Electron pockets in the Fermi surface of hole-doped high-Tc superconductors

High-temperature superconductivity in copper oxides occurs when the materials are chemically tuned to have a carrier concentration intermediate between their metallic state at high doping and their insulating state at zero doping. The underlying evolution of the electron system in the absence of superconductivity is still unclear, and a question of central importance is whether it involves any intermediate phase with broken symmetry. The Fermi surface of the electronic states in the underdoped 'YBCO' materials YBa2Cu3O(y) and YBa2Cu4O8 was recently shown to include small pockets, in contrast with the large cylinder that characterizes the overdoped regime, pointing to a topological change in the Fermi surface. Here we report the observation of a negative Hall resistance in the magnetic-field-induced normal state of YBa2Cu3O(y) and YBa2Cu4O8, which reveals that these pockets are electron-like rather than hole-like. We propose that these electron pockets most probably arise from a reconstruction of the Fermi surface caused by the onset of a density-wave phase, as is thought to occur in the electron-doped copper oxides near the onset of antiferromagnetic order. Comparison with materials of the La2CuO4 family that exhibit spin/charge density-wave order suggests that a Fermi surface reconstruction also occurs in those materials, pointing to a generic property of high-transition-temperature (T(c)) superconductors.     

Resonance as a measure of pairing correlations in the high-Tc superconductor YBa2Cu3O6.6

One of the most striking properties of the high-transition-temperature (high-Tc) superconductors is that they are all derived from insulating antiferromagnetic parent compounds. The intimate relationship between magnetism and superconductivity in these copper oxide materials has intrigued researchers from the outset, because it does not exist in conventional superconductors. Evidence for this link comes from neutron-scattering experiments that show the unambiguous presence of short-range antiferromagnetic correlations (excitations) in the high-Tc superconductors. Even so, the role of such excitations in the pairing mechanism for superconductivity is still a subject of controversy. For YBa2Cu3O(6+x), where x controls the hole-doping level, the most prominent feature in the magnetic excitation spectrum is a sharp resonance (refs 6-11). Here we show that for underdoped YBa2Cu3O6.6, where x and Tc are below their optimal values, modest magnetic fields suppress the resonance significantly, much more so for fields approximately perpendicular to the CuO2 planes than for parallel fields. Our results indicate that the resonance measures pairing and phase coherence, suggesting that magnetism plays an important role in high-Tc superconductivity. The persistence of a field effect above Tc favours mechanisms in which the superconducting electron pairs are pre-formed in the normal state of underdoped copper oxide superconductors, awaiting transition to the superconducting state.     

The structure of the high-energy spin excitations in a high-transition-temperature superconductor

In conventional superconductors, lattice vibrations (phonons) mediate the attraction between electrons that is responsible for superconductivity. The high transition temperatures (high-T(c)) of the copper oxide superconductors has led to collective spin excitations being proposed as the mediating excitations in these materials. The mediating excitations must be strongly coupled to the conduction electrons, have energy greater than the pairing energy, and be present at T(c). The most obvious feature in the magnetic excitations of high-T(c) superconductors such as YBa2Cu3O6+x is the so-called 'resonance'. Although the resonance may be strongly coupled to the superconductivity, it is unlikely to be the main cause, because it has not been found in the La2-x(Ba,Sr)(x)CuO4 family and is not universally present in Bi2Sr2CaCu2O8+delta (ref. 9). Here we use inelastic neutron scattering to characterize possible mediating excitations at higher energies in YBa2Cu3O6.6. We observe a square-shaped continuum of excitations peaked at incommensurate positions. These excitations have energies greater than the superconducting pairing energy, are present at T(c), and have spectral weight far exceeding that of the 'resonance'. The discovery of similar excitations in La2-xBa(x)CuO4 (ref. 10) suggests that they are a general property of the copper oxides, and a candidate for mediating the electron pairing.     

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.     

Link between spin fluctuations and electron pairing in copper oxide superconductors

Although it is generally accepted that superconductivity is unconventional in the high-transition-temperature copper oxides, the relative importance of phenomena such as spin and charge (stripe) order, superconductivity fluctuations, proximity to a Mott insulator, a pseudogap phase and quantum criticality are still a matter of debate. In electron-doped copper oxides, the absence of an anomalous pseudogap phase in the underdoped region of the phase diagram and weaker electron correlations suggest that Mott physics and other unidentified competing orders are less relevant and that antiferromagnetic spin fluctuations are the dominant feature. Here we report a study of magnetotransport in thin films of the electron-doped copper oxide La(2?-?x)Ce(x)CuO(4). We show that a scattering rate that is linearly dependent on temperature--a key feature of the anomalous normal state properties of the copper oxides--is correlated with the electron pairing. We also show that an envelope of such scattering surrounds the superconducting phase, surviving to zero temperature when superconductivity is suppressed by magnetic fields. Comparison with similar behaviour found in organic superconductors strongly suggests that the linear dependence on temperature of the resistivity in the electron-doped copper oxides is caused by spin-fluctuation scattering.     

