Stripe phases in high-temperature superconductors

Ordering Effect of Charge-Charge Repulsion in Doped Antiferromagnetic Lattices: A Coupled Cluster Study

In quantum chemistry, single-reference Coupled Cluster theory, and its refinements introduced by Bartlett, has become a "gold-standard" predictive method for taking into account electronic correlations in molecules. In this article, we introduce a new formalism based on a Coupled Cluster expansion of the wave function that is suited to describe model periodic systems and apply this methodology to the case of hole-doped antiferromagnetic two-dimensional (2D)-square spin-lattices as a proof of concept. More precisely, we focus our study on 1/5 and 1/7 doping ratios and discuss the possible ordering effect due to large hole-hole repulsion. Starting from one of the equivalent single determinants exhibiting a full spin alternation and the most remote location of the holes as a single reference, the method incorporates some corrections to the traditional Coupled Cluster formalism to take into account the nonadditivity of excitation energies to multiply excited determinants. The amplitudes of the excitations, which are possible on the excited determinants but impossible on the reference, are evaluated perturbatively, while their effect is treated as a dressing in the basic equations. The expansion does not show any sign of divergence of the wave operator. Finally, the probabilities of holes moving toward the first- and second-neighboring sites are reported, which confirms the importance of the hole-hole repulsion and offers a picture of how stripes expand around its central line in the "stripe phases" observed in cuprates.

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.

Emergence of Competing Stripe Phases in Undoped Infinite-Layer Nickelates

Recent discovery of superconductivity in infinite-layer nickelates has ignited renewed theoretical and experimental interest in the role of electronic correlations in their properties. Here, using first-principles simulations, we show that the parent compound of the nickelate family, LaNiO_{2}, hosts competing low-energy stripe phases, similar to doped cuprates. The stripe states are shown to be driven by multiorbital electronic mechanisms and Peierls distortions. Our study indicates that both strong correlations and electron-phonon coupling effects play a key role in the physics of infinite-layer nickelates, and sheds light on the microscopic origin of electronic inhomogeneity and the lack of long-range order in the nickelates.

Variational Monte Carlo study of stripes as a function of doping in thet-t'Hubbard model

We perform variational Monte Carlo simulations of the single-band Hubbard model on the square lattice with both nearest (t) and next-nearest (t') neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair-pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Semiconductor moiré materials

Moiré materials have emerged as a platform for exploring the physics of strong electronic correlations and non-trivial band topology. Here we review the recent progress in semiconductor moiré materials, with a particular focus on transition metal dichalcogenides. Following a brief overview of the general features in this class of materials, we discuss recent theoretical and experimental studies on Hubbard physics, Kane-Mele-Hubbard physics and equilibrium moiré excitons. We also comment on the future opportunities and challenges in the studies of transition metal dichalcogenide and other semiconductor moiré materials.

Anomalous phase separation in a correlated electron system: Machine-learning-enabled large-scale kinetic Monte Carlo simulations

SignificancePhase separation is crucial to the functionalities of many correlated electron materials with notable examples including colossal magnetoresistance in manganites and high-Tc superconductivity in cuprates. However, the nonequilibrium phase-separation dynamics in such systems are poorly understood theoretically, partly because the required multiscale modeling is computationally very demanding. With the aid of machine-learning methods, we have achieved large-scale dynamical simulations in a representative correlated electron system. We observe an unusual relaxation process that is beyond the framework of classical phase-ordering theories. We also uncover a correlation-induced freezing behavior, which could be a generic feature of phase separation in correlated electron systems.

Superconductivity in a quintuple-layer square-planar nickelate

Since the discovery of high-temperature superconductivity in copper oxide materials¹, there have been sustained efforts to both understand the origins of this phase and discover new cuprate-like superconducting materials². One prime materials platform has been the rare-earth nickelates and, indeed, superconductivity was recently discovered in the doped compound Nd_0.8Sr_0.2NiO₂ (ref. ³). Undoped NdNiO₂ belongs to a series of layered square-planar nickelates with chemical formula Nd_n+1Ni_nO_2n+2 and is known as the 'infinite-layer' (n = ∞) nickelate. Here we report the synthesis of the quintuple-layer (n = 5) member of this series, Nd₆Ni₅O₁₂, in which optimal cuprate-like electron filling (d^8.8) is achieved without chemical doping. We observe a superconducting transition beginning at ~13 K. Electronic structure calculations, in tandem with magnetoresistive and spectroscopic measurements, suggest that Nd₆Ni₅O₁₂ interpolates between cuprate-like and infinite-layer nickelate-like behaviour. In engineering a distinct superconducting nickelate, we identify the square-planar nickelates as a new family of superconductors that can be tuned via both doping and dimensionality.

