continuous as well as discontinuous) in the excitonic⟨d+f⟩expectation average providing new set of physical properties and technological applications, like possibilities of faster switching ferroelectrics and controlling their optical properties with magnetic fields. Moreover, effects of some other interactions (which may be present in reald-fmaterials) on the stability of excitonic phase are examined and it is shown that the Hubbard interaction in thed-electron subsystem, the interbandd-fCoulomb interaction, as well as the exchanged-finteraction stabilize significantly excitonic correlations below the quantum critical point, while the anisotropic spin-dependent interaction of the Ising type betweenfanddelectrons as well as thef-electron hopping suppress the excitonic correlations for magnetic fields below as well as above the quantum critical point.

Ubiquitous coexisting electron-mode couplings in high-temperature cuprate superconductors

In conventional superconductors, electron-phonon coupling plays a dominant role in generating superconductivity. In high-temperature cuprate superconductors, the existence of electron coupling with phonons and other boson modes and its role in producing high-temperature superconductivity remain unclear. The evidence of electron-boson coupling mainly comes from angle-resolved photoemission (ARPES) observations of [Formula: see text]70-meV nodal dispersion kink and [Formula: see text]40-meV antinodal kink. However, the reported results are sporadic and the nature of the involved bosons is still under debate. Here we report findings of ubiquitous two coexisting electron-mode couplings in cuprate superconductors. By taking ultrahigh-resolution laser-based ARPES measurements, we found that the electrons are coupled simultaneously with two sharp modes at [Formula: see text]70meV and [Formula: see text]40meV in different superconductors with different dopings, over the entire momentum space and at different temperatures above and below the superconducting transition temperature. These observations favor phonons as the origin of the modes coupled with electrons and the observed electron-mode couplings are unusual because the associated energy scales do not exhibit an obvious energy shift across the superconducting transition. We further find that the well-known "peak-dip-hump" structure, which has long been considered a hallmark of superconductivity, is also omnipresent and consists of "peak-double dip-double hump" finer structures that originate from electron coupling with two sharp modes. These results provide a unified picture for the [Formula: see text]70-meV and [Formula: see text]40-meV energy scales and their evolutions with momentum, doping and temperature. They provide key information to understand the origin of these energy scales and their role in generating anomalous normal state and high-temperature superconductivity.

Quantum criticality enabled by intertwined degrees of freedom

Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals. Typical settings involve local spins. Systems that contain entwined degrees of freedom offer new platforms to realize unusual forms of quantum criticality. Here, we study the fate of an SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which provides an effective description of a multipolar Kondo lattice, using a renormalization-group method. We show that at zero temperature, a generic trajectory in the model's parameter space contains two quantum critical points, which are associated with the destruction of Kondo entanglement in the orbital and spin channels, respectively. Our asymptotically exact results reveal an overall phase diagram, provide the theoretical basis to understand puzzling recent experiments of a multipolar heavy fermion metal, and point to a means of designing different forms of quantum criticality and strange metallicity in a variety of strongly correlated systems.

Switching between Mott-Hubbard and Hund Physics in Moiré Quantum Simulators

Mott-Hubbard and Hund electron correlations have been realized thus far in separate classes of materials. Here, we show that a single moiré homobilayer encompasses both kinds of physics in a controllable manner. We develop a microscopic multiband model that we solve by dynamical mean-field theory to nonperturbatively address the local many-body correlations. We demonstrate how tuning with twist angle, dielectric screening, and hole density allows us to switch between Mott-Hubbard and Hund correlated states in a twisted WSe₂ bilayer. The underlying mechanism is based on controlling Coulomb-interaction-driven orbital polarization and the energetics of concomitant local singlet and triplet spin configurations. From a comparison to recent experimental transport data, we find signatures of a filling-controlled transition from a triplet charge-transfer insulator to a Hund-Mott metal. Our finding establishes twisted transition-metal dichalcogenides as a tunable platform for exotic phases of quantum matter emerging from large local spin moments.