Small phonon contribution to the photoemission kink in the copper oxide superconductors

Despite over two decades of intense research efforts, the origin of high-temperature superconductivity in the copper oxides remains elusive. Angle-resolved photoemission spectroscopy experiments have revealed a kink in the dispersion relations (energy versus wavevector) of electronic states in the copper oxides at binding energies of 50-80 meV, raising the hope that this anomaly could be a key to understanding high-temperature superconductivity. The kink is often interpreted in terms of interactions between the electrons and a bosonic field. Although there is no consensus on the nature of the bosons (or even whether a boson model is appropriate), both phonons and spin fluctuations have been proposed as possible candidates. Here we report first-principles calculations of the role of phonons and the electron-phonon interaction in the photoemission spectra of La(2 - x)Sr(x)CuO4. Our calculations within the standard formalism demonstrate that the phonon-induced renormalization of the electron energies and the Fermi velocity is almost one order of magnitude smaller than the effect observed in photoemission experiments. Therefore, our result rules out electron-phonon interaction in bulk La(2 - x)Sr(x)CuO4 as the exclusive origin of the measured kink. Our conclusions are consistent with those reached independently in a recent study of the related compound YBa2Cu3O7.     

Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor

Despite twenty years of research, the phase diagram of high-transition-temperature superconductors remains enigmatic. A central issue is the origin of the differences in the physical properties of these copper oxides doped to opposite sides of the superconducting region. In the overdoped regime, the material behaves as a reasonably conventional metal, with a large Fermi surface. The underdoped regime, however, is highly anomalous and appears to have no coherent Fermi surface, but only disconnected 'Fermi arcs'. The fundamental question, then, is whether underdoped copper oxides have a Fermi surface, and if so, whether it is topologically different from that seen in the overdoped regime. Here we report the observation of quantum oscillations in the electrical resistance of the oxygen-ordered copper oxide YBa2Cu3O6.5, establishing the existence of a well-defined Fermi surface in the ground state of underdoped copper oxides, once superconductivity is suppressed by a magnetic field. The low oscillation frequency reveals a Fermi surface made of small pockets, in contrast to the large cylinder characteristic of the overdoped regime. Two possible interpretations are discussed: either a small pocket is part of the band structure specific to YBa2Cu3O6.5 or small pockets arise from a topological change at a critical point in the phase diagram. Our understanding of high-transition-temperature (high-T(c)) superconductors will depend critically on which of these two interpretations proves to be correct.     

An hour-glass magnetic spectrum in an insulating, hole-doped antiferromagnet

Superconductivity in layered copper oxide compounds emerges when charge carriers are added to antiferromagnetically ordered CuO(2) layers. The carriers destroy the antiferromagnetic order, but strong spin fluctuations persist throughout the superconducting phase and are intimately linked to superconductivity. Neutron scattering measurements of spin fluctuations in hole-doped copper oxides have revealed an unusual 'hour-glass' feature in the momentum-resolved magnetic spectrum that is present in a wide range of superconducting and non-superconducting materials. There is no widely accepted explanation for this feature. One possibility is that it derives from a pattern of alternating spin and charge stripes, and this idea is supported by measurements on stripe-ordered La(1.875)Ba(0.125)CuO(4) (ref. 15). Many copper oxides without stripe order, however, also exhibit an hour-glass spectrum. Here we report the observation of an hour-glass magnetic spectrum in a hole-doped antiferromagnet from outside the family of superconducting copper oxides. Our system has stripe correlations and is an insulator, which means that its magnetic dynamics can conclusively be ascribed to stripes. The results provide compelling evidence that the hour-glass spectrum in the copper oxide superconductors arises from fluctuating stripes.     