Non-Fermi liquid behavior below the Néel temperature in the frustrated heavy fermion magnet UAu2

The term Fermi liquid is almost synonymous with the metallic state. The association is known to break down at quantum critical points (QCPs), but these require precise values of tuning parameters, such as pressure and applied magnetic field, to exactly suppress a continuous phase transition temperature to the absolute zero. Three-dimensional non-Fermi liquid states, apart from superconductivity, that are unshackled from a QCP are much rarer and are not currently well understood. Here, we report that the triangular lattice system uranium diauride (UAu₂) forms such a state with a non-Fermi liquid low-temperature heat capacity [Formula: see text] and electrical resistivity [Formula: see text] far below its Néel temperature. The magnetic order itself has a novel structure and is accompanied by weak charge modulation that is not simply due to magnetostriction. The charge modulation continues to grow in amplitude with decreasing temperature, suggesting that charge degrees of freedom play an important role in the non-Fermi liquid behavior. In contrast with QCPs, the heat capacity and resistivity we find are unusually resilient in magnetic field. Our results suggest that a combination of magnetic frustration and Kondo physics may result in the emergence of this novel state.

Emergence of quenched disorder as a dominant control for complex phase diagram of rare-earth nickelates

Competing interactions in complex materials tend to induce multiple quantum phases of comparable energetics close to the ground state stability. This requires novel strategies and tools to segregate such phases with desired control to manipulate the properties relevant for contemporary technologies. Here, we show 'quenched disorder (QD)' as a predominant control parameter to realize a broad range of the quantum phases of bulkRNiO₃(R= rare-earth ion) phase diagram in a La_xEu_1-xNiO₃compounds by systematic introduction of QD. Using static and terahertz dynamic transport studies on epitaxial thin films, we demonstrate various phases such as Fermi to non-Fermi liquid crossover, bad metallic behavior, quantum criticality, preservation of orbital and charge order symmetry and increased electronic inhomogeneity responsible for Maxwell-Wagner type of dielectric response, etc. The underlying mechanisms are unveiled by the anomalous responses of microscopic quantities such as scattering rate, plasma frequency, spectral weight, effective mass, and disorder. The results and methodology implemented here can be a generic pursuit of disorder based unified control to extract quantum phases submerged in competing energetics in all complex materials.

Stripe phases in WSe2/WS2 moiré superlattices

Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions^1-11. However, identifying and studying such stripe phases remains challenging. Here we uncover stripe phases in WSe₂/WS₂ moiré superlattices by combining optical anisotropy and electronic compressibility measurements. We find strong electronic anisotropy over a large doping range peaked at 1/2 filling of the moiré superlattice. The 1/2 state is incompressible and assigned to an insulating stripe crystal phase. Wide-field imaging reveals domain configurations with a preferential alignment along the high-symmetry axes of the moiré superlattice. Away from 1/2 filling, we observe additional stripe crystals at commensurate filling 1/4, 2/5 and 3/5, and compressible electronic liquid crystal states at incommensurate fillings. Our results demonstrate that two-dimensional semiconductor moiré superlattices are a highly tunable platform from which to study the stripe phases and their interplay with other symmetry breaking ground states.

Charge order lock-in by electron-phonon coupling in La1.675Eu0.2Sr0.125CuO4

Charge order is universal to all hole-doped cuprates. Yet, the driving interactions remain an unsolved problem. Electron-electron interaction is widely believed to be essential, whereas the role of electron-phonon interaction is unclear. We report an ultrahigh-resolution resonant inelastic x-ray scattering (RIXS) study of the in-plane bond-stretching phonon mode in stripe-ordered cuprate La1.675Eu0.2Sr0.125CuO4 Phonon softening and lifetime shortening are found around the charge ordering wave vector. In addition to these self-energy effects, the electron-phonon coupling is probed by its proportionality to the RIXS cross section. We find an enhancement of the electron-phonon coupling around the charge-stripe ordering wave vector upon cooling into the low-temperature tetragonal structure phase. These results suggest that, in addition to electronic correlations, electron-phonon coupling contributes substantially to the emergence of long-range charge-stripe order in cuprates.

