Charge-ordered Phase Research Articles

Terahertz spectroscopy of collective charge density wave dynamics at the atomic scale.

Charge density waves are wave-like modulations of a material's electron density that display collective amplitude and phase dynamics. The interaction with atomic impurities induces strong spatial heterogeneity of the charge-ordered phase. Direct real-space observation of phase excitation dynamics of such defect-induced charge modulation is absent. Here, by utilizing terahertz pump-probe spectroscopy in a scanning tunnelling microscope, we measure the ultrafast collective dynamics of the charge density wave in the transition metal dichalcogenide 2H-NbSe2 with atomic spatial resolution. The tip-enhanced electric field of the terahertz pulses excites oscillations of the charge density wave that vary in magnitude and frequency on the scale of individual atomic impurities. Overlapping phase excitations originating from the randomly distributed atomic defects in the surface create this spatially structured response of the charge density wave. This ability to observe collective charge order dynamics with local probes makes it possible to study the dynamics of correlated materials at the intrinsic length scale of their underlying interactions.

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.

Superstructure of Fe5-xGeTe2 Determined by Te K-Edge Extended X-ray Absorption Fine Structure and Te Kα X-ray Fluorescence Holography.

The local structure of the two-dimensional van der Waals material, Fe5-xGeTe2, which exhibits unique structural/magnetic phase transitions, was investigated by Te K-edge extended X-ray absorption fine structure (EXAFS) and Te Kα X-ray fluorescence holography (XFH) over a wide temperature range. The formation of a trimer of Te atoms at low temperatures has been fully explored using these methods. An increase in the Te-Fe distance at approximately 150 K was suggested by EXAFS and presumably indicates the formation of a Te trimer. Moreover, XFH displayed clear atomic images of Te atoms. Additionally, the distance between the Te atoms shortened, as confirmed from the atomic images reconstructed from XFH, indicating the formation of a trimer of Te atoms, i.e., a charge-ordered superstructure. Furthermore, Te Kα XFH provided unambiguous atomic images of Fe atoms occupying the Fe1 site; the images were not clearly observed in the Ge Kα XFH that was previously reported because of the low occupancy of Fe and Ge atoms. In this study, EXAFS and XFH clearly showed the local structure around the Te atom; in particular, the formation of Te trimers caused by charge-ordered phase transitions was clearly confirmed. The charge-ordered phase transition is fully discussed based on the structural variation at low temperatures, as established from EXAFS and XFH.

Surface triggered stabilization of metastable charge-ordered phase in SrTiO3

Charge ordering (CO), characterized by a periodic modulation of electron density and lattice distortion, has been a fundamental topic in condensed matter physics, serving as a potential platform for inducing novel functional properties. The charge-ordered phase is known to occur in a doped system with high d-electron occupancy, rather than low occupancy. Here, we report the realization of the charge-ordered phase in electron-doped (100) SrTiO3 epitaxial thin films that have the lowest d-electron occupancy i.e., d1-d0. Theoretical calculation predicts the presence of a metastable CO state in the bulk state of electron-doped SrTiO3. Atomic scale analysis reveals that (100) surface distortion favors electron-lattice coupling for the charge-ordered state, and triggering the stabilization of the CO phase from a correlated metal state. This stabilization extends up to six unit cells from the top surface to the interior. Our approach offers an insight into the means of stabilizing a new phase of matter, extending CO phase to the lowest electron occupancy and encompassing a wide range of 3d transition metal oxides.

H-wave – A Python package for the Hartree-Fock approximation and the random phase approximation

