Stripe phases in high-temperature superconductors

Coexistence of periodic modulation of quasiparticle states and superconductivity in Bi2Sr2CaCu2O8+delta

In this article we show, using scanning tunneling spectroscopy, the existence of static striped density of electronic states in nearly optimally doped Bi2Sr2CaCu2O8+delta in zero field. This modulation is aligned with the Cu-O bonds, with a periodicity of four lattice constants, and exhibits features characteristic of a two-dimensional system of line objects. We further show that the density of states modulation manifests itself as a shift of states from above to below the superconducting gap. The fact that a single energy scale (i.e., the gap) appears for both superconductivity and stripes suggests that these two effects have the same origin.

Broken time-reversal symmetry in strongly correlated ladder structures

We provide, for the first time, in a doped strongly correlated system (two-leg ladder), a controlled theoretical demonstration of the existence of a state in which long-range ordered orbital currents are arranged in a staggered pattern, coexisting with a charge density wave. The method used is the highly accurate density-matrix renormalization group technique. This brings us closer to recent proposals that this order is realized in the enigmatic pseudogap phase of the cuprate high temperature superconductors.

High-energy spin dynamics in La1.69Sr0.31NiO4

To test the prediction that the dispersion of the magnetic resonance in superconducting YBa2Cu3O(6+x) is similar to magnons in an incommensurate antiferromagnet, we have mapped out the spin dynamics in a stripe-ordered nickelate, La(2-x)SrxNiO4, with x approximately equal to 0.31, using inelastic neutron scattering. We observe spin-wave excitations up to 80 meV emerging from the incommensurate magnetic peaks with a surprisingly large and almost isotropic spin velocity: variant Planck's over 2 pi c(s) approximately 0.32 eV A. A comparison indicates that the inferred spin-excitation spectrum is not, by itself, an adequate model for the magnetic resonance feature of the superconductor.

Vortex charges in high-temperature superconductors

Based on a model Hamiltonian with competing antiferromagnetic (AF) and d-wave superconductivity interactions, the vortex charge is investigated by solving the Bogoliubov-de Gennes equations. We found that the vortex charge is negative when a sufficient strength of AF order is induced inside the vortex core; otherwise, it is positive. By tuning the on-site Coulomb repulsion U or the doping parameter delta, a transition between the positive and negative vortex charges may occur. The vortex charge at optimal doping has also been studied as a function of magnetic field. Recent NMR and Hall effect experiments may be understood in terms of the present results.

Antiferromagnetism and hole pair checkerboard in the vortex state of high T(c) superconductors

We propose a microscopic state for the vortex phase of BSCO superconductors. Around the vortex core or above H(c2), the d wave hole pairs form a checkerboard localized in the antiferromagnetic background. We discuss this theory in connection with recent STM experiments.

Atomic scale imaging and spectroscopy of a CuO(2) plane at the surface of Bi(2)Sr(2)CaCu(2)O(8+delta)

We have used a scanning tunneling microscope to demonstrate that a single CuO2 plane can form a stable and atomically ordered layer at the surface of Bi(2)Sr(2)CaCu(2)O(8+delta). In contrast to previous studies on high-T(c) surfaces, the CuO2-terminated surface exhibits a strongly suppressed tunneling conductance at low voltages. We consider a number of different explanations for this phenomena and propose that it may be caused by how the orbital symmetry of the CuO2 plane's electronic states affects the tunneling process.

Freezing of a stripe liquid

The existence of a stripe-liquid phase in a layered nickelate, La(1.725)Sr(0.275)NiO(4), is demonstrated through neutron scattering measurements. We show that incommensurate magnetic fluctuations evolve continuously through the charge-ordering temperature, although an abrupt decrease in the effective damping energy is observed on cooling through the transition. The energy and momentum dependence of the magnetic scattering are parametrized with a damped-harmonic-oscillator model describing overdamped spin waves in the antiferromagnetic domains defined instantaneously by charge stripes.

Bond-stretching-phonon anomalies in stripe-ordered La1.69Sr0.31NiO4

We report a neutron scattering study of bond-stretching phonons in La1.69Sr0.31NiO4, a doped antiferromagnet in which the added holes order in diagonal stripes at 45 to the Ni-O bonds. For the highest-energy longitudinal optical mode along the bonds, a softening of 20% is observed between the Brillouin zone center and the zone boundary. At 45 to the bonds, a splitting of the same magnitude is found across much of the zone. Surprisingly, the charge-ordering wave vector plays no apparent role in the anomalous dispersions. The implications for related anomalies in the cuprates are discussed.