Using Uniaxial Stress to Probe the Relationship between Competing Superconducting States in a Cuprate with Spin-stripe Order

We report muon spin rotation and magnetic susceptibility experiments on in-plane stress effects on the static spin-stripe order and superconductivity in the cuprate system La_{2-x}Ba_{x}CuO_{4} with x=0.115. An extremely low uniaxial stress of ∼0.1  GPa induces a substantial decrease in the magnetic volume fraction and a dramatic rise in the onset of 3D superconductivity, from ∼10 to 32 K; however, the onset of at-least-2D superconductivity is much less sensitive to stress. These results show not only that large-volume-fraction spin-stripe order is anticorrelated with 3D superconducting coherence but also that these states are energetically very finely balanced. Moreover, the onset temperatures of 3D superconductivity and spin-stripe order are very similar in the large stress regime. These results strongly suggest a similar pairing mechanism for spin-stripe order and the spatially modulated 2D and uniform 3D superconducting orders, imposing an important constraint on theoretical models.

Evidence for a vestigial nematic state in the cuprate pseudogap phase

The CuO₂ antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E| < [Formula: see text], where [Formula: see text] is the PG energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite-Q density-wave (DW) state and a Q = 0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken-symmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures T _DW and T _NE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy [Formula: see text] Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi₂Sr₂CaCu₂O₈.

On the mechanism behind the inverse melting in systems with competing interactions

The competition between a short range attractive interaction and a nonlocal repulsive interaction promote the appearance of modulated phases. In this work we present the microscopic mechanisms leading to the emergence of inverse transitions in such systems by considering a thorough mean-field analysis of a variety of minimal models with different competing interactions. We identify the specific connections between the characteristic energy of the homogeneous and modulated phases and the observed reentrant behaviors in the phase diagram. In particular, we find that reentrance is appreciable when the characteristic energy cost of the homogeneous and modulated phases are comparable to each other, and for systems in which the local order parameter is limited. In the asymptotic limit of high energy cost of the homogeneous phase we observe that the degree of reentrance decreases exponentially with the ratio of the characteristic energy cost of homogeneous and modulated phases. These mean-field results are confronted with Langevin simulations of an effective coarse grained model, confirming the expected extension of the reentrance in the phase diagram. These results shed new light on many systems undergoing inverse melting transitions by qualitatively improving the understanding of the interplay of entropy and energy around the inverse melting points.

Straight motion of half-integer topological defects in thin Fe-N magnetic films with stripe domains

In thin magnetic films with perpendicular magnetic anisotropy, a periodic “up-down” stripe-domain structure can be originated at remanence, on a mesoscopic scale (~100 nm) comparable with film thickness, by the competition between short-range exchange coupling and long-range dipolar interaction. However, translational order is perturbed because magnetic edge dislocations are spontaneously nucleated. Such topological defects play an important role in magnetic films since they promote the in-plane magnetization reversal of stripes and, in superconductor/ferromagnet hybrids, the creation of superconducting vortex clusters. Combining magnetic force microscopy experiments and micromagnetic simulations, we investigated the motion of two classes of magnetic edge dislocations, randomly distributed in an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{N}}}_{2}^{+}$$\end{document}N2+-implanted Fe film. They were found to move in opposite directions along straight trajectories parallel to the stripes axis, when driven by a moderate dc magnetic field. Using the approximate Thiele equation, analytical expressions for the forces acting on such magnetic defects and a microscopic explanation for the direction of their motion could be obtained. Straight trajectories are related to the presence of a periodic stripe domain pattern, which imposes the gyrotropic force to vanish even if a nonzero, half-integer topological charge is carried by the defects in some layers across the film thickness.