H-wave is an open-source software package for performing the Hartree–Fock approximation (HFA) and random phase approximation (RPA) for a wide range of Hamiltonians of interacting fermionic systems. In HFA calculations, H-wave examines the stability of several symmetry-broken phases, such as anti-ferromagnetic and charge-ordered phases, in the given Hamiltonians at zero and finite temperatures. Furthermore, H-wave calculates the dynamical susceptibilities using RPA to examine the instability toward the symmetry-broken phases. By preparing a simple input file for specifying the Hamiltonians, users can perform HFA and RPA for standard Hamiltonians in condensed matter physics, such as the Hubbard model and its extensions. Additionally, users can use a Wannier90-like format to specify fermionic Hamiltonians. A Wannier90 format is implemented in RESPACK to derive ab initio Hamiltonians for solids. HFA and RPA for the ab initio Hamiltonians can be easily performed using H-wave. In this paper, we first explain the basis of HFA and RPA, and the basic usage of H-wave, including download and installation. Thereafter, the input file formats implemented in H-wave, including the Wannier90-like format for specifying the interacting fermionic Hamiltonians, are discussed. Finally, we present several examples of H-wave such as zero-temperature HFA calculations for the extended Hubbard model on a square lattice, finite-temperature HFA calculations for the Hubbard model on a cubic lattice, and RPA in the extended Hubbard model on a square lattice. Program summaryProgram Title:H-waveCPC Library link to program files:https://doi.org/10.17632/9gr6pxhfjm.1Developer's repository link:https://github.com/issp-center-dev/H-waveCode Ocean capsule:https://codeocean.com/capsule/6875177Licensing provisions: GNU General Public License version 3Programming language: Python3External routines/libraries: NumPy, SciPy, Tomli, Requests.Nature of problem: Physical properties of strongly correlated electrons are examined such as ground state phase structure and response functions at zero and finite temperatures.Solution method: Calculations based on the unrestricted Hartree-Fock approximation and the random phase approximation are performed for the quantum lattice models such as the Hubbard model and its extensions.

Cationic mismatch effect on structural and magnetic behavior of La0.5-xEuxCa0.5-yBayMnO3 charge-ordered manganites

In this research, we have tried to investigate the effect of the cationic disorder on charge ordering and magnetic phase separation in La0.5-xEuxCa0.5-yBayMnO3 (x = 0, 0.05, and 0.1) compounds synthesized by using the sol-gel method. All the samples possess the same average ionic radius at A site <rA> and the same Mn3+/Mn4+ ratio. Our analysis confirmed the chemical composition by energy dispersive X-ray spectroscopy and verified the structural integrity and purity of the phase by X-ray diffraction, revealing an orthorhombic structure with Pnma space group, which is in agreement with the tolerance factor. The important mismatch effect observed in the substituted specimens induces drastic effects on the structural and microstructural properties. Magnetic measurements indicate a great reduction of Curie temperature for substituted samples (from 250 K for x = 0 to 90 K for x = 0.05 and 85 K for x = 0.1), which indicates a weakening of ferromagnetic double exchange interactions induced by cationic disorder. The Arrott plots and the magnetocaloric study of the Eu−based samples indicate the persistence of the antiferromagnetic charge-ordered state characterizing the pristine compound (x = 0) as well as the presence of a first-ordered metamagnetic transition for all the studied samples, which is ascribed to the presence of antiferromagnetic domains. Such transition induced the appearance of a shoulder peak near 100 K in the magnetic entropy change curves for high magnetic field values, resulting in an extra cooling efficiency.

Dynamics and resilience of the unconventional charge density wave in ScV6Sn6 bilayer kagome metal

Long-range electronic ordering descending from a metallic parent state constitutes a rich playground to study the interplay of structural and electronic degrees of freedom. In this framework, kagome metals are in the most interesting regime where both phonon and electronically mediated couplings are significant. Several of these systems undergo a charge density wave transition. However, to date, the origin and the main driving force behind this charge order is elusive. Here, we use the kagome metal ScV6Sn6 as a platform to investigate this problem, since it features both a kagome-derived nested Fermi surface and van-Hove singularities near the Fermi level, and a charge-ordered phase that strongly affects its physical properties. By combining time-resolved reflectivity, first principles calculations and photo-emission experiments, we identify the structural degrees of freedom to play a fundamental role in the stabilization of charge order, indicating that ScV6Sn6 features an instance of charge order predominantly originating from phonons.

Direct observation of the collective modes of the charge density wave in the kagome metal CsV3Sb5

A recently discovered group of kagome metals AV[Formula: see text]Sb[Formula: see text] (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this charge-ordered parent phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations-the collective modes-has not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV[Formula: see text]Sb[Formula: see text] and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for a better understanding of the unconventional phases hosted on the kagome lattice.

Phase Transition Field Effect Transistor Observed in an α-(BEDT-TTF)2I3 Single Crystal

The metal–insulator transition induced by the gate electric field in the charge order phase of the α-(BEDT-TTF)2I3 single-crystal field-effect transistor (FET) structure was clearly observed near the phase transition temperature. An abrupt increase in the electrical conductance induced by the applied gate electric field was evident, which corresponds to the partial dissolution of the charge order phase triggered by the gate electric field. The estimated nominal dissolved charge order region (i.e., the gate-induced metallic region) was overestimated in 130–150 K, suggesting additional effects such as Joule heating. On the other hand, in the lower temperature region below 120 K, the corresponding dissolved charge order was several monolayers of BEDT-TTF, suggesting that it is possible to dissolve the charge order phase within the bistable temperature region.