A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor

To understand the origin of superconductivity, it is crucial to ascertain the nature and origin of the primary carriers available to participate in pairing. Recent quantum oscillation experiments on high-transition-temperature (high-T(c)) copper oxide superconductors have revealed the existence of a Fermi surface akin to that in normal metals, comprising fermionic carriers that undergo orbital quantization. The unexpectedly small size of the observed carrier pocket, however, leaves open a variety of possibilities for the existence or form of any underlying magnetic order, and its relation to d-wave superconductivity. Here we report experiments on quantum oscillations in the magnetization (the de Haas-van Alphen effect) in superconducting YBa(2)Cu(3)O(6.51) that reveal more than one carrier pocket. In particular, we find evidence for the existence of a much larger pocket of heavier mass carriers playing a thermodynamically dominant role in this hole-doped superconductor. Importantly, characteristics of the multiple pockets within this more complete Fermi surface impose constraints on the wavevector of any underlying order and the location of the carriers in momentum space. These constraints enable us to construct a possible density-wave model with spiral or related modulated magnetic order, consistent with experimental observations.     

Two-dimensional geometry of spin excitations in the high-transition-temperature superconductor YBa2Cu3O6+x

The fundamental building block of the copper oxide superconductors is a Cu4O4 square plaquette. The plaquettes in most of these materials are slightly distorted to form a rectangular lattice, for which an influential theory predicts that high-transition-temperature (high-T(c)) superconductivity is nucleated in 'stripes' aligned along one of the axes. This theory received strong support from experiments that indicated a one-dimensional character for the magnetic excitations in the high-T(c) material YBa2Cu3O6.6 (ref. 4). Here we report neutron scattering data on 'untwinned' YBa2Cu3O6+x crystals, in which the orientation of the rectangular lattice is maintained throughout the entire volume. Contrary to the earlier claim, we demonstrate that the geometry of the magnetic fluctuations is two-dimensional. Rigid stripe arrays therefore appear to be ruled out over a wide range of doping levels in YBa2Cu3O6+x, but the data may be consistent with liquid-crystalline stripe order. The debate about stripes has therefore been reopened.     

One-dimensional nature of the magnetic fluctuations in YBa2Cu3O6.6

There is increasing evidence that inhomogeneous distributions of charge and spin--so-called 'striped phases'--play an important role in determining the properties of the high-temperature superconductors. For example, recent neutron-scattering measurements on the YBa2Cu3O(7-x) family of materials show both spin and charge fluctuations that are consistent with the striped-phase picture. But the fluctuations associated with a striped phase are expected to be one-dimensional, whereas the magnetic fluctuations observed to date appear to display two-dimensional symmetry. We show here that this apparent two-dimensionality results from measurements on twinned crystals, and that similar measurements on substantially detwinned crystals of YBa2Cu3O6.6 reveal the one-dimensional character of the magnetic fluctuations, thus greatly strengthening the striped-phase interpretation. Moreover, our results also suggest that superconductivity originates in charge stripes that extend along the b crystal axis, where the superfluid density is found to be substantially larger than for the a direction.     

Negative lattice expansion from the superconductivity--antiferromagnetism crossover in ruthenium copper oxides

The mechanism of high-transition-temperature (high-T(c)) superconductivity in doped copper oxides is an enduring problem. Antiferromagnetism is established as the competing order, but the relationship between the two states in the intervening 'pseudogap' regime has become a central puzzle. The role of the crystal lattice, which is important in conventional superconductors, also remains unclear. Here we report an anomalous increase of the distance between copper oxide planes on cooling, which results in negative thermal volume expansion, for layered ruthenium copper oxides that have been doped to the boundary of antiferromagnetism and superconductivity. We propose that a crossover between these states is driven by spin ordering in the ruthenium oxide layers, revealing a novel mechanism for negative lattice expansion in solids. The differences in volume and lattice strain between the distinct superconducting and antiferromagnetic states can account for the phase segregation phenomena found extensively in low-doped copper oxides, and show that Cooper pair formation is coupled to the lattice. Unusually large variations of resistivity with magnetic field are found in these ruthenium copper oxides at low temperatures through coupling between the ordered Ru and Cu spins.     

Superconductivity in two-dimensional CoO2 layers

Since the discovery of high-transition-temperature (high-T(c)) superconductivity in layered copper oxides, many researchers have searched for similar behaviour in other layered metal oxides involving 3d-transition metals, such as cobalt and nickel. Such attempts have so far failed, with the result that the copper oxide layer is thought to be essential for superconductivity. Here we report that Na(x)CoO2*yH2O (x approximately 0.35, y approximately 1.3) is a superconductor with a T(c) of about 5 K. This compound consists of two-dimensional CoO2 layers separated by a thick insulating layer of Na+ ions and H2O molecules. There is a marked resemblance in superconducting properties between the present material and high-T(c) copper oxides, suggesting that the two systems have similar underlying physics.     

