Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+delta

Pairing of electrons in conventional superconductors occurs at the superconducting transition temperature T(c), creating an energy gap Delta in the electronic density of states (DOS). In the high-T(c) superconductors, a partial gap in the DOS exists for a range of temperatures above T(c) (ref. 2). A key question is whether the gap in the DOS above T(c) is associated with pairing, and what determines the temperature at which incoherent pairs form. Here we report the first spatially resolved measurements of gap formation in a high-T(c) superconductor, measured on Bi2Sr2CaCu2O8+delta samples with different T(c) values (hole concentration of 0.12 to 0.22) using scanning tunnelling microscopy. Over a wide range of doping from 0.16 to 0.22 we find that pairing gaps nucleate in nanoscale regions above T(c). These regions proliferate as the temperature is lowered, resulting in a spatial distribution of gap sizes in the superconducting state. Despite the inhomogeneity, we find that every pairing gap develops locally at a temperature T(p), following the relation 2Delta/k(B)T(p) = 7.9 +/- 0.5. At very low doping (< or =0.14), systematic changes in the DOS indicate the presence of another phenomenon, which is unrelated and perhaps competes with electron pairing. Our observation of nanometre-sized pairing regions provides the missing microscopic basis for understanding recent reports of fluctuating superconducting response above T(c) in hole-doped high-T(c) copper oxide superconductors.     

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.     

Unconventional superconductivity in PuCoGa5

In the Bardeen-Cooper-Schrieffer theory of superconductivity, electrons form (Cooper) pairs through an interaction mediated by vibrations in the underlying crystal structure. Like lattice vibrations, antiferromagnetic fluctuations can also produce an attractive interaction creating Cooper pairs, though with spin and angular momentum properties different from those of conventional superconductors. Such interactions have been implicated for two disparate classes of materials--the copper oxides and a set of Ce- and U-based compounds. But because their transition temperatures differ by nearly two orders of magnitude, this raises the question of whether a common pairing mechanism applies. PuCoGa5 has a transition temperature intermediate between those classes and therefore may bridge these extremes. Here we report measurements of the nuclear spin-lattice relaxation rate and Knight shift in PuCoGa5, which demonstrate that it is an unconventional superconductor with properties as expected for antiferromagnetically mediated superconductivity. Scaling of the relaxation rates among all of these materials (a feature not exhibited by their Knight shifts) establishes antiferromagnetic fluctuations as a likely mechanism for their unconventional superconductivity and suggests that related classes of exotic superconductors may yet be discovered.     

排斥型有效互作用下的超导电性

分析了电子间在有效排斥互作用下的超导电性．发现当能带宽度Ｗ＞Ｅｃ，ｏ（）时，存在电子对；当Ｗ＜Ｅｃ，ｏ时，电子对消失．从而认为在电子对消失的区域，描写超导电性的应该是某种准粒子对，而不是电子对．     

Imaging the granular structure of high-Tc superconductivity in underdoped Bi2Sr2CaCu2O8+delta.

Granular superconductivity occurs when microscopic superconducting grains are separated by non-superconducting regions; Josephson tunnelling between the grains establishes the macroscopic superconducting state. Although crystals of the copper oxide high-transition-temperature (high-Tc) superconductors are not granular in a structural sense, theory suggests that at low levels of hole doping the holes can become concentrated at certain locations resulting in hole-rich superconducting domains. Granular superconductivity arising from tunnelling between such domains would represent a new view of the underdoped copper oxide superconductors. Here we report scanning tunnelling microscope studies of underdoped Bi2Sr2CaCu2O8+delta that reveal an apparent segregation of the electronic structure into superconducting domains that are approximately 3 nm in size (and local energy gap <50 meV), located in an electronically distinct background. We used scattering resonances at Ni impurity atoms as 'markers' for local superconductivity; no Ni resonances were detected in any region where the local energy gap Delta > 50 +/- 2.5 meV. These observations suggest that underdoped Bi2Sr2CaCu2O8+delta is a mixture of two different short-range electronic orders with the long-range characteristics of a granular superconductor.     

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.     