Tunable spin and valley excitations of correlated insulators in Γ-valley moiré bands.

Moiré superlattices formed from transition metal dichalcogenides support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley degree of freedom affects optoelectronic properties in the constituent transition metal dichalcogenides, it has yet to be fully explored in moiré systems. Here we establish twisted double-bilayer WSe2 as an experimental platform to study electronic correlations within Γ-valley moiré bands. Through local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré fillings. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with spin-polaron quasiparticle excitations. In addition, an applied displacement field induces a metal-insulator transition driven by tuning between Γ- and K-valley moiré bands. Our results demonstrate control over the spin and valley character of the correlated ground and excited states in this system.

Quantum dephasing of kagome superconductivity

Recent observations for a pressurized kagome superconductor through transport, muon spin relaxation, nuclear magnetic resonance, and point contact spectroscopy demonstrate striking fluctuating superconductivity at a magic pressure. This discovery may hint at a new quantum dephasing mechanism, which can be discussed from the perspectives of correlation and topology. Three outstanding questions should be considered in decoding this mechanism: one is the intrinsic phase fragile nature of kagome superconductivity; second is the role of Coulomb interactions within different charge-ordered phases; third is the geometrical phase compatibility between superconductivity and different charge orders.

Kagome qubit ice

Topological phases of spin liquids with constrained disorder can host a kinetics of fractionalized excitations. However, spin-liquid phases with distinct kinetic regimes have proven difficult to observe experimentally. Here we present a realization of kagome spin ice in the superconducting qubits of a quantum annealer, and use it to demonstrate a field-induced kinetic crossover between spin-liquid phases. Employing fine control over local magnetic fields, we show evidence of both the Ice-I phase and an unconventional field-induced Ice-II phase. In the latter, a charge-ordered yet spin-disordered topological phase, the kinetics proceeds via pair creation and annihilation of strongly correlated, charge conserving, fractionalized excitations. As these kinetic regimes have resisted characterization in other artificial spin ice realizations, our results demonstrate the utility of quantum-driven kinetics in advancing the study of topological phases of spin liquids.

Magnetic impurities in a charge-ordered background

We investigate how magnetic impurities may affect a system exhibiting a charge-density wave (CDW) in its ground state. We consider a disordered Hubbard-Holstein model with a homogeneous electron-phonon interaction but with a (randomly chosen) fraction of sites displaying a nonzero Coulomb repulsion $U$ and perform state-of-the-art finite-temperature quantum Monte Carlo simulations. For a single magnetic impurity, charge-charge correlations hamper the spin-spin ones around the repulsive site, thus requiring a strong enough value of $U$ to create nonnegligible antiferromagnetic (AFM) correlations. As the number of magnetic impurities increases, these AFM correlations become deleterious to CDW order and its features. First, the critical temperature is drastically reduced and seems to vanish $\ensuremath{\sim}40%$ of impurities (for fixed $U/\ensuremath{\lambda}=2$), which we correlate with the classical percolation threshold. We also notice that just a small amount of disorder suffices to create a bad insulating state, with the suppression of both Peierls and spin gaps, even within the charge-ordered phase. Finally, we have also found that pairing correlations are enhanced at large doping, driven by the competition between CDW and AFM tendencies.

Orbital Degree of Freedom in Conducting Platinum–Dithiolene Complex Salts

We report experimental evidence for the orbital degrees of freedom in anion–radical salts consisting of metal–dithiolene complexes, obtained by a simple method. We observed the NIR absorption spectra of the 2D molecular conductors Me4Q[Pt(dmit)2]2 (Q = N, P, and Sb, dmit = 1,3-dithiole-2-thione-4,5-dithiolate), which shows a phase transition from the metallic phase to the semiconducting and charge-ordered phase, and analyzed the orbital levels of dimers [Pt(dmit)2]2 near the Fermi energy. The highest-energy electrons in the charge-ordered phase occupied the bonding orbitals, whereas those in the metallic phase occupied the antibonding orbitals. The redistribution of charges and the replacement of the outermost orbitals co-occurred for all dimers in Me4Q[Pt(dmit)2]2. This phenomenon differs from that in palladium analogs, in which the replacement of the outermost orbitals does not occur or occurs only for half of all dimers. Our experimental results revealed that anion–radical salts consisting of metal–dithiolene complexes have a variety of orbital distributions.

