Charge Ordering Research Articles

Engineering phase competition between stripe order and superconductivity in La1.88Sr0.12CuO4

Unconventional superconductivity often couples to other electronic orders in a cooperative or competing fashion. Identifying external stimuli that tune between these two limits is of fundamental interest. Here, we show that strain perpendicular to the copper-oxide planes couples directly to the competing interaction between charge stripe order and superconductivity in La1.88Sr0.12CuO4 (LSCO). Compressive c-axis pressure amplifies stripe order within the superconducting state, while having no impact on the normal state. By contrast, strain dramatically diminishes the magnetic field enhancement of stripe order in the superconducting state. These results suggest that c-axis strain acts as tuning parameter of the competing interaction between charge stripe order and superconductivity. This interpretation implies a uniaxial pressure-induced ground state in which the competition between charge order and superconductivity is reduced.

Unidirectional Charge Orders Induced by Oxygen Vacancies on SrTiO3(001).

The discovery of high-mobility two-dimensional electron gas and low carrier density superconductivity in multiple SrTiO3-based heterostructures has stimulated intense interest in the surface properties of SrTiO3. The recent discovery of high-Tc superconductivity in the monolayer FeSe/SrTiO3 led to the upsurge and underscored the atomic precision probe of the surface structure. By performing atomically resolved cryogenic scanning tunneling microscopy/spectroscopy characterization on dual-TiO2-δ-terminated SrTiO3(001) surfaces with (√13 × √13), c(4 × 2), mixed (2 × 1), and (2 × 2) reconstructions, we disclosed universally broken rotational symmetry and contrasting bias- and temperature-dependent electronic states for apical and equatorial oxygen sites. With the sequentially evolved surface reconstructions and simultaneously increasing equatorial oxygen vacancies, the surface anisotropy reduces and the work function lowers. Intriguingly, unidirectional stripe orders appear on the c(4 × 2) surface, whereas local (4 × 4) order emerges and eventually forms long-range unidirectional c(4 × 4) charge order on the (2 × 2) surface. This work reveals robust unidirectional charge orders induced by oxygen vacancies due to strong and delicate electronic-lattice interaction under broken rotational symmetry, providing insights into understanding the complex behaviors in perovskite oxide-based heterostructures.

Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model

Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model

Spiral to stripe transition in the two-dimensional Hubbard model

We obtain an almost complete understanding of the mean-field phase diagram of the two-dimensional Hubbard model on a square lattice with a sizable next-nearest-neighbor hopping and a moderate interaction strength. In particular, we clarify the nature of the transition region between the spiral and the stripe phase. Complementing previous [] real-space Hartree-Fock calculations on large finite lattices, we solve the mean-field equations for coplanar unidirectional magnetic order directly in the thermodynamic limit, and we determine the nature of the magnetic states right below the mean-field critical temperature T* by a Landau free-energy analysis. While the magnetic order for filling factors n≥1 is always of Néel type, for n≤1 the following sequence of magnetic states is found as a function of increasing hole-doping: Néel, planar circular spiral, multispiral, and collinear spin-charge stripe states. Multispiral states are superpositions of several spirals with distinct wave vectors, and lead to concomitant charge order. We finally point out that nematic and charge orders inherited from the magnetic order can survive even in the presence of fluctuations, and we present a corresponding qualitative phase diagram. Published by the American Physical Society 2024

Hidden Charge Order and Multiple Electronic Instabilities in EuTe4.

The rare-earth telluride compound EuTe4 exhibits a charge density wave (CDW) and an unconventional thermal hysteresis transition. Herein, we report a comprehensive study of the CDW states in EuTe4 by using low-temperature scanning tunneling microscopy. Two types of charge orders are observed at 4 K, including a newly discovered spindle-shaped pattern and a typical stripe-like pattern. As an exotic charge order, the spindle-shaped CDW is off-axis and barely visible at 77 K, indicating that it is a hidden order developed at low temperature. Based on our first-principles calculations, we reveal the origins of the observed electronic instabilities. The spindle-shaped charge order stems from a subsequent transition based on the stripe-like CDW phase. Our work demonstrates that the competition and cooperation between multiple charge orders can generate exotic quantum phases.

Optical manipulation of the charge-density-wave state in RbV3Sb5.

Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents1-4. The recently discovered kagome superconductors AV3Sb5 (where A is K, Rb or Cs)5,6 display an exotic charge-density-wave (CDW) state andhave emerged as astrong candidate for materialshosting a loop currentphase. The idea that the CDW breaks time-reversal symmetry7-14 is, however, being intensely debated due to conflicting experimental data15-17. Here we use laser-coupled scanning tunnelling microscopy to study RbV3Sb5. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong nonlinear electron-phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry breaking. We show that the simplest CDW that satisfies these constraints is an out-of-phase combination of bond charge order and loop currents that we dub a congruent CDW flux phase. Our laser scanning tunnelling microscopy data open the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials.

Discovery of charge order above room-temperature in the prototypical kagome superconductor La(Ru1−xFex)3Si2

The kagome lattice is an intriguing and rich platform for discovering, tuning and understanding the diverse phases of quantum matter, crucial for advancing modern and future electronics. Despite considerable efforts, accessing correlated phases at room temperature has been challenging. Using single-crystal X-ray diffraction, we discovered charge order above room temperature in La(Ru1−xFex)3Si2 (x = 0, 0.01, 0.05), where charge order related to out-of-plane Ru atom displacements appears below TCO,I ≃ 400 K. The secondary charge ordered phase emerges below TCO,II ≃ 80–170 K. Furthermore, first principles calculations reveal both the kagome flat band and the van Hove point near the Fermi energy in LaRu3Si2, driven by Ru-dz2 orbitals. Our results identify LaRu3Si2 as the kagome superconductor with the highest known charge ordering temperature, offering a promising avenue for researching room temperature quantum phases and developing related technologies.

Investigation of spin excitations and charge order in bulk crystals of the infinite-layer nickelate LaNiO2

Recent x-ray spectroscopic studies have revealed spin excitations and charge density waves in thin films of infinite-layer (IL) nickelates. However, clarifying whether the origin of these phenomena is intrinsic to the material class or attributable to impurity phases in the films has presented a major challenge. Here we utilize topotactic methods to synthesize bulk crystals of the IL nickelate LaNiO2 with crystallographically oriented surfaces. We examine these crystals using resonant inelastic x-ray scattering (RIXS) at the Ni L3-edge to elucidate the spin and charge correlations in the bulk of the material. While we detect the presence of prominent spin excitations in the crystals, fingerprints of charge order are absent at the ordering vectors identified in previous thin-film studies. These results contribute to the understanding of the bulk properties of LaNiO2 and establish topotactically synthesized crystals as viable complementary specimens for spectroscopic investigations. Published by the American Physical Society 2024

Evidence for electron-hole crystals in a Mott insulator.

The coexistence of correlated electron and hole crystals enables the realization of quantum excitonic states, capable of hosting counterflow superfluidity and topological orders with long-range quantum entanglement. Here we report evidence for imbalanced electron-hole crystals in a doped Mott insulator, namely, α-RuCl3, through gate-tunable non-invasive van der Waals doping from graphene. Real-space imaging via scanning tunnelling microscopy reveals two distinct charge orderings at the lower and upper Hubbard band energies, whose origin is attributed to the correlation-driven honeycomb hole crystal composed of hole-rich Ru sites and rotational-symmetry-breaking paired electron crystal composed of electron-rich Ru-Ru bonds, respectively. Moreover, a gate-induced transition of electron-hole crystals is directly visualized, further corroborating their nature as correlation-driven charge crystals. The realization and atom-resolved visualization of imbalanced electron-hole crystals in a doped Mott insulator opens new doors in the search for correlated bosonic states within strongly correlated materials.

Pseudo-transition between antiferromagnetic and charge orders in a minimal spin-pseudospin model of one-dimensional cuprates

This study rigorously investigates the phenomenon of a pseudo-transition in a minimal spin-pseudospin model, serving as a simplified model of one-dimensional cuprate chains [CuO]∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\\infty $$\\end{document}, by making use of the transfer-matrix method. The studied spin-pseudospin model of one-dimensional cuprate chains [CuO]∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\\infty $$\\end{document} reveals a peculiar pseudo-transition between a charged-ordered phase and an antiferromagnetic phase, which is accompanied with anomalous behavior of magnetic and thermodynamic quantities. While the entropy and short-range correlations undergo near the pseudo-transition steep continuous changes reminiscent of a discontinuous phase transition, the specific heat displays a sizable sharp peak akin to a continuous phase transition.Graphic A density plot of the specific heat of one-dimensional spin-pseudospin model of cuprate chain in the inter-site interaction versus temperature plane, which serves as a pseudo-phase diagram involving charged-ordered (CO) and antiferromagnetic (AF) phases

Atomic-scale visualization of a cascade of magnetic orders in the layered antiferromagnet GdTe3

GdTe3 is a layered antiferromagnet which has attracted attention due to its exceptionally high mobility, distinctive unidirectional incommensurate charge density wave (CDW), superconductivity under pressure, and a cascade of magnetic transitions between 7 and 12 K, with as yet unknown order parameters. Here, we use spin-polarized scanning tunneling microscopy to directly image the charge and magnetic orders in GdTe3. Below 7 K, we find a striped antiferromagnetic phase with twice the periodicity of the Gd lattice and perpendicular to the CDW. As we heat the sample, we discover a spin density wave with the same periodicity as the CDW between 7 and 12 K; the viability of this phase is supported by our Landau free energy model. Our work reveals the order parameters of the magnetic phases in GdTe3 and shows how the interplay between charge and spin can generate a cascade of magnetic orders.

