Charge Ordering Research Articles

Orbital selective commensurate modulations of the local density of states in ScV6Sn6 probed by nuclear spins

The kagome network is a unique platform that harbors a diversity of special electronic states due to its inherent band structure features comprising Dirac cones, van Hove singularities, and flat bands. Some kagome-based metals have recently been found to exhibit favorable properties, including superconductivity, charge order, and signatures of an anomalous Hall effect. The kagome system ScV6Sn6 is a promising candidate for studying the emergence of an unconventional charge order and accompanying effects. We use 51V nuclear magnetic resonance to explore the local properties of the charge ordered phase in single crystalline ScV6Sn6, aided by density functional theory. We show the local charge symmetry of V to reflect a commensurate modulation with q=13,13,13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\bf{q}}}=\\left(\\frac{1}{3},\\frac{1}{3},\\frac{1}{3}\\right)$$\\end{document}, the density of states to drop by about a factor of 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{2}$$\\end{document} during the phase transition, and an unusual orientation dependent change in the shift splitting symmetry to reveal orbital selective modulations of the local density of states.

Information-theoretic quantities as effective descriptors of electrophilicity and nucleophilicity in density functional theory.

Electrophilicity and nucleophilicity are two vastly important chemical concepts gauging the capability of atoms in molecules to accept and donate the maximal number of electrons. In our earlier studies, we proposed to simultaneously quantify them using the Kullback-Leibler divergence from the information-theoretic approach in density functional theory. However, several issues with this scheme remain to be clarified such as its general validity, predictability, and relationship with other information-theoretic quantities. In this work, we revisit the matter with bigger datasets and deeper theoretical insights. Five information-theoretic quantities including Kullback-Leibler divergence, Hirshfeld charge, Ghost-Berkowitz-Parr entropy, and second and third orders of relative Onicescu information energy are found to be reliable and robust descriptors of electrophilicity and nucleophilicity propensities. Employing these five descriptors, we design a list of new compounds and predict their electrophilicity and nucleophilicity scales. This work should markedly improve our confidence and capability in applying information-theoretic quantities to evaluate electrophilicity and nucleophilicity propensities and henceforth pave the route for more applications of these quantities from information-theoretic approach in density functional theory in the future. All structures were fully optimized at the M06-2X/6-311 + G(d) level of DFT functional using the Gaussian 16 package (version C01) with integration grids and tight self-consistent-field convergence. The solvent effect was taken into account by using the implicit solvent model (CPCM) in the CH2Cl2 solvent, and all 3D contour surfaces of Fukui function, local temperature, and ITA (information-theoretic approach) quantities were generated by GaussView. The Multiwfn 3.8 program was used to calculate the ITA indexes and atomic charges.

Avoided metallicity in a hole-doped Mott insulator on a triangular lattice

Doping of a Mott insulator gives rise to a wide variety of exotic emergent states, from high-temperature superconductivity to charge, spin, and orbital orders. The physics underpinning their evolution is, however, poorly understood. A major challenge is the chemical complexity associated with traditional routes to doping. Here, we study the Mott insulating CrO2 layer of the delafossite PdCrO2, where an intrinsic polar catastrophe provides a clean route to doping of the surface. From scanning tunnelling microscopy and angle-resolved photoemission, we find that the surface stays insulating accompanied by a short-range ordered state. From density functional theory, we demonstrate how the formation of charge disproportionation results in an insulating ground state of the surface that is disparate from the hidden Mott insulator in the bulk. We demonstrate that voltage pulses induce local modifications to this state which relax over tens of minutes, pointing to a glassy nature of the charge order.

From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands.