Pressure-induced charge orders and their postulated coupling to magnetism in hexagonal multiferroic LuFe2O4

Hexagonal LuFe2O4 is a promising charge order (CO) driven multiferroic material with high charge and spin-ordering temperatures. The coexisting charge and spin orders on Fe3+/Fe2+ sites result in magnetoelectric behaviors, but the coupling mechanism between the charge and spin orders remains elusive. Here, by tuning external pressure, we reveal three charge-ordered phases with suggested correlation to magnetic orders in LuFe2O4: (i) a centrosymmetric incommensurate three-dimensional CO with ferrimagnetism, (ii) a non-centrosymmetric incommensurate quasi-two-dimensional CO with ferrimagnetism, and (iii) a centrosymmetric commensurate CO with antiferromagnetism. Experimental in situ single-crystal X-ray diffraction and X-ray magnetic circular dichroism measurements combined with density functional theory calculations suggest that the charge density redistribution caused by pressure-induced compression in the frustrated double-layer [Fe2O4] cluster is responsible for the correlated spin-charge phase transitions. The pressure-enhanced effective Coulomb interactions among Fe-Fe bonds drive the frustrated (1/3, 1/3) CO to a less frustrated (1/4, 1/4) CO, which induces the ferrimagnetic to antiferromagnetic transition. Our results not only elucidate the coupling mechanism among charge, spin, and lattice degrees of freedom in LuFe2O4, but also provide a new way to tune the spin-charge orders in a highly controlled manner.

Spin and charge modulations of a half-filled extended Hubbard model

We introduce and analyze an extended Hubbard model, in which intersite Coulomb interaction as well as a staggered local potential (SLP) are considered, on the square lattice at half band filling, in the thermodynamic limit. Using both Hartree-Fock approximation and Kotliar and Ruckenstein slave boson formalism, we show that the model harbors charge order (CO) as well as joint spin and charge modulations (SCO) at finite values of the SLP, while the spin density wave (SDW) is stabilized for vanishing SLP, only. We determine their phase boundaries and the variations of the order parameters in dependence on the SLP, as well as on the on-site and nearest-neighbor interactions. Domains of coexistence of CO and SCO phases, suitable for resistive switching experiments, are unraveled. We show that the novel SCO systematically turns into the more conventional SDW phase when the zero-SLP limit is taken. We also discuss the nature of the different phase transitions, both at zero and finite temperature. In the former case, no continuous CO to SDW (or SCO) phase transition occurs. In contrast, a paramagnetic phase (PM), which is accompanied with continuous phase transitions towards both spin or charge ordered phases, sets in at finite temperature. A good quantitative agreement with numerical simulations is demonstrated, and a comparison between the two used approaches is performed.

Anomalous Ca Content Dependence of Dielectric Properties of Charge-Ordered Pr1−xCaxMnO3 as a Signature of Charge-Ordered Phase Modulation

Low-temperature dielectric properties of charge/orbital-ordered manganite, Pr1−xCaxMnO3 for 0.40 ≤ x ≤ 0.50, was investigated systematically as a function of Ca content, x. The Ca content dependence of dielectric permittivity and dissipation factor exhibited distinct maxima near x~0.45. The overall dielectric response of charge-ordered Pr1−xCaxMnO3 was dominated by dielectric polarization induced by polaron hopping and exhibited thermally activated relaxation behaviour. The thermally activated dielectric relaxation behaviour over the investigated temperature range was further analysed with the help of two models: the small polaron hopping model and the Mott three-dimensional variable range hopping model. The estimated polaron transport parameters also displayed non-monotonic variation with x and exhibited a broad minima between x = 0.425 and 0.45. Considering the previous work reported so far, the charge order pattern of Pr1−xCaxMnO3 below x = 0.425 was most likely to be of Zener-polaron type, while near x = 0.50 was checker-board type and for in-between compositions; neither pure checker-board type nor pure Zener-polaron type can be considered a ground state. The observed results suggest that a modulation of the checkerboard-type charge/orbital ordering pattern in Pr1−xCaxMnO3 possibly takes place in the Ca content range of investigation, 0.40 ≤ x ≤ 0.50.

