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 × âˆš13), 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.

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.

A microscopic view of checkerboard and striped charge orders through doping antiferromagnetic Mott insulator.

The emergence of charge order in doped Mott insulators has received considerable attention due to its relevance to a variety of realistic materials and experiments. To investigate the interplay between magnetic and charge order, we have studied the semiclassical Kondo lattice model, which includes both electronic and magnetic degrees of freedom. By combining Langevin dynamical simulations with the kernel polynomial method, our results reveal the presence of charged stripe order, checkerboard order, and non-uniform charge disorder in the near-half-filling regime. Importantly, our simulations show that both the doping level and the strength of thes-dexchange coupling play a crucial role in facilitating charge order formation. These phases give rise to distinct electronic structures as well as excitations in the magnetic dynamics, providing insights into the underlying mechanism of charge ordering phenomena.

The influence of charge ordering in the microscopic structure of monohydroxy alcohols.

While radiation scattering data provides insight inside the microstructure of liquids, the Debye relation relating the scattering intensityI(k) to the atom-atom structure factorsSab(k)shows that, ultimately, it is these individual structure correlation functions which contain the relevant information about the micro-structure. However, these quantities are not observables, except in few cases where one can invert the Debye relation to obtain the structure functions. In the majority of other cases, the need for model dependent computer simulations is unavoidable. The resulting calculations reveal that the scattering pre-peak is the result of cancellations between positive pre-peaks and negative anti-peaks contributions from the atom-atom structure factors. What of systems where this cancellation is such that it entirely suppresses the scattering pre-peak? One would be tempted to falsely conclude that there is no underlying micro-heterogeneity. Hence, the structure functions appear as hidden variables, and it is important to understand the relation between their features and the micro-structure of the system. Through the computer simulation study of various mono-ols, ranging from methanol to 1-nonanol, as well as the branched octanols, we show how the features of the atom-atom pair correlation functiongab(r)affect that of the structure factorsSab(k), and reveal that the micro-structure is ultimately the result of the charge ordering between different atoms in the system.

Valence-Ordered Thin-Film Nickelate with Tri-component Nickel Coordination Prepared by Topochemical Reduction.

The metal-hydride-based "topochemical reduction" process has produced several thermodynamically unstable phases across various transition metal oxide series with unusual crystal structures and nontrivial ground states. Here, by such an oxygen (de-)intercalation method we synthesis a samarium nickelate with ordered nickel valences associated with tri-component coordination configurations. This structure, with a formula of Sm9Ni9O22 as revealed by four-dimensional scanning transmission electron microscopy (4D-STEM), emerges from the intricate planes of {303}pc ordered apical oxygen vacancies. X-ray spectroscopy measurements and ab initio calculations show the coexistence of square planar, pyramidal, and octahedral Ni sites with mono-, bi-, and tri-valences. It leads to an intense orbital polarization, charge-ordering, and a ground state with a strong electron localization marked by the disappearance of ligand-hole configuration at low temperature. This nickelate compound provides another example of previously inaccessible materials enabled by topotactic transformations and presents an interesting platform where mixed Ni valence can give rise to exotic phenomena.

Melting of Unidirectional Charge Density Waves across Twin Domain Boundaries in GdTe3.

Solids undergoing a transition from order to disorder experience a proliferation of topological defects. The melting process generates transient quantum states. However, their dynamic nature with a femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamic melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe3. Combining the STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discovered a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

Charge Distribution across Capped and Uncapped Infinite-Layer Neodymium Nickelate Thin Films.