Emergent Quantum Phenomena of a Noncentrosymmetric Charge Density Wave in 1T-Transition Metal Dichalcogenides.

1T-transition metal dichalcogenides (TMDs) have been an exciting platform for exploring the intertwinement of charge density waves and strong correlation phenomena. While the David star structure has been conventionally considered as the underlying charge order in the literature, recent scanning tunneling probe experiments on several monolayer 1T-TMD materials have motivated a new, alternative structure, namely, the anion-centered David star structure. In this Letter, we show that this novel anion-centered David star structure manifestly breaks inversion symmetry, resulting in flat bands with pronounced Rashba spin-orbit couplings. These distinctive features unlock novel possibilities and functionalities for 1T-TMDs, including the giant spin Hall effect, the emergence of Chern bands, and spin liquid that spontaneously breaks crystalline rotational symmetry. Our findings establish promising avenues for exploring emerging quantum phenomena of monolayer 1T-TMDs with this novel noncentrosymmetric structure.

Magnetic topological phases in the double exchange model with spin–orbit coupling

The double exchange model with the spin–orbit coupling is studied by the dynamical mean field theory. It reveals a competition between the magnetic, charge orderings and the non-trivial topology of the ground state. The spin exchange tends to maintain the magnetic ordering, and at the same time it tries to suppress the charge ordering. The spin–orbit coupling maintains nontrivial topology of the ground state, whereas the magnetic ordering tries to destroy it. As a result, a rich phase diagram is obtained. The competition leads to a half topological ground state, where spin-up electrons form a nontrivial topological state, while spin-down electrons are in the topological trivial insulating state.

Free energy of a two-liquid system of charge carriers in strongly coupled electron and phonon fields and common nature of three phases in hole-doped cuprates

Hole-doped cuprates exhibit partially coexisting pseudogap (PG), charge ordering (CO) and superconductivity; we show that there exists a class of systems in which they have a single nature as it has recently been supposed. Since the charge-ordered phase exhibits large frozen deformation of the lattice, we develop a method for calculating the phase diagram of a system with strong long-range (Fröhlich) electron–phonon interaction. Using a variational approach, we calculate the free energy of a two-liquid system of carriers with cuprate-like dispersion comprising a liquid of autolocalized carriers (large polarons and bipolarons) and Fermi liquid of delocalized carriers. Comparing it with the free energy of pure Fermi liquid and calculating (with standard methods of Bose liquid theory) a temperature of the superfluid transition in the large-bipolaron liquid we identify regions in the phase diagram with the presence of PG (caused by the impact of the (bi)polarons potential on delocalized quasiparticles), CO and superconductivity. They are located in the same places in the diagram as in hole-doped cuprates, and, as in the latter, the shape of the calculated phase diagram is resistant to wide-range changes in the characteristics of the system. As in cuprates, the calculated temperature of the superconducting transition increases with the number of conducting planes in the unit cell, the superfluid density decreases with doping at overdoping, the bipolaron density (and bipolaronic plasmon energy) saturates at optimal doping. Thus, the similarity of the considered system with hole-doped cuprates is not limited to the phase diagram. The results obtained allow us to discuss ways of increasing the temperature of the superfluid transition in the large-bipolaron liquid and open up the possibility of studying the current-carrying state and properties of the bipolaron condensate.

Formation and Manipulation of Diatomic Rotors at the Symmetry-Breaking Surfaces of a Kagome Superconductor.

Construction of diatomic rotors, which is crucial for artificial nanomachines, remains challenging due to surface constraints and limited chemical design. Here we report the construction of diatomic Cr-Cs and Fe-Cs rotors where a Cr or Fe atom switches around a Cs atom at the Sb surface of the newly discovered kagome superconductor CsV3Sb5. The switching rate is controlled by the bias voltage between the rotor and scanning tunneling microscope (STM) tip. The spatial distribution of rates exhibits C2 symmetry, possibly linked to the symmetry-breaking charge orders of CsV3Sb5. We have expanded the rotor construction to include different transition metals (Cr, Fe, V) and alkali metals (Cs, K). Remarkably, designed configurations of rotors are achieved through STM manipulation. Rotor orbits and quantum states are precisely controlled by tuning the inter-rotor distance. Our findings establish a novel platform for the controlled fabrication of atomic motors on symmetry-breaking quantum materials, paving the way for advanced nanoscale devices.