A four unit cell periodic pattern of quasi-particle states surrounding vortex cores in Bi2Sr2CaCu2O8+delta

Scanning tunneling microscopy is used to image the additional quasi-particle states generated by quantized vortices in the high critical temperature superconductor Bi2Sr2CaCu2O8+delta. They exhibit a copper-oxygen bond-oriented "checkerboard" pattern, with four unit cell (4a0) periodicity and a approximately 30 angstrom decay length. These electronic modulations may be related to the magnetic field-induced, 8a0 periodic, spin density modulations with decay length of approximately 70 angstroms recently discovered in La1.84Sr0.16CuO4. The proposed explanation is a spin density wave localized surrounding each vortex core. General theoretical principles predict that, in the cuprates, a localized spin modulation of wavelength lambda should be associated with a corresponding electronic modulation of wavelength lambda/2, in good agreement with our observations.

First time determination of the microscopic structure of a stripe phase: low temperature NMR in La(2)NiO(4.17)

The experimental observations of stripes in superconducting cuprates and insulating nickelates clearly show the modulation in charge and spin density. However, these have proven to be rather insensitive to the harmonic structure and (site or bond) ordering. Using (139)La NMR in La(2)NiO(4+delta) with delta = 0.17, we show that in the 1/3 hole doped nickelate below the freezing temperature the stripes are strongly solitonic and site ordered with Ni(3+) ions carrying S = 1/2 in the domain walls and Ni(2+) ions with S = 1 in the domains.

Nodal quasiparticles in stripe ordered superconductors

We study the properties of a quasi-one-dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple caricature of a striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi-liquid normal state. Even in this limit, " d-wave-like" order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasiparticle spectrum, or gapless "nodal" quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.

Thermodynamics of the interplay between magnetism and high-temperature superconductivity

Copper-oxide-based high-temperature superconductors have complex phase diagrams with multiple ordered phases. It even appears that the highest superconducting transition temperatures for certain cuprates are found in samples that display simultaneous onset of magnetism and superconductivity. We show here how the thermodynamics of fluid mixtures-a touchstone for chemistry as well as hard and soft condensed matter physics-accounts for this startling observation, as well as many other properties of the cuprates in the vicinity of the instability toward "striped" magnetism.

Particle-hole symmetry in the antiferromagnetic state of the cuprates

In the layered cuprate perovskites, the occurrence of high-temperature superconductivity seems deeply related to the unusual nature of the hole excitations. The limiting case of a very small number of holes diffusing in the antiferromagnetic (AF) background may provide important insights into this problem. We have investigated the transport properties in a series of crystals of YBa(2)Cu(3)O(y), and found that the temperature dependencies of the Hall coefficient R(H) and thermopower S change abruptly as soon as the AF phase boundary is crossed. In the AF state at low temperatures T, both R(H) and S are unexpectedly suppressed to nearly zero over a broad interval of T. We argue that this suppression arises from near-exact symmetry in the particle-hole currents. From the trends in R(H) and S, we infer that the symmetry is increasingly robust as the hole density x becomes very small (x approximately 0.01). We discuss implications for electronic properties both within the AF state and outside.

Diamagnetic activity above Tc as a precursor to superconductivity in La2-xSrxCuO4 thin films

Superconductors show zero resistance to electric current, and expel magnetic flux (the Meissner effect) below the transition temperature (Tc). In conventional superconductors, the 'Cooper pairs' of electrons that are responsible for superconductivity form only below Tc. In the unconventional high-Tc superconductors, however, a strong electron correlation is essential for pair formation: there is evidence that some pairs are formed above Tc in samples that have less than the optimal density of charge carriers (underdoped) and an energy gap-the 'pseudogap'-appears to be present. Moreover, excitations that look like the vortices that carry magnetic flux inside the superconducting state have been reported above Tc (refs 6, 7). Although the origin of the pseudogap remains controversial, phase fluctuations above Tc, leading to some form of local superconductivity or local pairing, seem essential. Here we report magnetic imaging (scanning SQUID microscopy) of La2-xSrxCuO4 thin films. Clear quantized vortex patterns are visible below Tc (18-19 K), and we observe inhomogeneous magnetic domains that persist up to 80 K. We interpret the data as suggesting the existence of diamagnetic regions that are precursors to the Meissner state.

