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In the traditional Bardeen-Cooper-Schrieffer theory of superconductivity, the amplitude for the propagation of a pair of electrons with momentum k and -k has a log singularity as the temperature decreases. This so-called Cooper instability arises from the presence of an electron Fermi sea. It means that an attractive interaction, no matter how weak, will eventually lead to a pairing instability. However, in the pseudogap regime of the cuprate superconductors, where parts of the Fermi surface are destroyed, this log singularity is suppressed, raising the question of how pairing occurs in the absence of a Fermi sea. Here we report Hubbard model numerical results and the analysis of angular-resolved photoemission experiments on a cuprate superconductor. In contrast to the traditional theory, we find that in the pseudogap regime the pairing instability arises from an increase in the strength of the spin-fluctuation pairing interaction as the temperature decreases rather than the Cooper log instability.

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T(cdw). Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at T(cdw) marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in 'pseudogap' states.

In order to understand the origin of high-temperature superconductivity in copper oxides, we must understand the normal state from which it emerges. Here, we examine the evolution of the normal state electronic excitations with temperature and carrier concentration in Bi(2)Sr(2)CaCu(2)O(8+δ) using angle-resolved photoemission. In contrast to conventional superconductors, where there is a single temperature scale T(c) separating the normal from the superconducting state, the high-temperature superconductors exhibit two additional temperature scales. One is the pseudogap scale T(∗), below which electronic excitations exhibit an energy gap. The second is the coherence scale T(coh), below which sharp spectral features appear due to increased lifetime of the excitations. We find that T(∗) and T(coh) are strongly doping dependent and cross each other near optimal doping. Thus the highest superconducting T(c) emerges from an unusual normal state that is characterized by coherent excitations with an energy gap.

In the underdoped high temperature superconductors, instead of a complete Fermi surface above Tc, only disconnected Fermi arcs appear, separated by regions that still exhibit an energy gap. We show that in this pseudogap phase, the energy-momentum relation of electronic excitations near EF behaves like the dispersion of a normal metal on the Fermi arcs, but like that of a superconductor in the gapped regions. We argue that this dichotomy in the dispersion is difficult to reconcile with a competing order parameter, but is consistent with pairing without condensation.

We present angle-resolved photoemission spectroscopy data on moderately underdoped La1.855Sr0.145CuO4 at temperatures below and above the superconducting transition temperature. Unlike previous studies of this material, we observe sharp spectral peaks along the entire underlying Fermi surface in the superconducting state. These peaks trace out an energy gap that follows a simple d-wave form, with a maximum superconducting gap of 14 meV. Our results are consistent with a single gap picture for the cuprates. Furthermore our data on the even more underdoped sample La1.895Sr0.105CuO4 also show sharp spectral peaks, even at the antinode, with a maximum superconducting gap of 26 meV.

Angle resolved photoemission on underdoped Bi2Sr2CaCu2O8 reveals that the magnitude and d-wave anisotropy of the superconducting state energy gap are independent of temperature all the way up to T{c}. This lack of T variation of the entire k-dependent gap is in marked contrast to mean field theory. At T{c} the point nodes of the d-wave gap abruptly expand into finite length "Fermi arcs." This change occurs within the width of the resistive transition, and thus the Fermi arcs are not simply thermally broadened nodes but rather a unique signature of the pseudogap phase.

The autocorrelation of angle resolved photoemission data from the high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta) shows distinct peaks in momentum space which disperse with binding energy in the superconducting state, but not in the pseudogap phase. Although it is tempting to attribute a nondispersive behavior in momentum space to charge ordering, a deconstruction of the autocorrelation reveals that the nondispersive peaks arise from the tips of the Fermi arcs, which themselves do not change with binding energy.

The electronic structure of single crystals Na0.6CoO2, which are closely related to the superconducting Na0.3CoO2.yH(2)O (T(c) approximately 5 K), is studied by angle-resolved photoelectron spectroscopy. While the measured Fermi surface (FS) is consistent with the large FS enclosing the Gamma point from the band theory, the predicted small FS pockets near the K points are absent. In addition, the band dispersion is found to be highly renormalized, and anisotropic along the two principal axes (Gamma-K, Gamma-M). Our measurements also indicate that an extended flatband is formed slightly above E(F) along Gamma-K.

Angle resolved photoemission spectroscopy (ARPES) and resistivity measurements are used to explore the overdoped region of the high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta). We find evidence for a new crossover line in the phase diagram between a coherent metal phase, for lower temperatures and higher doping, and an incoherent metal phase, for higher temperatures and lower doping. The former is characterized by two well-defined spectral peaks in ARPES due to coherent bilayer splitting and superlinear behavior in the resistivity, whereas the latter is characterized by a single broad spectral feature in ARPES and a linear temperature dependence of the resistivity.

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.

A change in 'symmetry' is often observed when matter undergoes a phase transition-the symmetry is said to be spontaneously broken. The transition made by underdoped high-transition-temperature (high-Tc) superconductors is unusual, in that it is not a mean-field transition as seen in other superconductors. Rather, there is a region in the phase diagram above the superconducting transition temperature Tc (where phase coherence and superconductivity begin) but below a characteristic temperature T* where a 'pseudogap' appears in the spectrum of electronic excitations. It is therefore important to establish if T* is just a cross-over temperature arising from fluctuations in the order parameter that will establish superconductivity at Tc (refs 3, 4), or if it marks a phase transition where symmetry is spontaneously broken. Here we report that, for a material in the pseudogap state, left-circularly polarized photons give a different photocurrent from right-circularly polarized photons. This shows that time-reversal symmetry is spontaneously broken below T*, which therefore corresponds to a phase transition.

We study the doping and temperature dependence of the single-particle coherent weight, z(A), for high- T(c) superconductors Bi(2)Sr(2)CaCu(2)O(8+x) using angle-resolved photoemission. We find that at low temperatures the coherent weight z(A) at (pi,0) is proportional to the carrier concentration x and that the temperature dependence of z(A) is similar to that of the c-axis superfluid density. We show that, for a wide range of carrier concentration, the superconducting transition temperature scales with the product of the low-temperature coherent weight and the maximum superconducting gap.

Angle-resolved photoemission data in the superconducting state of Bi2Sr2CaCu2O8+delta show a kink in the dispersion along the zone diagonal, which is related via a Kramers-Krönig analysis to a drop in the low energy scattering rate. As one moves towards (pi,0), this kink evolves into a spectral dip. The occurrence of these anomalies in the dispersion and line shape throughout the zone indicates the presence of a new energy scale in the superconducting state.