Magnetic order driven ultrafast phase transition in NdNiO3

Ultrashort x-ray pulses can be used to disentangle magnetic and structural dynamics and are accordingly utilized here to study the photoexcitation of $\mathrm{Nd}\mathrm{Ni}{\mathrm{O}}_{3}$ (NNO), a model nickelate exhibiting structural and magnetic dynamics that conspire to induce an insulator-to-metal transition (IMT). During the course of the photoinduced IMT with above-gap excitation, we observe an ultrafast ($&lt;180$ fs) quenching of magnetic order followed by a time delayed collapse of the insulating phase probed by x-ray absorption and THz transmission (450 fs) that correlates with the slowest optical phonon mode involved in the structural transition. A simultaneous order-disorder response at the Ni site and displacive response at the Nd site coexist in the ultrafast magnetic response. Crucially, we observe the optical phonon through its coherent coupling with Nd magnetic order, demonstrating that the magnetic and structural degrees of freedom both contribute in driving the IMT. Density functional theory calculations reveal a consistent scenario where optically driven intersite charge transfer drives a collapse of antiferromagnetic order that in turn destabilizes the charge-ordered phase resulting in an IMT. These experiments provide different modalities for the control of electronic phase transitions in quantum materials based on the ultrafast interplay between structural and magnetic orders created by femtosecond photoexcitation.

Physical properties and phase diagram of single crystal REBaMn2O6 (RE = Sm, Eu, Gd, Tb, Dy, and Y)

We have carried out a systematic study on antiferromagnetic and charge ordering phase transitions in double-perovskite manganite compounds REBaMn2O6 (RE ​= ​Sm, Eu, Gd, Tb, Dy, and Y) by using single-crystalline samples. In YBaMn2O6, a tiny anomaly near 480 ​K as well as a first-order phase transition near 520 ​K are found in the temperature dependence of resistivity. Synchrotron x-ray single-crystal structure analysis shows that the unit cell is doubled first in the ab plane and further doubled along the c-axis as the temperature decreases. One of the most possible electronic phases between 480 ​K and 520 ​K is Zener polaron ordering. Mn atoms are paired in the ab-plane with seven 3d-electrons localized on each pair. The 3d-electron distribution in each pair begins to become asymmetric below 480 ​K. Similar two-step transitions are also observed for RE ​= ​Tb and Dy. The antiferromagnetic transition at TN ​≃ ​180 ​K is accompanied by a large hysteresis, which is attributable to a simultaneous rearrangement of charge order. The charge rearrangement temperature gradually rises with increasing the RE ionic radius. In SmBaMn2O6, the Néel temperature (TN) is 175 ​K and is lower than charge rearrangement temperature (≃ 200 ​K). These transitions are summarized in a phase diagram with respect to temperature and the ionic radius of RE3+.

Effects of vanadium doping on the charge ordering and low-temperature spin-glass phase in Pr0.45Ca0.55MnO3

We report structural, magnetic, and dielectric properties of the Pr0.45Ca0.55Mn1-xVxO3 (x = 0.05 and 0.1) polycrystalline compounds, prepared by solid state reaction method. Pnma space group and orthorhombic crystal structure of the compounds are confirmed by the Rietveld refinement of X-ray diffraction data. Magnetic study reveals a multiple-phase-separated metastable magnetic behavior with charge ordered phase followed by a spin-glass state at the low-temperature region. For a single change of vanadium content from x = 0.05–0.1, the charge ordering temperature decreases from 245 K to 239 K, the antiferromagnetic ordering temperature decreases from 131 K to 127 K, and the ferromagnetic cluster-glass ordering temperature increases from 41 K to 44 K. This indicates the weakening of charge ordering strength and development of ferromagnetic components in the antiferromagnetic background, which is also confirmed by isothermal hysteresis. Colossal dielectric constant is observed in both samples. In the measured temperature range, an implication of a ferroelectric phase transition around 253 K is observed in Pr0.45Ca0.55Mn0.90V0.10O3 compound. The calculated results indicate that the low-temperature relaxation follows variable range hopping behavior, whereas the high-temperature one takes place according to the Arrhenius model. The fitting parameters ascribe the low-temperature relaxation process to the hopping of polaron charge carriers at localized sites, whereas the high-temperature relaxation is related to Maxwell-Wagner relaxation, caused by blocking of charge carriers at grain boundaries.