Copper oxide superconductors: sharp-mode coupling in high-Tc superconductors

In conventional superconductivity, sharp phonon modes (oscillations in the crystal lattice) are exchanged between electrons within a Cooper pair, enabling superconductivity. A critical question in the study of copper oxides with high critical transition temperature (Tc) is whether such sharp modes (which may be more general, including, for example, magnetic oscillations) also play a critical role in the pairing and hence the superconductivity. Hwang et al. report evidence that sharp modes (either phononic or magnetic in origin) are not important for superconductivity in these materials, but we show here that their conclusions are undermined by the insensitivity of their experiment to a crucial physical effect.     

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.     

Imaging the effects of individual zinc impurity atoms on superconductivity in Bi2Sr2CaCu2O8+delta

Although the crystal structures of the copper oxide high-temperature superconductors are complex and diverse, they all contain some crystal planes consisting of only copper and oxygen atoms in a square lattice: superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substituting a single impurity atom for a copper atom strongly perturbs the surrounding electronic environment and can therefore be used to probe high-temperature superconductivity at the atomic scale. This has provided the motivation for several experimental and theoretical studies. Scanning tunnelling microscopy (STM) is an ideal technique for the study of such effects at the atomic scale, as it has been used very successfully to probe individual impurity atoms in several other systems. Here we use STM to investigate the effects of individual zinc impurity atoms in the high-temperature superconductor Bi2Sr2CaCu2O8+delta. We find intense quasiparticle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within approximately 15 A of the scattering sites. Imaging of the spatial dependence of the quasiparticle density of states in the vicinity of the impurity atoms reveals the long-sought four-fold symmetric quasiparticle 'cloud' aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in these materials.     

Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy

Electronic charges introduced in copper-oxide (CuO(2)) planes generate high-transition-temperature (T(c)) superconductivity but, under special circumstances, they can also order into filaments called stripes. Whether an underlying tendency towards charge order is present in all copper oxides and whether this has any relationship with superconductivity are, however, two highly controversial issues. To uncover underlying electronic order, magnetic fields strong enough to destabilize superconductivity can be used. Such experiments, including quantum oscillations in YBa(2)Cu(3)O(y) (an extremely clean copper oxide in which charge order has not until now been observed) have suggested that superconductivity competes with spin, rather than charge, order. Here we report nuclear magnetic resonance measurements showing that high magnetic fields actually induce charge order, without spin order, in the CuO(2) planes of YBa(2)Cu(3)O(y). The observed static, unidirectional, modulation of the charge density breaks translational symmetry, thus explaining quantum oscillation results, and we argue that it is most probably the same 4a-periodic modulation as in stripe-ordered copper oxides. That it develops only when superconductivity fades away and near the same 1/8 hole doping as in La(2-x)Ba(x)CuO(4) (ref.?1) suggests that charge order, although visibly pinned by CuO chains in YBa(2)Cu(3)O(y), is an intrinsic propensity of the superconducting planes of high-T(c) copper oxides.     

电-声机制致高温超导特性随掺杂量演变

利用极性晶体中慢电子的运动规律提出基于BCS机理的分析模型.分析发现,掺杂导致铜氧化物的费米面电子分为低能费米电子和高能电子,并产生快电子效应.欠掺杂区高能电子与晶格振动发生作用形成赝隙,费米电子与晶格作用形成超导隙.赝隙和超导隙的竞争平衡导致欠掺杂区超导隙2Δ0和κBTc比值与高能费米电子速度vF^＊成正比,与费米速度vF成反比.掺杂量（x）与高能费米速度（vF^＊）相图是解释高温超导相图的基础.利用模型和（x-vF^＊）相图能够对欠掺杂区赝隙温度、能隙与κBTc比例随掺杂量增加而线性下降的现象给出简单解释,即最佳掺杂区2Δ0和κBTc比值为7.6、过掺杂区为4.3的常数.显示系统随掺杂量增加由＂非传统＂行为向接近传统行为再到金属行为演变的规律.     