Pathways to equilibrium orientation fluctuations in finite stripe-forming systems

Small-angle orientation fluctuations in ordered stripe-forming systems free of topological defects can exhibit aging and anisotropic growth of two length scales. In infinitely extended systems, the stripe orientation field develops a dominant modulation length λ_{∥}^{*}(t) in the direction parallel to the stripes, which increases with time t as λ_{∥}^{*}(t)∼t^{1/4}. Simultaneously, the orientation correlation length ξ_{⊥}(t) in the direction perpendicular to the stripes increases as ξ_{⊥}(t)∼t^{1/2} [Riesch et al., Interface Focus 7, 20160146 (2017)2042-889810.1098/rsfs.2016.0146]. Here we show that finite systems of size L_{⊥}×L_{∥} with periodic boundary conditions reach equilibrium when the dominant modulation length λ_{∥}^{*}(t) reaches the system size L_{∥} in the stripe direction. The equilibration time τ_{eq}^{∥} is solely determined by L_{∥}, with τ_{eq}^{∥}∼L_{∥}^{4}. In systems with L_{⊥}<L_{∥}^{2}/2πλ_{p}, where λ_{p} is the undulation penetration length, the initial aging and coarsening dynamics changes at the crossover time τ_{C}^{⊥}∼L_{⊥}^{2} to an aging and coarsening dynamics described by the one-dimensional Mullins-Herring equation, before reaching equilibrium at τ_{∥}^{eq}. Our work reveals the two pathways to equilibrium in stripe phases with periodic boundary conditions, the finite-size scaling behavior of equilibrium orientation fluctuations, and the characteristic exponents associated with the influence of a finite system size.

Scaling of Memories and Crossover in Glassy Magnets

Glassiness is ubiquitous and diverse in characteristics in nature. Understanding their differences and classification remains a major scientific challenge. Here, we show that scaling of magnetic memories with time can be used to classify magnetic glassy materials into two distinct classes. The systems studied are high temperature superconductor-related materials, spin-orbit Mott insulators, frustrated magnets, and dilute magnetic alloys. Our bulk magnetization measurements reveal that most densely populated magnets exhibit similar memory behavior characterized by a relaxation exponent of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-n\approx 0.6(1)$$\end{document}1−n≈0.6(1). This exponent is different from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-{\boldsymbol{n}}\approx 1/3$$\end{document}1−n≈1/3 of dilute magnetic alloys that was ascribed to their hierarchical and fractal energy landscape, and is also different from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-{\boldsymbol{n}}=1$$\end{document}1−n=1 of the conventional Debye relaxation expected for a spin solid, a state with long range order. Furthermore, our systematic study on dilute magnetic alloys with varying magnetic concentration exhibits crossovers among the two glassy states and spin solid.

Scaling properties of ageing orientation fluctuations in stripe phases

We investigate the non-equilibrium dynamics of an ordered stripe-forming system free of topological defects. In particular, we study the ageing and the coarsening of orientation fluctuations parallel and perpendicular to the stripes via computer simulations based on a minimal phase-field model (model B with Coulomb interactions). Under the influence of noise, the stripe orientation field develops fluctuations parallel to the stripes, with the dominant modulation length λ*∥ increasing with time t as λ*∥ ∼ t1/4 and the correlation length perpendicular to the stripes ξ⊥θ increasing as ξ⊥θ ∼ t1/2. We explain these anisotropic coarsening dynamics with an analytic theory based on the linear elastic model for stripe displacements first introduced by Landau and Peierls. We thus obtain the scaling forms and the scaling exponents characterizing the correlation functions and the structure factor of the stripe orientation field. Our results reveal how the coarsening of orientation fluctuations prevents a periodically modulated phase free of topological defects from reaching equilibrium.

Liquid crystal phases of two-dimensional dipolar gases and Berezinskii-Kosterlitz-Thouless melting

Liquid crystals are phases of matter intermediate between crystals and liquids. Whereas classical liquid crystals have been known for a long time and are used in electro-optical displays, much less is known about their quantum counterparts. There is growing evidence that quantum liquid crystals play a central role in many electron systems including high temperature superconductors, but a quantitative understanding is lacking due to disorder and other complications. Here, we analyse the quantum phase diagram of a two-dimensional dipolar gas, which exhibits stripe, nematic and supersolid phases. We calculate the stiffness constants determining the stability of the nematic and stripe phases, and the melting of the stripes set by the proliferation of topological defects is analysed microscopically. Our results for the critical temperatures of these phases demonstrate that a controlled study of the interplay between quantum liquid and superfluid phases is within experimental reach for the first time, using dipolar gases.