Charge ordering (CO) phenomena have been widely debated in strongly-correlated electron systems mainly regarding their role in high-temperature superconductivity. Here, the structural and charge distribution in NdNiO2 thin films prepared with and without capping layers, and characterized by the absence and presence of CO are elucidated. The microstructural and spectroscopic analysis is done by scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) and hard X-ray photoemission spectroscopy (HAXPES). Capped samples show Ni1+ , with an out-of-plane (o-o-p) lattice parameter of around 3.30 Å indicating good stabilization of the infinite-layer structure. Bulk-sensitive HAXPES on Ni-2p shows weak satellite features indicating large charge-transfer energy. The uncapped samples evidence an increase of the o-o-p parameter up to 3.65 Å on the thin film top with a valence toward Ni2+ in this region. Here, 4D-STEM demonstrates (303)-oriented stripes which emerge from partially occupied apical oxygen. Those stripes form quasi-2D coherent domains viewed as rods in the reciprocal space with Δqz ≈ 0.24 reciprocal lattice units (r.l.u.) extension located at Q = ( ± 1 3 , 0 , ± 1 3 $\pm \frac{1}{3},0,\pm \frac{1}{3}$ ) and ( ± 2 3 , 0 , ± 2 3 $\pm \frac{2}{3},0,\pm \frac{2}{3}$ ) r.l.u. The stripes associated with oxygen re-intercalation concomitant with hole doping suggest a possible link to the previously reported CO in infinite-layer nickelate thin films.

A model of d-wave superconductivity, antiferromagnetism, and charge order on the square lattice.

We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking "d-density wave" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.

Probing the Origin of Chiral Charge Density Waves in the Two-Dimensional Limits.

Chirality generates spontaneous symmetry breaking and profoundly influences the topology, charge, and spin orders of materials. The chiral charge density wave (CDW) exhibits macroscopic chirality in the achiral crystal during the spontaneous electronic phase transitions. However, the mechanism of chiral CDW formation is shrouded in controversy. In this work, we report that two-dimensional H-phase TaS2 synthesized by molecular-beam epitaxy (MBE) shows a predominantly chiral CDW phase. Scanning tunneling microscopy (STM) imaging of the CDW reconstruction spots reveals a clockwise or anticlockwise intensity variation along the STM-imaged spots. First-principles calculations further show that the rotational symmetry of the momentum-dependent electron-phonon coupling is broken, giving rise to chirality. Our work provides new insights into the physical origin of the chiral charge-ordered states, shedding light on a general ordering rule in chiral CDWs.

Moiré Phonons in Magic-Angle Twisted Bilayer Graphene.

Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states. In this work, we study the phonon properties in magic-angle TBG based on many-body classical potential and interatomic forces generated by a deep neural network trained with data from ab initio calculations. We have discovered a number of soft modes which can exhibit dipolar, quadrupolar, and octupolar vibrational patterns in real space, as well as some time-reversal breaking chiral phonon modes. We have further studied the phonon effects on the electronic structures by freezing certain soft phonon modes. We find that if a soft quadrupolar phonon mode is assumed to be frozen, the system would exhibit a charge order which is perfectly consistent with recent experiments. Moreover, once some low-frequency C2z-breaking modes get frozen, the Dirac points at the charge neutrality point would be gapped out, which provides an alternative perspective to the origin of correlated insulator state at charge neutrality point.

Phonon-Induced Pairing in Quantum Dot Quantum Simulator.

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas.

The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to S=1/2 fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite W1 and W2 (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive W1>0, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state (T=0) diagram for W2≤0 as well as finite temperature (T>0) phase diagrams for W2=0 are presented. Two different types of charge order within 3×3 unit cell can occur. At T=0, for W2=0 phase separated states are degenerated with homogeneous phases (but T>0 removes this degeneration), whereas attractive W2<0 stabilizes phase separation at incommensurate fillings. For U/W1<0 and U/W1>1/2 only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive 0

Strain-Stabilized (π, π) Order at the Surface of Fe1+xTe.