Cu、O同位素效应与高Tc超导体超导电性机理

Cu元素、O元素在铜氧化物高Tc超导体中对超导电性的产生,超导转变温度的变化,掺杂元素的特征效应具有决定性作用。对Cu元素、O元素的性质特征认识,成键特点,以及在铜氧化物高Tc超导体中的同位素效应清楚的理解,对全面揭示高Tc铜氧化物超导体超导电性机理具有关键作用。通过分析Cu元素、O元素在铜氧化物超导体中的同位素效应,得出了高Tc铜氧化物超导电性的机理仍是电声机制,CuO2平面上的Cu元素,O元素的声子直接参于电声子配对,CuO2平面上的Cu、O元素的键态的声子模对电声配对具有决定性作用。     

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.     

Observation of a pairing pseudogap in a two-dimensional Fermi gas

Pairing of fermions is ubiquitous in nature, underlying many phenomena. Examples include superconductivity, superfluidity of (3)He, the anomalous rotation of neutron stars, and the crossover between Bose-Einstein condensation of dimers and the BCS (Bardeen, Cooper and Schrieffer) regime in strongly interacting Fermi gases. When confined to two dimensions, interacting many-body systems show even more subtle effects, many of which are not understood at a fundamental level. Most striking is the (as yet unexplained) phenomenon of high-temperature superconductivity in copper oxides, which is intimately related to the two-dimensional geometry of the crystal structure. In particular, it is not understood how the many-body pairing is established at high temperature, and whether it precedes superconductivity. Here we report the observation of a many-body pairing gap above the superfluid transition temperature in a harmonically trapped, two-dimensional atomic Fermi gas in the regime of strong coupling. Our measurements of the spectral function of the gas are performed using momentum-resolved photoemission spectroscopy, analogous to angle-resolved photoemission spectroscopy in the solid state. Our observations mark a significant step in the emulation of layered two-dimensional strongly correlated superconductors using ultracold atomic gases.     

How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+delta

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles-the excitations resulting from the breaking of Cooper pairs-should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi(2)Sr(2)CaCu(2)O(8+delta) in r-space and k-space simultaneously. We find that although the low-energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy-independent way. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.     

Resonance in the electron-doped high-transition-temperature superconductor Pr0.88LaCe0.12CuO4-delta

In conventional superconductors, the interaction that pairs the electrons to form the superconducting state is mediated by lattice vibrations (phonons). In high-transition-temperature (high-T(c)) copper oxides, it is generally believed that magnetic excitations might play a fundamental role in the superconducting mechanism because superconductivity occurs when mobile 'electrons' or 'holes' are doped into the antiferromagnetic parent compounds. Indeed, a sharp magnetic excitation termed 'resonance' has been observed by neutron scattering in a number of hole-doped materials. The resonance is intimately related to superconductivity, and its interaction with charged quasi-particles observed by photoemission, optical conductivity, and tunnelling suggests that it might play a part similar to that of phonons in conventional superconductors. The relevance of the resonance to high-T(c) superconductivity, however, has been in doubt because so far it has been found only in hole-doped materials. Here we report the discovery of the resonance in electron-doped superconducting Pr0.88LaCe0.12CuO4-delta (T(c) = 24 K). We find that the resonance energy (E(r)) is proportional to T(c) via E(r) approximately 5.8k(B)T(c) for all high-T(c) superconductors irrespective of electron- or hole-doping. Our results demonstrate that the resonance is a fundamental property of the superconducting copper oxides and therefore must be essential in the mechanism of superconductivity.     

Interplay of electron-lattice interactions and superconductivity in superconductivity in Bi2Sr2CaCu2O8+delta