Symmetry-breaking orders can not only compete with each other, but also be interwined, and the interwined topological and symmetry-breaking orders make the situation more intriguing. This work examines the archetypal correlated flat band model on a checkerboard lattice at filling ν = 2/3 and we find the unique interplay between smectic charge order and topological order gives rise to two novel quantum states. As the interaction strength increases, the system first transitions from a Fermi liquid into FQAH smectic (FQAHS) state, where FQAH topological order coexists cooperatively with smectic charge order with enlarged ground-state degeneracy and interestingly, the Hall conductivity is σxy = ν = 2/3, different from the band-folding or doping scenarios. Further increasing the interaction strength, the system undergoes another quantum phase transition and evolves into a polar smectic metal (PSM) state. This emergent PSM is an anisotropic non-Fermi liquid, whose interstripe tunneling is irrelevant while it is metallic inside each stripe. Different from the FQAHS and conventional smectic orders, this PSM spontaneously breaks the two-fold rotational symmetry, resulting in a nonzero electric dipole moment and ferroelectric order. In addition to the exotic ground states, large-scale numerical simulations are also used to study low-energy excitations and thermodynamic characteristics. We find the onset temperature of the incompressible FQAHS state, which also coincides with the onset of non-polar smectic order, is dictated by the magneto-roton modes. Above this onset temperature, the PSM state exists at intermediate-temperature regime. Although the T = 0 quantum phase transition between PSM and FQAHS is first order, the thermal FQAHS-PSM transition could be continuous. We expect the features of the exotic states and thermal phase transitions could be accessed in future experiments.

Evolution from a charge-ordered insulator to a high-temperature superconductor in Bi2Sr2(Ca,Dy)Cu2O8+δ

How Cooper pairs form and condense has been the main challenge in the physics of copper-oxide high-temperature superconductors. Great efforts have been made in the ‘underdoped’ region of the phase diagram, through doping a Mott insulator or cooling a strange metal. However, there is still no consensus on how superconductivity emerges when electron-electron correlations dominate and the Fermi surface is missing. To address this issue, here we carry out high-resolution resonant inelastic X-ray scattering and scanning tunneling microscopy studies on prototype cuprates Bi2Sr2Ca0.6Dy0.4Cu2O8+δ near the onset of superconductivity, combining bulk and surface, momentum- and real-space information. We show that an incipient charge order exists in the antiferromagnetic regime down to 0.04 holes per CuO2 unit, entangled with a particle-hole asymmetric pseudogap. The charge order induces an intensity anomaly in the bond-buckling phonon branch, which exhibits an abrupt increase once the system enters the superconducting dome. Our results suggest that the Cooper pairs grow out of a charge-ordered insulating state, and then condense accompanied by an enhanced interplay between charge excitations and electron-phonon coupling.

Incommensurate charge super-modulation and hidden dipole order in layered kitaev material α-RuCl3

The magnetism of Kitaev materials has been widely studied, but their charge properties and the coupling to other degrees of freedom are less known. Here we investigate the charge states of α-RuCl3, a promising Kitaev quantum spin liquid candidate, in proximity to graphite. We discover that few-layered α-RuCl3 experiences a clear modulation of charge states, where a Mott-insulator to weak charge-transfer-insulator transition in the 2D limit occurs by means of heterointerfacial polarization. More notably, distinct signals of incommensurate charge and lattice super-modulations, regarded as an unconventional charge order, accompanied in the insulator. Our theoretical calculations have reproduced the incommensurate charge order by taking into account the antiferroelectricity of α-RuCl3 that is driven by dipole order in the internal electric fields. The findings imply that there is strong coupling between the charge, spin, and lattice degrees of freedom in layered α-RuCl3 in the heterostructure, which offers an opportunity to electrically access and tune its magnetic interactions inside the Kitaev compounds.

Impeding conduction by breaking the charge carrier hopping in charge-ordered perovskite BaBiO3 ([formula omitted]): Experimental and theoretical electronic structural correlations

BaBiO3 (BBO), a charge-ordered perovskite with mixed-valent states of Bi (Bi3+ and Bi5+), is known for its charge density wave (CDW) semiconducting and topological insulating properties. BBO has been extensively investigated for its superconducting, electrical, and photocatalytic properties. The present study aims to understand the alterations in the CDW and electronic properties of BaBi0.53+Bi0.55+O3 by valence-selective substitution of Bi3+ and Bi5+ with La3+ and Nb5+, respectively, in the solid solutions BaBi0.5−x3+LaxBi0.55+O3 and BaBi0.53+Bi0.5−y5+NbyO3 (x = y = 0.0, 0.1, 0.3, and 0.5). The samples synthesized via high-temperature solid-state reaction method were characterized by powder X-ray diffraction and various spectroscopic techniques (FT-IR, Laser Raman, EPR, XPS, and UPS). Impedance analysis revealed an upsurge in total impedance with the substitution of Bi3+/Bi5+ by La3+/Nb5+ indicating the blocking of electron/hole hopping by disruption of the charge ordering of redox pair Bi3+ and Bi5+. The valence-selective substitution of Bi3+/Bi5+ in BaBiO3 resulted in an alteration of the electronic structure and changes in the bandwidth of BaBi0.5−x3+LaxBi0.55+O3 and BaBi0.53+Bi0.5−y5+NbyO3 (x = y = 0.0, 0.1, 0.3, and 0.5) solid solutions, which were confirmed by both theoretical density of states (DOS) calculations and experimental ultraviolet photoelectron spectroscopic (UPS) studies.