Spin-stripe phase in a frustrated zigzag spin-1/2 chain

Motifs of periodic modulations are encountered in a variety of natural systems, where at least two rival states are present. In strongly correlated electron systems, such behaviour has typically been associated with competition between short- and long-range interactions, for example, between exchange and dipole-dipole interactions in the case of ferromagnetic thin films. Here we show that spin-stripe textures may develop also in antiferromagnets, where long-range dipole-dipole magnetic interactions are absent. A comprehensive analysis of magnetic susceptibility, high-field magnetization, specific heat and neutron diffraction measurements unveils β-TeVO4 as a nearly perfect realization of a frustrated (zigzag) ferromagnetic spin-1/2 chain. Notably, a narrow spin-stripe phase develops at elevated magnetic fields due to weak frustrated short-range interchain exchange interactions, possibly assisted by the symmetry-allowed electric polarization. This concept provides an alternative route for the stripe formation in strongly correlated electron systems and may help understanding of other widespread, yet still elusive, stripe-related phenomena.

Charge order from orbital-dependent coupling evidenced by NbSe2

Niobium diselenide has long served as a prototype of two-dimensional charge ordering, believed to arise from an instability of the electronic structure analogous to the one-dimensional Peierls mechanism. Despite this, various anomalous properties have recently been identified experimentally, which cannot be explained by Peierls-like weak-coupling theories. Here, we consider instead a model with strong electron-phonon coupling, taking into account both the full momentum and orbital dependence of the coupling matrix elements. We show that both are necessary for a consistent description of the full range of experimental observations. We argue that NbSe2 is typical in this sense, and that any charge-ordered material in more than one dimension will generically be shaped by the momentum and orbital dependence of its electron-phonon coupling as well as its electronic structure. The consequences will be observable in many charge-ordered materials, including cuprate superconductors.

Aging of orientation fluctuations in stripe phases

Stripe patterns, observed in a large variety of physical systems, often exhibit a slow nonequilibrium dynamics because ordering is impeded by the presence of topological defects. Using computer simulations based on a well-established model for stripe formation, we show that a slow dynamics and aging occur also in stripe patterns free of topological defects. For a wide range of noise strengths, the two-time orientation correlation function follows a scaling form that is typical for systems exhibiting a growing length scale. In our case, the underlying mechanism is the coarsening of orientation fluctuations, ultimately leading to power-law spatial correlations perpendicular to the stripes. Our results show that even for the smallest amount of noise, stripe phases without topological defects do not reach equilibrium. This constitutes an important aspect of the dynamics of modulated phases.

Stripe systems with competing interactions on quasi-one dimensional periodic substrates

We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of increasing substrate strength or period we show that a remarkable variety of distinct orderings can be realized, including modulated stripes, prolate clump phases, two dimensional ordered kink structures, crystalline void phases, and smectic phases. Additionally in some cases the stripes align perpendicular to the substrate troughs. Our results suggest that a new route to self assembly for systems with competing interactions can be achieved through the addition of a simple periodic modulated substrate.

Competing states in the t-J model: uniform D-wave state versus stripe state

Variational studies of the t-J model on the square lattice based on infinite projected-entangled pair states confirm an extremely close competition between a uniform d-wave superconducting state and different stripe states. The site-centered stripe with an in-phase d-wave order has an equal or only slightly lower energy than the stripe with antiphase d-wave order. The optimal stripe filling is not constant but increases with J/t. A nematic anisotropy reduces the pairing amplitude and the energies of stripe phases are lowered relative to the uniform state with increasing nematicity.

