J. M. Tranquada

How to detect fluctuating stripes in the high-temperature superconductors

We discuss fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies for extracting information concerning such local order from experiments are derived with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems - the exactly solvable one dimensional electron gas with an impurity, and a weakly-interacting 2D electron gas. We extensively review experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies. We adduce evidence that stripe correlations are widespread in the cuprates. Finally, we compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi liquid state, and strong coupling, in which the magnetism is associated with well defined localized spins, and stripes are viewed as a form of micro-phase separation. We present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

Quantum magnetic excitations from stripes in copper oxide superconductors

In the copper oxide parent compounds of the high-transition-temperature superconductors the valence electrons are localized—one per copper site—by strong intra-atomic Coulomb repulsion. A symptom of this localization is antiferromagnetism, where the spins of localized electrons alternate between up and down. Superconductivity appears when mobile ‘holes’ are doped into this insulating state, and it coexists with antiferromagnetic fluctuations. In one approach to describing the coexistence, the holes are believed to self-organize into ‘stripes’ that alternate with antiferromagnetic (insulating) regions within copper oxide planes, which would necessitate an unconventional mechanism of superconductivity. There is an apparent problem with this picture, however: measurements of magnetic excitations in superconducting YBa2Cu3O6+x near optimum doping are incompatible with the naive expectations for a material with stripes. Here we report neutron scattering measurements on stripe-ordered La1.875Ba0.125CuO4. We show that the measured excitations are, surprisingly, quite similar to those in YBa2Cu3O6+x (refs 9, 10) (that is, the predicted spectrum of magnetic excitations is wrong). We find instead that the observed spectrum can be understood within a stripe model by taking account of quantum excitations. Our results support the concept that stripe correlations are essential to high-transition-temperature superconductivity.

Coexistence of, and Competition between, Superconductivity and Charge-Stripe Order in La{sub 1.6-{ital x}}Nd{sub 0.4}Sr{sub {ital x}}CuO{sub 4}

Previously we have presented evidence for stripe order of holes and spins in La{sub 1.6-x}Nd{sub 0.4}Sr{sub x}CuO{sub 4} with x=0.12. Here we show, via neutron diffraction measurements of magnetic scattering, that similar order occurs in crystals with x=0.15 and 0.20. Zero-field-cooled magnetization measurements show that all three compositions are also superconducting, with the superconducting transition temperature increasing as the low-temperature staggered magnetization decreases.These results directly demonstrate an intimate connection between stripe correlations and superconductivity. {copyright} {ital 1997} {ital The American Physical Society}

Two spin-state transitions in LaCoO3

Neutron-diffraction measurements have revealed a new anomalous thermal lattice expansion of LaCoO 3 near 500 K that indicates the existence of a second spin-state transition, in addition to the one previously established near 100 K. The anomalous expansion and the temperature dependence of the Co magnetic moments are successfully interpreted in a wide temperature range based on a simple model assuming low-spin (LS, S =0), intermediate-spin (IS, S =1), and high-spin (HS, S =2) states of Co atoms. The first spin transition, near 100 K, is from LS to IS, and the second, near 500 K, is from IS to a mixed state of IS and HS. The fitted model parameters indicate that the initially-large energy difference between IS and HS states decreases towards zero as the second transition proceeds. The large drop in resistivity associated with the latter transition appears to be correlated with the population of the HS state.

Stripe phases in high-temperature superconductors

Stripe phases are predicted and observed to occur in a class of strongly correlated materials describable as doped antiferromagnets, of which the copper-oxide superconductors are the most prominent representatives. The existence of stripe correlations necessitates the development of new principles for describing charge transport and especially superconductivity in these materials.

Colloquium : Theory of intertwined orders in high temperature superconductors

Understanding high temperature superconductors is a central problem in condensed matter physics. Many experiments have uncovered ordering tendencies which are responsible for the complex phase diagram of high temperature superconductors. This Colloquium discusses the interplay between different order parameters in these materials. Considering the intertwining of these orders leads to new experimentally observable consequences, shedding new light into the physics of these fascinating materials.

Electron–phonon coupling reflecting dynamic charge inhomogeneity in copper oxide superconductors

The attempt to understand copper oxide superconductors is complicated by the presence of multiple strong interactions in these systems. Many believe that antiferromagnetism is important for superconductivity, but there has been renewed interest in the possible role of electron–lattice coupling. The conventional superconductor MgB2 has a very strong electron–lattice coupling, involving a particular vibrational mode (phonon) that was predicted by standard theory and confirmed quantitatively by experiment. Here we present inelastic scattering measurements that show a similarly strong anomaly in the Cu–O bond-stretching phonon in the copper oxide superconductors La2-xSrxCuO4 (with x = 0.07, 0.15). Conventional theory does not predict such behaviour. The anomaly is strongest in La1.875Ba0.125CuO4 and La1.48Nd0.4Sr0.12CuO4, compounds that exhibit spatially modulated charge and magnetic order, often called stripe order; it occurs at a wave vector corresponding to the charge order. These results suggest that this giant electron–phonon anomaly, which is absent in undoped and over-doped non-superconductors, is associated with charge inhomogeneity. It follows that electron–phonon coupling may be important to our understanding of superconductivity, although its contribution is likely to be indirect.

Stripe order, depinning, and fluctuations inLa1.875Ba0.125CuO4andLa1.875Ba0.075Sr0.050CuO4

We present a neutron scattering study of stripe correlations measured on a single crystal of La

Local Magnetic Order vs Superconductivity in a Layered Cuprate

_{1.875}

Microstructure and structural defects in MgB2 superconductor

Ba