Effects of electronic correlation on topological properties of Kagome semimetal Ni3In2S2.

Kagome metals gain attention as they manifest a spectrum of quantum phenomena such as superconductivity, charge order, frustrated magnetism, and allied correlated states of condensed matter. With regard to electronic band structure, several of them exhibit non-trivial topological characteristics. Here, we present a thorough investigation on the growth and the physical properties of single crystals of Ni3In2S2 which is established to be a Dirac nodal line Kagome semimetal. Extensive characterization is attained through temperature and field-dependent resistivity, angle-dependent magnetoresistance and specific heat measurements. The central question we seek to address is the effect of electronic correlations in suppressing the manifestation of topological characteristics. In most metals, the Fermi liquid behaviour is restricted to a narrow range of temperatures. Here we show that Ni3In2S2 follows the Fermi-liquid behaviour up to 86K. This phenomenon is further supported by a high Kadowaki-Woods ratio obtained through specific heat analysis. Different interpretations of the magneto-transport study reveal that magnetoresistance exhibits linear behavior, suggesting the presence of Dirac semi-metallic signatures at lower temperatures. The angle-dependent magneto-transport study obeys the Voigt-Thomson formula. This, on the contrary, implies the classical origin of magnetoresistance. Thus, the effect of strong electron correlation in Ni3In2S2 manifests itself in the anisotropic magneto-transport. Furthermore, the magnetization measurement shows the presence of de-Haas van Alphen oscillations. Calculations of Berry phase provide insights into the topological features in the Kagome semimetal Ni3In2S2.&#xD.

Real-Space Imaging of Intrinsic Symmetry-Breaking Spin Textures in a Kagome Lattice.

The electronic orders in kagome materials have emerged as a fertile platform for studying exotic quantum states, and their intertwining with the unique kagome lattice geometry remains elusive. While various unconventional charge orders with broken symmetry is observed, the influence of kagome symmetry on magnetic order has so far not been directly observed. Here, using a high-resolution magnetic force microscopy, it is, for the first time, observed a new lattice form of noncollinear spin textures in the kagome ferromagnet in zero magnetic field. Under the influence of the sixfold rotational symmetry of the kagome lattice, the spin textures are hexagonal in shape and can further form a honeycomb lattice structure. Subsequent thermal cycling measurements reveal that these spin textures transform into a non-uniform in-plane ferromagnetic ground state at low temperatures and can fully rebuild at elevated temperatures, showing a strong second-order phase transition feature. Moreover, some out-of-plane magnetic moments persist at low temperatures, supporting the Kane-Mele scenario in explaining the emergence of the Dirac gap. The observations establish that the electronic properties, including both charge and spin orders, are strongly coupled with the kagome lattices.

Magnetoelectric effect in multiferroic nickelate perovskite YNiO3

The interaction of magnetic order and spontaneous polarization is a fundamental coupling with the prospect for the control of electronic properties and magnetism. The connection among magnetic order, charge localization and associated metal-insulator transition (MIT) are cornerstones for materials control. Materials that combine both effects are therefore of great interest for testing models that claim the occurrence of spontaneous polarization from magnetic and charge order. One class of materials proposed to combine these functionalities is the family of RNiO3 (R: Lanthanide or Yttrium), whose members show a clear MIT and an antiferromagnetic ground state and for which an electric polarization has been predicted. Here, using resonant magnetic x-ray scattering with circular polarization and an applied electric field we show that YNiO3 possess a magnetic structure containing domains of spin-rotations that are consistent with an electric polarization. We show a reversal of the magnetic structure with the applied electric field confirming that charge ordered RNiO3 are magnetoelectric type II multiferroics with a MIT.