Observation of electronic inhomogeneity and charge density waves in a bilayer La(2-2x)Sr(1+2x)Mn2O7 single crystal

We employed a scanning tunneling microscope to image the (001) surface topography and local density of states (LDOS) in La(2-2x)Sr(1+2x)Mn(2)O(7) (x=0.32, LSMO) single crystals below the Curie temperature (T(C)≈120 K). The LDOS maps revealed a stripelike modulation propagating along the tetragonal a axis with a wavelength of about 16 Å, which is indicative of a charge density wave (CDW). The observed CDW in the x=0.32 sample is far from the Fermi surface nesting instability as compared with the data of angle resolved photoemission spectroscopy in an x=0.40 sample. The stripe model developed previously for cuprates can explain the observed CDW in our LSMO sample, indicating that competing interactions between localized and itinerant phases are the origin of the spatial modulations present intrinsically in cuprates and manganites.

d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry

A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the two-dimensional geometry of the Fermi surface (FS). Phase diagrams on the σ0 − α plane—here, σ0 is the ratio between the energy gaps in the parent pure CDW and superconducting states, and the quantity 2α is connected with the degree of dielectric (CDW) FS gapping—were obtained for various possible configurations of the order parameters in the momentum space. Relevant tunnel and photoemission experimental data for high-Tc oxides are compared with theoretical predictions. A brief review of the results obtained earlier for the coexistence between s-wave superconductivity and CDWs is also given.

Localization of electrons due to orbitally ordered bi-stripes in the bilayer manganite La(2-2x)Sr(1+2x)Mn2O7 (x ~ 0.59)

Electronic phases with stripe patterns have been intensively investigated for their vital roles in unique properties of correlated electronic materials. How these real-space patterns affect the conductivity and other properties of materials (which are usually described in momentum space) is one of the major challenges of modern condensed matter physics. By studying the electronic structure of La(2-2x)Sr(1+2x)Mn(2)O(7) (x ∼ 0.59) and in combination with earlier scattering measurements, we demonstrate the variation of electronic properties accompanying the melting of so-called bi-stripes in this material. The static bi-stripes can strongly localize the electrons in the insulating phase above T(c) ∼ 160 K, while the fraction of mobile electrons grows, coexisting with a significant portion of localized electrons when the static bi-stripes melt below T(c). The presence of localized electrons below T(c) suggests that the melting bi-stripes exist as a disordered or fluctuating counterpart. From static to melting, the bi-stripes act as an atomic-scale electronic valve, leading to a "colossal" metal-insulator transition in this material.

Quasiparticle interference of C2-symmetric surface states in a LaOFeAs parent compound

We present scanning tunneling microscopy studies of the LaOFeAs parent compound of iron pnictide superconductors. High resolution spectroscopic imaging reveals strong standing wave patterns induced by quasiparticle interference of two-dimensional surface states. Fourier analysis shows that the distribution of scattering wave vectors exhibits pronounced twofold (C(2)) symmetry, strongly reminiscent of the nematic electronic state found in CaFe(1.94)Co(0.06)As(2). The implications of these results to the electronic structure of the pnictide parent states will be discussed.

Universality of striped morphologies

We present a method for predicting the low-temperature behavior of spherical and Ising spin models with isotropic potentials. For the spherical model the characteristic length scales of the ground states are exactly determined but the morphology is shown to be degenerate with checkerboard patterns, stripes and more complex morphologies having identical energy. For the Ising models we show that the discretization breaks the degeneracy causing striped morphologies to be energetically favored and therefore they arise universally as ground states to potentials whose Hankel transforms have nontrivial minima.

Direct NMR evidence of phase solitons in the spin ground state of overdoped manganites

Charge ordering phenomena in overdoped La1-xCaxMnO3 (LCMO) manganites with x>or=0.5 are generally believed to be associated with the formation of charge stripes composed of alternating Mn3+ and Mn4+ charges. However, a number of recent experiments indicate that instead of stripes the charge in these systems is spatially organized in a uniform charge density wave. At the same time theory predicts that the ground state is modulated by an incommensurate (IC) orbital and charge soliton lattice. Here, by using nuclear magnetic resonance we provide the first direct evidence that the spin ground state in overdoped LCMO manganites is IC modulated with phase solitons. At higher temperatures the solitonic superstructure is replaced by a uniform spin-density wave, subjected to coherent slow fluctuations, showing a striking similarity with slow fluctuations in the striped phase of high T{c} cuprates and nickelates.