Unusual magnetic order in the pseudogap region of the superconductor HgBa2CuO4+delta

The pseudogap region of the phase diagram is an important unsolved puzzle in the field of high-transition-temperature (high-T(c)) superconductivity, characterized by anomalous physical properties. There are open questions about the number of distinct phases and the possible presence of a quantum-critical point underneath the superconducting dome. The picture has remained unclear because there has not been conclusive evidence for a new type of order. Neutron scattering measurements for YBa(2)Cu(3)O(6+delta) (YBCO) resulted in contradictory claims of no and weak magnetic order, and the interpretation of muon spin relaxation measurements on YBCO and of circularly polarized photoemission experiments on Bi(2)Sr(2)CaCu(2)O(8+delta)(refs 12, 13) has been controversial. Here we use polarized neutron diffraction to demonstrate for the model superconductor HgBa(2)CuO(4+delta) (Hg1201) that the characteristic temperature T* marks the onset of an unusual magnetic order. Together with recent results for YBCO, this observation constitutes a demonstration of the universal existence of such a state. The findings appear to rule out theories that regard T* as a crossover temperature rather than a phase transition temperature. Instead, they are consistent with a variant of previously proposed charge-current-loop order that involves apical oxygen orbitals, and with the notion that many of the unusual properties arise from the presence of a quantum-critical point.     

Crystallization of charge holes in the spin ladder of Sr14Cu24O41

Determining the nature of the electronic phases that compete with superconductivity in high-transition-temperature (high-T(c)) superconductors is one of the deepest problems in condensed matter physics. One candidate is the 'stripe' phase, in which the charge carriers (holes) condense into rivers of charge that separate regions of antiferromagnetism. A related but lesser known system is the 'spin ladder', which consists of two coupled chains of magnetic ions forming an array of rungs. A doped ladder can be thought of as a high-T(c) material with lower dimensionality, and has been predicted to exhibit both superconductivity and an insulating 'hole crystal' phase in which the carriers are localized through many-body interactions. The competition between the two resembles that believed to operate between stripes and superconductivity in high-T(c) materials. Here we report the existence of a hole crystal in the doped spin ladder of Sr14Cu24O41 using a resonant X-ray scattering technique. This phase exists without a detectable distortion in the structural lattice, indicating that it arises from many-body electronic effects. Our measurements confirm theoretical predictions, and support the picture that proximity to charge ordered states is a general property of superconductivity in copper oxides.     

Superconductivity phase diagram of Na(x)CoO2*1.3H2O

The microscopic origin of superconductivity in the high-transition-temperature (high-T(c)) copper oxides remains the subject of active inquiry; several of their electronic characteristics are well established as universal to all the known materials, forming the experimental foundation that all theories must address. The most fundamental of those characteristics, for both the copper oxides and other superconductors, is the dependence of the superconducting T(c) on the degree of electronic band filling. The recent report of superconductivity near 4 K in the layered sodium cobalt oxyhydrate, Na(0.35)CoO2*1.3H2O, is of interest owing to both its triangular cobalt-oxygen lattice and its generally analogous chemical and structural relationships to the copper oxide superconductors. Here we show that the superconducting T(c) of this compound displays the same kind of behaviour on chemical doping that is observed in the high-T(c) copper oxides. Specifically, the optimal superconducting T(c) occurs in a narrow range of sodium concentrations (and therefore electron concentrations) and decreases for both underdoped and overdoped materials, as observed in the phase diagram of the copper oxide superconductors. The analogy is not perfect, however, suggesting that Na(x)CoO2*1.3H2O, with its triangular lattice geometry and special magnetic characteristics, may provide insights into systems where coupled charge and spin dynamics play an essential role in leading to superconductivity.     

Antiferromagnetic order as the competing ground state in electron-doped Nd1.85Ce0.15CuO4

Superconductivity in the high-transition-temperature (high-T(c)) copper oxides competes with other possible ground states. The physical explanation for superconductivity can be constrained by determining the nature of the closest competing ground state, and establishing if that state is universal among the high-T(c) materials. Antiferromagnetism has been theoretically predicted to be the competing ground state. A competing ground state is revealed when superconductivity is destroyed by the application of a magnetic field, and antiferromagnetism has been observed in hole-doped materials under the influence of modest fields. None of the previous experiments have revealed the quantum phase transition from the superconducting state to the antiferromagnetic state, because they failed to reach the upper critical field B(c2). Here we report the results of transport and neutron-scattering experiments on electron-doped Nd1.85Ce0.15CuO4 (refs 13, 14), where B(c2) can be reached. The applied field reveals a static, commensurate, anomalously conducting long-range ordered antiferromagnetic state, in which the induced moment scales approximately linearly with the field strength until it saturates at B(c2). This and previous experiments on the hole-doped materials therefore establishes antiferromagnetic order as a competing ground state in the high-T(c) copper oxide materials, irrespective of electron or hole doping.     