Tuning of charge order by uniaxial stress in a cuprate superconductor

Strongly correlated electron materials are often characterized by competition and interplay of multiple quantum states. For example, in high-temperature cuprate superconductors unconventional superconductivity, spin- and charge-density wave orders coexist. A key question is whether competing states coexist on the atomic scale or if they segregate into distinct regions. Using X-ray diffraction, we investigate the competition between charge order and superconductivity in the archetypal cuprate La2−xBaxCuO4, around x = 1/8-doping, where uniaxial stress restores optimal 3D superconductivity at σ3D ≈ 0.06 GPa. We find that the charge order peaks and the correlation length along the stripe are strongly reduced up to σ3D. Upon the increase of stress beyond this point, no further changes were observed. Simultaneously, the charge order onset temperature only shows a modest decrease. Our findings suggest that optimal 3D superconductivity is not linked to the absence of charge stripes but instead requires their arrangement into smaller regions. Our results provide insight into the length scales over which the interplay between superconductivity and charge order takes place.

Photoinduced inhomogeneous melting of charge order by ultrashort pulsed light excitation

Photoinduced inhomogeneous melting of charge order by ultrashort pulsed light excitation

Quantum Anomalous Hall Crystal at Fractional Filling of Moiré Superlattices.

We predict the emergence of a state of matter with intertwined ferromagnetism, charge order, and topology in fractionally filled moiré superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall conductance that is different than expected from the filling and Chern number of the band. Microscopic calculations show that this phase is robustly favored at half-filling (ν=1/2) at larger twist angles of the twisted semiconductor bilayer tMoTe_{2}.

Chiral kagome superconductivity modulations with residual Fermi arcs.

Superconductivity involving finite-momentum pairing1 can lead to spatial-gap and pair-density modulations, as well as Bogoliubov Fermi states within the superconducting gap. However, the experimental realization of their intertwined relations has been challenging. Here we detect chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5 using normal and Josephson scanning tunnelling microscopy down to 30 millikelvin with a resolved electronic energy difference at the microelectronvolt level. We observe a U-shaped superconducting gap with flat residual in-gap states. This gap shows chiral 2a×2a spatial modulations with magnetic-field-tunable chirality, which align with the chiral 2a×2a pair-density modulations observed through Josephson tunnelling. These findings demonstrate a chiral pair density wave (PDW) that breaks time-reversal symmetry. Quasiparticle interference imaging of the in-gap zero-energy states reveals segmented arcs, with high-temperature data linking them to parts of the reconstructed vanadium d-orbital states within the charge order. The detected residual Fermi arcs can be explained by the partial suppression of these d-orbital states through an interorbital 2a×2a PDW and thus serve as candidate Bogoliubov Fermi states. In addition, we differentiate the observed PDW order from impurity-induced gap modulations. Our observations not only uncover a chiral PDW order with orbital selectivity but also show the fundamental space-momentum correspondence inherent in finite-momentum-paired superconductivity.

Chiral Pair Density Waves with Residual Fermi Arcs in RbV3Sb5

Abstract The chiral 2 × 2 charge order has been reported and confirmed in the kagome superconductor RbV3Sb5, while its interplay with superconductivity remains elusive owing to its lowest superconducting transition temperature T C of about 0.85 K in the AV3Sb5 family (A = K, Rb, Cs) that severely challenges electronic spectroscopic probes. Here, utilizing dilution-refrigerator-based scanning tunneling microscopy down to 30 mK, we observe chiral 2 × 2 pair density waves with residual Fermi arcs in RbV3Sb5. We find a superconducting gap of 150 μeV with substantial residual in-gap states. The spatial distribution of this gap exhibits chiral 2 × 2 modulations, signaling a chiral pair density wave (PDW). Our quasi-particle interference imaging of the zero-energy residual states further reveals arc-like patterns. We discuss the relation of the gap modulations with the residual Fermi arcs under the space-momentum correspondence between PDW and Bogoliubov Fermi states.