Quantum fluctuations due to spinons, polarons, and stripes in the two-dimensional Hubbard model

Quantum fluctuations (QF's) in the two-dimensional Hubbard model are visualized by superposition of optimized nonorthogonal Slater determinants. In the half-filled system, QF's consist of rotational and translational motions of spinon-antispinon pairs, while in the lightly doped systems (delta=0.96), those motions of polarons form the QF's. It is shown that an attractive interaction works between two polarons, in the framework of a projected Hartree-Fock picture. At about 10% doping, the ground state has a stripe structure and QF's due to deviations from the uniform stripe. The present method gives the ground state energies comparable or in some cases superior to the variational Monte Carlo method with a Gutzwiller projection parameter.

Competition between the pseudogap and superconductivity in the high-T(c) copper oxides

In a classical Bardeen-Cooper-Schrieffer superconductor, pairing and coherence of electrons are established simultaneously below the critical transition temperature (T(c)), giving rise to a gap in the electronic energy spectrum. In the high-T(c) copper oxide superconductors, however, a pseudogap extends above T(c). The relationship between the pseudogap and superconductivity is one of the central issues in this field. Spectral gaps arising from pairing precursors are qualitatively similar to those caused by competing electronic states, rendering a standard approach to their analysis inconclusive. The issue can be settled, however, by studying the correlation between the weights associated with the pseudogap and superconductivity spectral features. Here we report a study of two spectral weights using angle-resolved photoemission spectroscopy. The weight of the superconducting coherent peak increases away from the node following the trend of the superconducting gap, but starts to decrease in the antinodal region. This striking non-monotonicity reveals the presence of a competing state. We demonstrate a direct correlation, for different values of momenta and doping, between the loss in the low-energy spectral weight arising from the opening of the pseudogap and a decrease in the spectral weight associated with superconductivity. We therefore conclude that the pseudogap competes with the superconductivity by depleting the spectral weight available for pairing.

Status of trivalent copper and charge-transfer excitons in high-TC cuprates

A chemical bonding approach based on tight-binding cluster and band calculations, taking into account on-site Coulomb repulsion (Hubbard U parameter) to differentiate doubly and singly occupied states, was applied to high- T C superconducting cuprates and related compounds. This work provides rational insight and explanations for issues such as (i) the actual oxidation number Cu (I+) for formally trivalent copper in oxides such as La 2Li 1/2Cu 1/2O 4, (ii) the dominant oxygen character of the doping holes in (CuO 2) ( n- ) planes, (iii) the Mott-Hubbard character of the insulator-to-metal transition triggered by hole doping, leading to an oxygen-to-copper charge transfer of avalanche type, (iv) the occurrence of an excitonic phase with anisotropic Frenkel-type excitons, (v) the role of Coulomb interactions between excitons and between doping holes and their exciton surroundings, and (vi) the on-time pairing of doping holes by means of an "excitonic glue".

Dimensional tuning of electronic states under strong and frustrated interactions

We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.

Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging

Electrons in correlated insulators are prevented from conducting by Coulomb repulsion between them. When an insulator-to-metal transition is induced in a correlated insulator by doping or heating, the resulting conducting state can be radically different from that characterized by free electrons in conventional metals. We report on the electronic properties of a prototypical correlated insulator vanadium dioxide in which the metallic state can be induced by increasing temperature. Scanning near-field infrared microscopy allows us to directly image nanoscale metallic puddles that appear at the onset of the insulator-to-metal transition. In combination with far-field infrared spectroscopy, the data reveal the Mott transition with divergent quasi-particle mass in the metallic puddles. The experimental approach used sets the stage for investigations of charge dynamics on the nanoscale in other inhomogeneous correlated electron systems.

Down to the quantum limit at the neutral-to-ionic phase transition of (BEDT-TTF)-(ClMe-TCNQ): symmetry analysis and phase diagram

We report on the neutral-to-ionic (N-I) phase transition in the one-dimensional organic complex (BEDT-TTF)-(ClMeTCNQ). The X-ray studies at room temperature show that the neutral phase of (BEDT-TTF)-(ClMeTCNQ) is already characterized by a polar long-range ordering, at variance with other charge-transfer compounds comprising noncentrosymmetric molecules. From a detailed neutron diffraction study of this complex under high pressure, we present the phase diagram of the N-I transition down to the quantum limit. We discuss the symmetry breaking associated with the transition and the evolution of its first-order character under pressure.