A key property of many quantum materials is that their ground state depends sensitively on small changes of an external tuning parameter, e.g., doping, magnetic field, or pressure, creating opportunities for potential technological applications. Here, we explore tuning of the ground state of the nonsuperconducting parent compound, Fe1+xTe, of the iron chalcogenides by uniaxial strain. Iron telluride exhibits a peculiar (π, 0) antiferromagnetic order unlike the (π, π) order observed in the Fe-pnictide superconductors. The (π, 0) order is accompanied by a significant monoclinic distortion. We explore tuning of the ground state by uniaxial strain combined with low-temperature scanning tunneling microscopy. We demonstrate that, indeed under strain, the surface of Fe1.1Te undergoes a transition to a (π, π)-charge-ordered state. Comparison with transport experiments on uniaxially strained samples shows that this is a surface phase, demonstrating the opportunities afforded by 2D correlated phases stabilized near surfaces and interfaces.

Single-water-dipole-layer-driven Reversible Charge Order Transition in 1T-TaS2.

Water-solid interactions are crucial for many fundamental phenomena and technological processes. Here, we report a scanning tunneling microscopy study about the charge density wave (CDW) transition in 1T-TaS2 driven by a single water dipole layer. At low temperature, pristine 1T-TaS2 is a prototypical CDW compound with 13 × 13 charge order. After growing a highly ordered water adlayer, a new charge order with 3 × 3 periodicity emerges on water-covered 1T-TaS2. After water desorption, the entire 1T-TaS2 surface appears as localized 13 × 13 CDW domains that are separated by residual-water-cluster-pinned CDW domain walls. First-principles calculations show that the electric dipole moments in the water adlayer attract electrons to the top layer of 1T-TaS2, which shifts the phonon softening mode and induces the 13 × 13 to 3 × 3 charge order transition. Our results pave the way for creating new collective quantum states of matter with a molecular dipole layer.

Disorder raises the critical temperature of a cuprate superconductor.

With the discovery of charge-density waves (CDWs) in most members of the cuprate high-temperature superconductors, the interplay between superconductivity and CDWs has become a key point in the debate on the origin of high-temperature superconductivity. Some experiments in cuprates point toward a CDW state competing with superconductivity, but others raise the possibility of a CDW-superconductivity intertwined order or more elusive pair-density waves (PDWs). Here, we have used proton irradiation to induce disorder in crystals of [Formula: see text] and observed a striking 50% increase of [Formula: see text], accompanied by a suppression of the CDWs. This is in sharp contrast with the behavior expected of a d-wave superconductor, for which both magnetic and nonmagnetic defects should suppress [Formula: see text] Our results thus make an unambiguous case for the strong detrimental effect of the CDW on bulk superconductivity in [Formula: see text] Using tunnel diode oscillator (TDO) measurements, we find indications for potential dynamic layer decoupling in a PDW phase. Our results establish irradiation-induced disorder as a particularly relevant tuning parameter for the many families of superconductors with coexisting density waves, which we demonstrate on superconductors such as the dichalcogenides and [Formula: see text].

Nature and evolution of incommensurate charge order in manganites visualized with cryogenic scanning transmission electron microscopy.

Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map, at atomic resolution, the nature of incommensurate charge-lattice order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature ([Formula: see text]93 K). In diffraction, the ordering wave vector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the ordered state forms lattice-locked regions over a few wavelengths interspersed with phase defects and changing periodicity. The cations undergo picometer-scale ([Formula: see text]6 pm to 11 pm) transverse displacements, suggesting that charge-lattice coupling is strong. We further unearth phase inhomogeneity in the periodic lattice displacements at room temperature, and emergent phase coherence at 93 K. Such local phase variations govern the long-range correlations of the charge-ordered state and locally change the periodicity of the modulations, resulting in wave vector shifts in reciprocal space. These atomically resolved observations underscore the importance of lattice coupling and phase inhomogeneity, and provide a microscopic explanation for putative "incommensurate" order in hole-doped oxides.

Microscopic States and the Verwey Transition of Magnetite Nanocrystals Investigated by Nuclear Magnetic Resonance.