An Oxygen Vacancy Memristor Ruled by Electron Correlations

Resistive switching effects offer new opportunities in the field of conventional memories as well as in the booming area of neuromorphic computing. Here the authors demonstrate memristive switching effects produced by a redox-driven oxygen exchange in tunnel junctions based on NdNiO₃ , a strongly correlated electron system characterized by the presence of a metal-to-insulator transition (MIT). Strikingly, a strong interplay exists between the MIT and the redox mechanism, which on the one hand modifies the MIT itself, and on the other hand radically affects the tunnel resistance switching and the resistance states' lifetime. That results in a very unique temperature behavior and endows the junctions with multiple degrees of freedom. The obtained results bring up fundamental questions on the interplay between electronic correlations and the creation and mobility of oxygen vacancies in nickelates, opening a new avenue toward mimicking neuromorphic functions by exploiting the electric-field control of correlated states.

Charge self-consistent electronic structure calculations with dynamical mean-field theory usingQuantum ESPRESSO, Wannier 90andTRIQS

We present a fully charge self-consistent implementation of dynamical mean field theory (DMFT) combined with density functional theory (DFT) for electronic structure calculations of materials with strong electronic correlations. The implementation uses theQuantum ESPRESSOpackage for the DFT calculations, theWannier90code for the up-/down-folding and theTRIQSsoftware package for setting up and solving the DMFT equations. All components are available under open source licenses, are MPI-parallelized, fully integrated in the respective packages, and use an hdf5 archive interface to eliminate file parsing. We show benchmarks for three different systems that demonstrate excellent agreement with existing DFT + DMFT implementations in otherab initioelectronic structure codes.

Electron-Phonon Coupling and Electron-Phonon Scattering in SrVO3

Understanding the physics of strongly correlated electronic systems has been a central issue in condensed matter physics for decades. In transition metal oxides, strong correlations characteristic of narrow d bands are at the origin of remarkable properties such as the opening of Mott gap, enhanced effective mass, and anomalous vibronic coupling, to mention a few. SrVO3 with V4+  in a 3d1  electronic configuration is the simplest example of a 3D correlated metallic electronic system. Here, the authors' focus on the observation of a (roughly) quadratic temperature dependence of the inverse electron mobility of this seemingly simple system, which is an intriguing property shared by other metallic oxides. The systematic analysis of electronic transport in SrVO3  thin films discloses the limitations of the simplest picture of e-e correlations in a Fermi liquid (FL); instead, it is shown show that the quasi-2D topology of the Fermi surface (FS) and a strong electron-phonon coupling, contributing to dress carriers with a phonon cloud, play a pivotal role on the reported electron spectroscopic, optical, thermodynamic, and transport data. The picture that emerges is not restricted to SrVO3  but can be shared with other 3d and 4d metallic oxides.

Hidden order and multipolar exchange striction in a correlated f-electron system

Second-order phase transitions in solids occur due to spontaneous symmetry breaking with an order parameter continuously emerging from the disordered high-temperature phase. In some materials, the phase transitions are clearly detected in thermodynamic functions (e.g., specific heat), but the microscopic order parameters remain “hidden” from researchers, in some cases for decades. Here, we show how such hidden-order parameters can be unambiguously identified and the corresponding ordered phase fully described using a first-principles many-body linear response theory. Considering the canonical “hidden-order” system neptunium dioxide, we also identify an unconventional mechanism of spontaneous multipolar exchange striction that induces an anomalous volume contraction of the hidden-order phase in NpO₂.

The nature of order in low-temperature phases of some materials is not directly seen by experiment. Such “hidden orders” (HOs) may inspire decades of research to identify the mechanism underlying those exotic states of matter. In insulators, HO phases originate in degenerate many-electron states on localized f or d shells that may harbor high-rank multipole moments. Coupled by intersite exchange, those moments form a vast space of competing order parameters. Here, we show how the ground-state order and magnetic excitations of a prototypical HO system, neptunium dioxide NpO₂, can be fully described by a low-energy Hamiltonian derived by a many-body ab initio force theorem method. Superexchange interactions between the lowest crystal-field quadruplet of Np⁴⁺ ions induce a primary noncollinear order of time-odd rank 5 (triakontadipolar) moments with a secondary quadrupole order preserving the cubic symmetry of NpO₂. Our study also reveals an unconventional multipolar exchange striction mechanism behind the anomalous volume contraction of the NpO₂ HO phase.