An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates

Removing electrons from the CuO2 plane of cuprates alters the electronic correlations sufficiently to produce high-temperature superconductivity. Associated with these changes are spectral-weight transfers from the high-energy states of the insulator to low energies. In theory, these should be detectable as an imbalance between the tunneling rate for electron injection and extraction-a tunneling asymmetry. We introduce atomic-resolution tunneling-asymmetry imaging, finding virtually identical phenomena in two lightly hole-doped cuprates: Ca(1.88)Na(0.12)CuO(2)Cl2 and Bi2Sr2Dy(0.2)Ca(0.8)Cu2O(8+delta). Intense spatial variations in tunneling asymmetry occur primarily at the planar oxygen sites; their spatial arrangement forms a Cu-O-Cu bond-centered electronic pattern without long-range order but with 4a(0)-wide unidirectional electronic domains dispersed throughout (a(0): the Cu-O-Cu distance). The emerging picture is then of a partial hole localization within an intrinsic electronic glass evolving, at higher hole densities, into complete delocalization and highest-temperature superconductivity.

Spin excitations in fluctuating stripe phases of doped cuprate superconductors

Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.

Fourfold structure of vortex-core states in Bi2Sr2CaCu2O8+delta

We present a detailed study of vortex-core spectroscopy in slightly overdoped Bi2Sr2CaCu2O8+delta using a low-temperature scanning tunneling microscope. Inside the vortex core, we observe a fourfold symmetric modulation of the local density of states with an energy-independent period of (4.3 +/- 0.3)a0. Furthermore, we demonstrate that this square modulation is related to the vortex-core states which are located at +/-6 meV. Since the core-state energy is proportional to the superconducting gap magnitude , our results strongly suggest the existence of a direct relation between the superconducting state and the local electronic modulations in the vortex core.

Spiral spin state in high-temperature copper-oxide superconductors: evidence from neutron scattering measurements

An effective spiral spin phase ground state provides a new paradigm for the high-temperature superconducting cuprates. It accounts for the recent neutron scattering observations of spin excitations regarding both the energy dispersion and the intensities, including the "universal" rotation by 45 degrees around the resonance energy . The intensity has a 2D character even in a single twin crystal. The value of is related to the nesting properties of the Fermi surface. The excitations above are shown to be due to in-plane spin fluctuations, a testable difference from the stripe model. The form of the exchange interaction function reveals the effects of the Fermi surface, and the unique shape predicts large quantum spin fluctuations in the ground state.

Complexity in Strongly Correlated Electronic Systems

A wide variety of experimental results and theoretical investigations in recent years have convincingly demonstrated that several transition metal oxides and other materials have dominant states that are not spatially homogeneous. This occurs in cases in which several physical interactions-spin, charge, lattice, and/or orbital-are simultaneously active. This phenomenon causes interesting effects, such as colossal magnetoresistance, and it also appears crucial to understand the high-temperature superconductors. The spontaneous emergence of electronic nanometer-scale structures in transition metal oxides, and the existence of many competing states, are properties often associated with complex matter where nonlinearities dominate, such as soft materials and biological systems. This electronic complexity could have potential consequences for applications of correlated electronic materials, because not only charge (semiconducting electronic), or charge and spin (spintronics) are of relevance, but in addition the lattice and orbital degrees of freedom are active, leading to giant responses to small perturbations. Moreover, several metallic and insulating phases compete, increasing the potential for novel behavior.

Delocalized fermions in underdoped cuprate superconductors

Low-temperature heat transport was used to investigate the ground state of high-purity single crystals of the lightly doped cuprate YBa2Cu3O6.33. Samples were measured with doping concentrations on either side of the superconducting phase boundary. We report the observation of delocalized fermionic excitations at zero energy in the nonsuperconducting state, which shows that the ground state of underdoped cuprates is a thermal metal. Its low-energy spectrum appears to be similar to that of the d-wave superconductor, i.e., nodal. The insulating ground state observed in underdoped La2-xSrxCuO4 is attributed to the competing spin-density-wave order.