57Fe nuclear magnetic resonance (NMR) of magnetite nanocrystals ranging in size from 7 nm to 7 µm is measured. The line width of the NMR spectra changes drastically around 120 K, showing microscopic evidence of the Verwey transition. In the region above the transition temperature, the line width of the spectrum increases and the spin-spin relaxation time decreases as the nanocrystal size decreases. The line-width broadening indicates the significant deformation of magnetic structure and reduction of charge order compared to bulk crystals, even when the structural distortion is unobservable. The reduction of the spin-spin relaxation time is attributed to the suppressed polaron hopping conductivity in ferromagnetic metals, which is a consequence of the enhanced electron-phonon coupling in the quantum-confinement regime. Our results show that the magnetic distortion occurs in the entire nanocrystal and does not comply with the simple model of the core-shell binary structure with a sharp boundary.

Stacked charge stripes in the quasi-2D trilayer nickelate La4Ni3O8.

The quasi-2D nickelate La4Ni3O8 (La-438), consisting of trilayer networks of square planar Ni ions, is a member of the so-called T' family, which is derived from the Ruddlesden-Popper (R-P) parent compound La4Ni3O10-x by removing two oxygen atoms and rearranging the rock salt layers to fluorite-type layers. Although previous studies on polycrystalline samples have identified a 105-K phase transition with a pronounced electronic and magnetic response but weak lattice character, no consensus on the origin of this transition has been reached. Here, we show using synchrotron X-ray diffraction on high-pO2 floating zone-grown single crystals that this transition is associated with a real space ordering of charge into a quasi-2D charge stripe ground state. The charge stripe superlattice propagation vector, q = (2/3, 0, 1), corresponds with that found in the related 1/3-hole doped single-layer R-P nickelate, La5/3Sr1/3NiO4 (LSNO-1/3; Ni(2.33+)), with orientation at 45° to the Ni-O bonds. The charge stripes in La-438 are weakly correlated along c to form a staggered ABAB stacking that reduces the Coulomb repulsion among the stripes. Surprisingly, however, we find that the charge stripes within each trilayer of La-438 are stacked in phase from one layer to the next, at odds with any simple Coulomb repulsion argument.

Nanoscale Superconducting Honeycomb Charge Order in IrTe2.

Entanglement of charge orderings and other electronic orders such as superconductivity is in the core of challenging physics issues of complex materials including high temperature superconductivity. Here, we report on the observation of a unique nanometer scale honeycomb charge ordering of the cleaved IrTe2 surface, which hosts a superconducting state. IrTe2 was recently established to exhibit an intriguing cascade of stripe charge orders. The stripe phases coexist with a hexagonal phase, which is formed locally and falls into a superconducting state below 3 K. The atomic and electronic structures of the honeycomb and hexagon pattern of this phase are consistent with the charge order nature, but the superconductivity does not survive on neighboring stripe charge order domains. The present work provides an intriguing physics issue and a new direction of functionalization for two-dimensional materials.

A new method applicable to study solid compounds with multiple polyhedral structures.

A new direct summation method, named as polyhedron method, is proposed to calculate Madelung energy. This method calculates sums of electrostatic interactions over sets of neutral polyhedron unit pairs rather than conventional ion pairs; this gives Madelung constant in a matrix. With robustly rapid convergence, polyhedron method is generally applicable for complex compounds containing multiple polyhedral building-blocks and numerical polyhedral connection modes. The matrical analysis suggests face-sharing between octahedral pairs and edge-sharing between tetrahedral pairs can be electrostatically stable, against Pauling's third rule. Further, the matrical calculation of Madelung energies offers a unique advantage to evaluate enormous configurations of cation distributions in a given lattice in a high-throughput manner. That is applicable to study solid solution composites, polymorphism, and defect structures, including but not limited to intermediate phase of delithiated cathode compounds, charge order or antisite defects, and extensively magnetic order. © 2016 Wiley Periodicals, Inc.