Origin of Distinct Insulating Domains in the Layered Charge Density Wave Material 1T-TaS2.

Vertical charge order shapes the electronic properties in layered charge density wave (CDW) materials. Various stacking orders inevitably create nanoscale domains with distinct electronic structures inaccessible to bulk probes. Here, the stacking characteristics of bulk 1T-TaS2 are analyzed using scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations. It is observed that Mott-insulating domains undergo a transition to band-insulating domains restoring vertical dimerization of the CDWs. Furthermore, STS measurements covering a wide terrace reveal two distinct band insulating domains differentiated by band edge broadening. These DFT calculations reveal that the Mott insulating layers preferably reside on the subsurface, forming broader band edges in the neighboring band insulating layers. Ultimately, buried Mott insulating layers believed to harbor the quantum spin liquid phase are identified. These results resolve persistent issues regarding vertical charge order in 1T-TaS2, providing a new perspective for investigating emergent quantum phenomena in layered CDWmaterials.

Unconventional superconductivity and charge ordering in an extended ionic Hubbard model on the triangular lattice

To address the issues of superconducting and charge properties in hydrated sodium cobalt, we investigate an extended ionic Hubbard model on the triangular lattice, which includes off-site attractions between sites with minor charges. Our quantum Monte Carlo simulations show that close to quarter filling, the off-site attractions induce a significant enhancement of d-wave and extended s-wave pairing correlations. Simultaneously, they render an increase of the charge structure factor at most of wave vectors. A combination with charge correlations in real space indicates the development of short-range finite-q charge density waves on the sites with minor charges. Our findings provide a new perspective on the superconducting mechanism in hydrated sodium cobalt based on the electronic structure which explicitly takes the effect of sodium atoms into account.

Van der Waals Engineering of Charge Density Waves in One-Dimensional Nb6Te6 Nanowires.

One-dimensional (1D) systems have played a crucial role in the development of fundamental physics and practical applications. Recently, transition metal monochalcogenide (TMM) wires based on molybdenum (Mo) and tungsten (W) have emerged as promising platforms for investigating 1D physics in pure van der Waals (vdW) platforms. Here, we report on the bottom-up fabrication of Nb6Te6 wires down to the single-wire limit. The unique properties of Nb6Te6 single wire enable the realization of 1D charge density wave (CDW) phases in an isolated single TMM wire. Moreover, we revealed the appealing regulation of 1D CDW orders by van der Waals interactions at either the 1D-2D interface (i.e., rotation of a single wire along its wire axis) or the 1D-1D interface. Two rotation angles (30° and 0°) give rise to 3 × 1 and zigzag chain CDW morphologies, respectively, which exhibit pronounced differences in atomic displacement by a factor of 2. The interwire vdW coupling overwhelms its counterpart at the 1D-2D interface, thus locking the rotation angle (at 0°) as well as the interwire atomic registries. In contrast, interestingly, the phases of the charge oscillations are independent of the adjacent wires. The ability to tailor 1D charge orders provides a crucial addition to the toll set of vdW integrations beyond two-dimensional materials.

Low-temperature behaviors of the dipolar magnet Dy3Sb3Zn2O14 with a strongly site-mixing disordered kagome lattice

Interesting behaviors may emerge in the magnetic frustrated materials with significant site-mixing disorder. We present the results of the structural, magnetic susceptibility, and specific heat measurements of Dy3Sb3Zn2O14 with ∼20 % Dy/Zn site-mixing disorder, which results in either a diluted 2D triangular lattice, or an intermediate structure between the kagome and pyrochlore lattice. In addition to the sharp anomaly of the temperature dependence of specific heat at T∼ 0.35 K, which was attributed to the emergent charge order state for the sample with less disorder, a broad peak at T∼ 1.5 K, and a small hump below T∼ 0.1 K are observed. The measured temperature dependence of specific heat and the Monte Carlo simulation suggest that the magnetic frustration persists despite of a strong site-mixing disorder.

Multisublattice Magnetic Structures in Charge Ordered Perovskite Manganites with High Doping Level

Multisublattice Magnetic Structures in Charge Ordered Perovskite Manganites with High Doping Level