Antiferromagnetic spin ladders effectively coupled by one-dimensional electron liquids

We study a model of the stripe state in strongly correlated systems consisting of an array of antiferromagnetic spin ladders, each with n(leg) legs, coupled to each other through the spin-exchange interaction to charged stripes in between each pair of ladders. The charged stripes are assumed to be Luttinger liquids in a spin-gap regime. An effective interaction for a pair of neighboring ladders is calculated by integrating out the gapped spin degrees of freedom in the charged stripes. The low energy effective theory of each ladder is a nonlinear sigma model with additional cross couplings of neighboring ladders, which favor either in-phase or antiphase short-range spin orderings depending on the physical parameters of the charged stripe.

Modulation instability and pattern formation in spatially incoherent light beams

We report on the experimental observation of modulation instability of partially spatially incoherent light beams in noninstantaneous nonlinear media and show that in such systems patterns can form spontaneously from noise. Incoherent modulation instability occurs above a specific threshold that depends on the coherence properties (correlation distance) of the wave packet and leads to a periodic train of one-dimensional filaments. At a higher value of nonlinearity, the incoherent one-dimensional filaments display a two-dimensional instability and break up into self-ordered arrays of light spots. This discovery of incoherent pattern formation reflects on many other nonlinear systems beyond optics. It implies that patterns can form spontaneously (from noise) in diverse nonlinear many-body systems involving weakly correlated particles, such as atomic gases at (or near) Bose-Einstein condensation temperatures and electrons in semiconductors at the vicinity of the quantum Hall regime.

Quantum theory of the smectic metal state in stripe phases

We present a theory of the electron smectic fixed point of the stripe phases of doped layered Mott insulators. We show that in the presence of a spin gap three phases generally arise: (a) a smectic superconductor, (b) an insulating stripe crystal, and (c) a smectic metal. The latter phase is a stable two-dimensional anisotropic non-Fermi liquid. In the absence of a spin gap there is also a more conventional Fermi-liquid-like phase. The smectic superconductor and smectic metal phases (or glassy versions thereof) may have already been seen in Nd-doped La2-xSrxCuO4.

Local magnetic order vs superconductivity in a layered cuprate

We report on the phase diagram for charge-stripe order in La1.6-xNd0. 4SrxCuO4, determined by neutron and x-ray scattering studies and resistivity measurements. From an analysis of the in-plane resistivity motivated by recent nuclear-quadrupole-resonance studies, we conclude that the transition temperature for local charge ordering decreases monotonically with x, and hence that local antiferromagnetic order is uniquely correlated with the anomalous depression of superconductivity at x approximately 1 / 8. This result is consistent with theories in which superconductivity depends on the existence of charge-stripe correlations.

Charge ordering in the TMTTF family of molecular conductors

Using one- and two-dimensional NMR spectroscopy applied to 13C spin-labeled (TMTTF)2AsF6 and (TMTTF)2PF6, we demonstrate the existence of an intermediate charge-ordered phase in the TMTTF family of charge-transfer salts. At ambient temperature, the spectra are characteristic of nuclei in equivalent molecules. Below a continuous charge-ordering transition temperature T(co), there is evidence for two inequivalent molecules with unequal electron densities. The absence of an associated magnetic anomaly indicates only the charge degrees of freedom are involved and the lack of evidence for a structural anomaly suggests that charge-lattice coupling is too weak to drive the transition.

Signature of superfluid density in the single-particle excitation spectrum of Bi(2)Sr(2)CaCu(2)O(8+delta)

We report that the doping and temperature dependence of photoemission spectra near the Brillouin zone boundary of Bi(2)Sr(2)CaCu(2)O(8+delta)exhibit unexpected sensitivity to the superfluid density. In the superconducting state, the photoemission peak intensity as a function of doping scales with the superfluid density and the condensation energy. As a function of temperature, the peak intensity shows an abrupt behavior near the superconducting phase transition temperature where phase coherence sets in, rather than near the temperature where the gap opens. This anomalous manifestation of collective effects in single-particle spectroscopy raises important questions concerning the mechanism of high-temperature superconductivity.

What angle-resolved photoemission experiments tell about the microscopic theory for high-temperature superconductors

Recent angular-resolved photoemission experiments on high-temperature superconductors are consistent with a phenomenological description of the normal state of these materials as marginal Fermi liquids. The experiments also provide constraints on microscopic theories.

Quantum criticality: competing ground states in low dimensions

Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high-temperature superconductors where electron motion occurs primarily on a two-dimensional square lattice, the quantum critical point between two such lowest energy states has nontrivial emergent excitations that control the physics over a significant portion of the phase diagram. Nonzero temperature dynamic properties near quantum critical points are described, using simple theoretical models. Possible quantum phases and transitions in the two-dimensional electron gas on a square lattice are discussed.