Superconductor-insulator transition in La2 - xSrxCuO4 at the pair quantum resistance

High-temperature superconductivity in copper oxides arises when a parent insulator compound is doped beyond some critical concentration; what exactly happens at this superconductor-insulator transition is a key open question. The cleanest approach is to tune the carrier density using the electric field effect; for example, it was learned in this way that weak electron localization transforms superconducting SrTiO(3) into a Fermi-glass insulator. But in the copper oxides this has been a long-standing technical challenge, because perfect ultrathin films and huge local fields (>10(9)?V?m(-1)) are needed. Recently, such fields have been obtained using electrolytes or ionic liquids in the electric double-layer transistor configuration. Here we report synthesis of epitaxial films of La(2-?x)Sr(x)CuO(4) that are one unit cell thick, and fabrication of double-layer transistors. Very large fields and induced changes in surface carrier density enable shifts in the critical temperature by up to 30?K. Hundreds of resistance versus temperature and carrier density curves were recorded and shown to collapse onto a single function, as predicted for a two-dimensional superconductor-insulator transition. The observed critical resistance is precisely the quantum resistance for pairs, R(Q) = h/(2e) = 6.45?kΩ, suggestive of a phase transition driven by quantum phase fluctuations, and Cooper pair (de)localization.     

Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x

The parent compounds of the copper oxide high-transition-temperature (high-Tc) superconductors are unusual insulators (so-called Mott insulators). Superconductivity arises when they are 'doped' away from stoichiometry. For the compound Bi2Sr2CaCu2O8+x, doping is achieved by adding extra oxygen atoms, which introduce positive charge carriers ('holes') into the CuO2 planes where the superconductivity is believed to originate. Aside from providing the charge carriers, the role of the oxygen dopants is not well understood, nor is it clear how the charge carriers are distributed on the planes. Many models of high-Tc superconductivity accordingly assume that the introduced carriers are distributed uniformly, leading to an electronically homogeneous system as in ordinary metals. Here we report the presence of an electronic inhomogeneity in Bi2Sr2CaCu2O8+x, on the basis of observations using scanning tunnelling microscopy and spectroscopy. The inhomogeneity is manifested as spatial variations in both the local density of states spectrum and the superconducting energy gap. These variations are correlated spatially and vary on the surprisingly short length scale of approximately 14 A. Our analysis suggests that this inhomogeneity is a consequence of proximity to a Mott insulator resulting in poor screening of the charge potentials associated with the oxygen ions left in the BiO plane after doping, and is indicative of the local nature of the superconducting state.     

A BCS-like gap in the superconductor SmFeAsO0.85F0.15

Since the discovery of superconductivity in the high-transition-temperature (high-T(c)) copper oxides two decades ago, it has been firmly established that the CuO(2) plane is essential for superconductivity and gives rise to a host of other very unusual properties. A new family of superconductors with the general composition of LaFeAsO(1-x)F(x) has recently been discovered and the conspicuous lack of the CuO(2) planes raises the tantalizing question of a different pairing mechanism in these oxypnictides. The superconducting gap (its magnitude, structure, and temperature dependence) is intimately related to pairing. Here we report the observation of a single gap in the superconductor SmFeAsO(0.85)F(0.15) with T(c) = 42 K as measured by Andreev spectroscopy. The gap value of 2Delta = 13.34 +/- 0.3 meV gives 2Delta/k(B)T(c) = 3.68 (where k(B) is the Boltzmann constant), close to the Bardeen-Cooper-Schrieffer (BCS) prediction of 3.53. The gap decreases with temperature and vanishes at T(c) in a manner consistent with the BCS prediction, but dramatically different from that of the pseudogap behaviour in the copper oxide superconductors. Our results clearly indicate a nodeless gap order parameter, which is nearly isotropic in size across different sections of the Fermi surface, and are not compatible with models involving antiferromagnetic fluctuations, strong correlations, the t-J model, and the like, originally designed for the high-T(c) copper oxides.