Constructing the electrostatic potential microenvironment in MMMs by poly(ionic liquid)s functionalized metal–organic frameworks for efficient CO2/CH4 separation

The construction of electrostatic potential microenvironment in MOF is an effective strategy to improve the separation performance of mixed matrix membranes (MMMs). Different functional groups of poly(ionic liquid)s (PIL-F, F=OH, COOH, NH2) are used to modify MOF to synthesize the PIL-F@MIL-101, which were incorporated into Pebax MH 1657 (Pebax) to prepare MMMs for CO2/CH4 separation. PIL-F@MIL-101 possess positive charge, and their order of positive charge is PIL-OH@MIL-101 > PIL-COOH@MIL-101 > PIL-NH2@MIL-101. The MMMs doped with 7.0 wt% PIL-OH@MIL-101 represented the optimal CO2 permeability of 1480.7 Barrer and CO2/CH4 selectivity of 35.2. The performance of Pebax/PIL-OH@MIL-101 approached the 2019 upper bound. It mainly considered to the following reasons: on one hand, the positively charged filler constructed the positively electrostatic potential microenvironment in MMMs, enhancing the electrostatic attraction with the negatively charged O atoms of CO2 and promoting the preferential transport of CO2. On the other hand, the positively electrostatic potential microenvironment in MMMs obstructs the transport of positively charged H atoms of CH4, improving the CO2/CH4 selectivity. The design on constructing electrostatic potential microenvironments in MMMs provides a promising strategy for efficient CO2 separation.

Nonequilibrium dynamics of suppression, revival, and loss of charge order in a laser-pumped electron-phonon system

Nonequilibrium dynamics of suppression, revival, and loss of charge order in a laser-pumped electron-phonon system

Conventional superconductivity in the doped kagome superconductor Cs(V0.86Ta0.14)3Sb5 from vortex lattice studies

A hallmark of unconventional superconductors is a complex electronic phase diagram where intertwined orders of charge-spin-lattice degrees of freedom compete and coexist. While the kagome metals such as CsV3Sb5 also exhibit complex behavior, involving coexisting charge density wave order and superconductivity, much is unclear about the microscopic origin of the superconducting pairing. We study the vortex lattice in the superconducting state of Cs(V0.86Ta0.14)3Sb5, where the Ta-doping suppresses charge order and enhances superconductivity. Using small-angle neutron scattering, a strictly bulk probe, we show that the vortex lattice exhibits a strikingly conventional behavior. This includes a triangular symmetry with a period consistent with 2e-pairing, a field dependent scattering intensity that follows a London model, and a temperature dependence consistent with a uniform superconducting gap. Our results suggest that optimal bulk superconductivity in Cs(V1−xTax)3Sb5 arises from a conventional Bardeen-Cooper-Schrieffer electron-lattice coupling, different from spin fluctuation mediated unconventional copper- and iron-based superconductors.

Discovery of a long-ranged charge order with 1/4 Ge1-dimerization in an antiferromagnetic Kagome metal

Exotic quantum states arise from the interplay of various degrees of freedom such as charge, spin, orbital, and lattice. Recently, a short-ranged charge order (CO) was discovered deep inside the antiferromagnetic phase of Kagome magnet FeGe, exhibiting close relationships with magnetism. Despite extensive investigations, the CO mechanism remains controversial, mainly because the short-ranged behavior hinders precise identification of CO superstructure. Here, combining multiple experimental techniques, we report the observation of a long-ranged CO in high-quality FeGe samples, which is accompanied with a first-order structural transition. With these high-quality samples, the distorted 2 × 2 × 2 CO superstructure is characterized by a strong dimerization along the c-axis of 1/4 of Ge1-sites in Fe3Ge layers, and in response to that, the 2 × 2 in-plane charge modulations are induced. Moreover, we show that the previously reported short-ranged CO might be related to large occupational disorders at Ge1-site, which upsets the equilibrium of the CO state and the ideal 1 × 1 × 1 structure with very close energies, inducing nanoscale coexistence of these two phases. Our study provides important clues for further understanding the CO properties in FeGe and helps to identify the CO mechanism.

Resolving Chemically Driven Charge Ordering in Infinite Layer Nickelates with Multislice Electron Ptychography and 4D-STEM

Resolving Chemically Driven Charge Ordering in Infinite Layer Nickelates with Multislice Electron Ptychography and 4D-STEM