Formation of electron pairs is essential to superconductivity. For conventional superconductors, tunnelling spectroscopy has established that pairing is mediated by bosonic modes (phonons); a peak in the second derivative of tunnel current d2I/dV2 corresponds to each phonon mode. For high-transition-temperature (high-T(c)) superconductivity, however, no boson mediating electron pairing has been identified. One explanation could be that electron pair formation and related electron-boson interactions are heterogeneous at the atomic scale and therefore challenging to characterize. However, with the latest advances in d2I/dV2 spectroscopy using scanning tunnelling microscopy, it has become possible to study bosonic modes directly at the atomic scale. Here we report d2I/dV2 imaging studies of the high-T(c) superconductor Bi2Sr2CaCu2O8+delta. We find intense disorder of electron-boson interaction energies at the nanometre scale, along with the expected modulations in d2I/dV2 (refs 9, 10). Changing the density of holes has minimal effects on both the average mode energies and the modulations, indicating that the bosonic modes are unrelated to electronic or magnetic structure. Instead, the modes appear to be local lattice vibrations, as substitution of 18O for 16O throughout the material reduces the average mode energy by approximately 6 per cent--the expected effect of this isotope substitution on lattice vibration frequencies. Significantly, the mode energies are always spatially anticorrelated with the superconducting pairing-gap energies, suggesting an interplay between these lattice vibration modes and the superconductivity.     

A distinct bosonic mode in an electron-doped high-transition-temperature superconductor

Despite recent advances in understanding high-transition-temperature (high-T(c)) superconductors, there is no consensus on the origin of the superconducting 'glue': that is, the mediator that binds electrons into superconducting pairs. The main contenders are lattice vibrations (phonons) and spin-excitations, with the additional possibility of pairing without mediators. In conventional superconductors, phonon-mediated pairing was unequivocally established by data from tunnelling experiments. Proponents of phonons as the high-T(c) glue were therefore encouraged by the recent scanning tunnelling microscopy experiments on hole-doped Bi2Sr2CaCu2O8-delta (BSCCO) that reveal an oxygen lattice vibrational mode whose energy is anticorrelated with the superconducting gap energy scale. Here we report high-resolution scanning tunnelling microscopy measurements of the electron-doped high-T(c) superconductor Pr0.88LaCe0.12CuO4 (PLCCO) (T(c) = 24 K) that reveal a bosonic excitation (mode) at energies of 10.5 +/- 2.5 meV. This energy is consistent with both spin-excitations in PLCCO measured by inelastic neutron scattering (resonance mode) and a low-energy acoustic phonon mode, but differs substantially from the oxygen vibrational mode identified in BSCCO. Our analysis of the variation of the local mode energy and intensity with the local gap energy scale indicates an electronic origin of the mode consistent with spin-excitations rather than phonons.     

High-transition-temperature superconductivity in the absence of the magnetic-resonance mode

The fundamental mechanism that gives rise to high-transition-temperature (high-T(c)) superconductivity in the copper oxide materials has been debated since the discovery of the phenomenon. Recent work has focused on a sharp 'kink' in the kinetic energy spectra of the electrons as a possible signature of the force that creates the superconducting state. The kink has been related to a magnetic resonance and also to phonons. Here we report that infrared spectra of Bi2Sr2CaCu2O8+delta (Bi-2212), shows that this sharp feature can be separated from a broad background and, interestingly, weakens with doping before disappearing completely at a critical doping level of 0.23 holes per copper atom. Superconductivity is still strong in terms of the transition temperature at this doping (T(c) approximately 55 K), so our results rule out both the magnetic resonance peak and phonons as the principal cause of high-T(c) superconductivity. The broad background, on the other hand, is a universal property of the copper-oxygen plane and provides a good candidate signature of the 'glue' that binds the electrons.     

The origin of multiple superconducting gaps in MgB2

Magnesium diboride, MgB2, has the highest transition temperature (T(c) = 39 K) of the known metallic superconductors. Whether the anomalously high T(c) can be described within the conventional BCS (Bardeen-Cooper-Schrieffer) framework has been debated. The key to understanding superconductivity lies with the 'superconducting energy gap' associated with the formation of the superconducting pairs. Recently, the existence of two kinds of superconducting gaps in MgB2 has been suggested by several experiments; this is in contrast to both conventional and high-T(c) superconductors. A clear demonstration of two gaps has not yet been made because the previous experiments lacked the ability to resolve the momentum of the superconducting electrons. Here we report direct experimental evidence for the two-band superconductivity in MgB2, by separately observing the superconducting gaps of the sigma and pi bands (as well as a surface band). The gaps have distinctly different sizes, which unambiguously establishes MgB2 as a two-gap superconductor.