Second-order dual fermion for multi-orbital systems

In dynamical mean-field theory, the correlations between electrons are assumed to be purely local. The dual fermion approach provides a systematic way of adding non-local corrections to the dynamical mean-field theory starting point. Initial applications of this method were largely restricted to the single-orbital Hubbard model. Here, we present an implementation of second-order dual fermion for general multi-orbital systems and use this approach to investigate spatial correlations in SrVO₃. In addition, the approach is benchmarked in several exactly solvable small systems.

Magnon Bose-Einstein condensation and superconductivity in a frustrated Kondo lattice

Motivated by recent experiments on magnetically frustrated heavy fermion metals, we theoretically study the phase diagram of the Kondo lattice model with a nonmagnetic valence bond solid ground state on a ladder. A similar physical setting may be naturally occurring in [Formula: see text], [Formula: see text], and [Formula: see text] compounds. In the insulating limit, the application of a magnetic field drives a quantum phase transition to an easy-plane antiferromagnet, which is described by a Bose-Einstein condensation of magnons. Using a combination of field theoretical techniques and density matrix renormalization group calculations we demonstrate that in one dimension this transition is stable in the presence of a metallic Fermi sea, and its universality class in the local magnetic response is unaffected by the itinerant gapless fermions. Moreover, we find that fluctuations about the valence bond solid ground state can mediate an attractive interaction that drives unconventional superconducting correlations. We discuss the extensions of our findings to higher dimensions and argue that depending on the filling of conduction electrons, the magnon Bose-Einstein condensation transition can remain stable in a metal also in dimensions two and three.

Fermi surface reconstruction in electron-doped cuprates without antiferromagnetic long-range order

Fermi surface (FS) topology is a fundamental property of metals and superconductors. In electron-doped cuprate Nd_2-x Ce _x CuO₄ (NCCO), an unexpected FS reconstruction has been observed in optimal- and overdoped regime (x = 0.15-0.17) by quantum oscillation measurements (QOM). This is all the more puzzling because neutron scattering suggests that the antiferromagnetic (AFM) long-range order, which is believed to reconstruct the FS, vanishes before x = 0.14. To reconcile the conflict, a widely discussed external magnetic-field-induced AFM long-range order in QOM explains the FS reconstruction as an extrinsic property. Here, we report angle-resolved photoemission (ARPES) evidence of FS reconstruction in optimal- and overdoped NCCO. The observed FSs are in quantitative agreement with QOM, suggesting an intrinsic FS reconstruction without field. This reconstructed FS, despite its importance as a basis to understand electron-doped cuprates, cannot be explained under the traditional scheme. Furthermore, the energy gap of the reconstruction decreases rapidly near x = 0.17 like an order parameter, echoing the quantum critical doping in transport. The totality of the data points to a mysterious order between x = 0.14 and 0.17, whose appearance favors the FS reconstruction and disappearance defines the quantum critical doping. A recent topological proposal provides an ansatz for its origin.

Transverse fields to tune an Ising-nematic quantum phase transition

The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.

Concealed d-wave pairs in the s± condensate of iron-based superconductors

A central question in iron-based superconductivity is the mechanism by which the paired electrons minimize their strong mutual Coulomb repulsion. In most unconventional superconductors, Coulomb repulsion is minimized through the formation of higher angular momentum Cooper pairs, with Fermi surface nodes in the pair wavefunction. The apparent absence of such nodes in the iron-based superconductors has led to a belief they form an s-wave ([Formula: see text]) singlet state, which changes sign between the electron and hole pockets. However, the multiorbital nature of these systems opens an alternative possibility. Here, we propose a new class of [Formula: see text] state containing a condensate of d-wave Cooper pairs, concealed by their entanglement with the iron orbitals. By combining the d-wave ([Formula: see text]) motion of the pairs with the internal angular momenta [Formula: see text] of the iron orbitals to make a singlet ([Formula: see text]), an [Formula: see text] superconductor with a nontrivial topology is formed. This scenario allows us to understand the development of octet nodes in potassium-doped Ba1-x KXFe2As2 as a reconfiguration of the orbital and internal angular momentum into a high spin ([Formula: see text]) state; the reverse transition under pressure into a fully gapped state can then be interpreted as a return to the low-spin singlet. The formation of orbitally entangled pairs is predicted to give rise to a shift in the orbital content at the Fermi surface, which can be tested via laser-based angle-resolved photoemission spectroscopy.