The Fermi surface, the locus in momentum space of gapless excitations, is a central concept in the theory of metals. Even though the optimally doped high temperature superconductors exhibit an anomalous normal state, angle resolved photoemission spectroscopy (ARPES) has revealed a large Fermi surface [1][2][3] despite the absence of well-defined elementary excitations (quasiparticles) above T c . However, the even more unusual behavior in the underdoped high temperature superconductors, which show a pseudogap above T c [4-6], requires us to carefully re-examine this concept. Here, we present the first results on how the Fermi surface is destroyed as a function of temperature in underdoped Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) using ARPES. We find the remarkable effect that different k points become gapped at different temperatures. This leads to a break up of the Fermi surface at a temperature T * into disconnected Fermi arcs which shrink with decreasing T , eventually collapsing to the point nodes of the d x 2 −y 2 superconducting ground state below T c . This novel behavior, where the Fermi surface does not form a continuous contour in momentum space as in conventional metals, is unprecedented in that it occurs in the absence of long range order. Moreover, although the d-wave superconducting gap below T c smoothly evolves into the pseudogap above T c , the gaps at different k points are not related to one another above T c the same way as they are below, implying an intimate, but non-trivial relation, between the two.ARPES probes the occupied part of the electron spectrum, and for quasi-2D systems its intensity I(k, ω) is proportional to the Fermi function f (ω) times the oneelectron spectral function A(k, ω) [3]. In Fig. 1, the solid curves are ARPES spectra for an underdoped 85K sample at three k points on the Fermi surface (determined above T * ) for various temperatures. To begin with let us look at the superconducting state data at T = 14K. At each k point, the sample spectra are pushed back to positive binding energy (ω < 0) due to the superconducting gap, and we also see a resolution limited peak associated with a well-defined quasiparticle excitation in the superconducting state. The superconducting gap, as estimated by the position of the sample leading edge midpoint, is seen to decrease as one moves from point a near M to b to c, closer to the diagonal Γ − Y direction, consistent with a d x 2 −y 2 order parameter. Next, consider the changes in Fig. 1 as a function of increasing T . At each k point the quasiparticle peak disappears above T c , but the suppression of spectral weight -the pseudogappersists well above T c , as noted in earlier work [4][5][6].The striking new feature which is apparent from Fig. 1 is that the pseudogap at different k points closes at different temperatures, with larger gaps persisting to higher T 's. At point a, nearM , there is a pseudogap at all T 's below 180K, at which the Bi2212 leading edge matches that of Pt. We take this as the definition of T * [5] above which the the l...

One of the main challenges in understanding high T C superconductivity is to disentangle the rich variety of states of matter that may coexist, cooperate, or compete with d-wave superconductivity. At center stage is the pseudogap phase, which occupies a large portion of the cuprate phase diagram surrounding the superconducting dome 1 . Using scanning tunneling microscopy, we find that a static, non-dispersive, "checkerboard"-like electronic modulation exists in a broad regime of the cuprate phase diagram and exhibits strong doping dependence. The continuous increase of checkerboard periodicity with hole density strongly suggests that the checkerboard originates from charge density wave formation in the anti-nodal region of the cuprate Fermi surface. These results reveal a coherent picture for static electronic orderings in the cuprates and shed important new light on the nature of the pseudogap phase. Author ContributionsWDW, MCB and KC shared equal responsibility for all aspects of this project from instrument construction through data collection and analysis. TK grew the samples and helped refine the STM. TT and HI contributed to sample growth. YW contributed to analysis and writing of the manuscript. EWH advised.

A pairing gap and coherence are the two hallmarks of superconductivity. In a classical BCS superconductor they are established simultaneously at T c . In the cuprates, however, an energy gap (pseudogap) extends above T c [1, 2, 3,4,5,6,7,8]. The origin of this gap is one of the central issues in high temperature superconductivity. Recent experimental evidence demonstrates that the pseudogap and the superconducting gap are associated with different energy scales [9,10,11,12,13,14]. It is however not clear whether they coexist independently or compete [9,12,14,15]. In order to understand the physics of cuprates and improve their superconducting properties it is vital to determine whether the pseudogap is friend or foe of high temperature supercondctivity [16]. Here we report evidence from angle resolved photoemission spectroscopy (ARPES) that the pseudogap and high temperature superconductivity represent two competing orders. We find that there is a direct correlation between a loss in the low energy spectral weight due to the pseudogap and a decrease of the coherent fraction of paired electrons. Therefore, the pseudogap competes with the superconductivity by depleting the spectral weight available for pairing in the region of momentum space where the superconducting gap is largest. This leads to a very unusual state in the underdoped cuprates, where only part of the Fermi surface develops coherence.Coherence in the superconducting state of the cuprates manifests itself by the appearance of a narrow peak in the ARPES lineshape [17], while the pseudogap [2, 3,4,12] depletes the low energy spectral weight below the pseudogap energy. The simplicity of the Bi 2 Sr 2 CuO 6+δ (Bi2201) spectra, as measured by ARPES, permits us to perform a straight forward quantitative analysis of the two features because the energy distribution curves (EDCs) in this single layer material lack the large renormalization effects (e.g. peak-hump-dip structure) and bilayer splitting that are present [6,7] in double layered Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212). This feature, however, means the spectral changes associated with the superconducting transition in Bi2201 are much more difficult to observe [18]. By acquiring very high resolution and stable ARPES data with high statistics, we are able to study the temperature and momentum dependence of the spectral weight near the chemical potential, with unprecedented accuracy. Experimental and sample preparation details are provided in the Supplementary Information. In Fig. 1 we examine the temperature dependence of the spectral lineshape in overdoped Bi2201 (T c =29K). Above the pseudogap temperature (T * ) (∼110K for this sample), the symmetrized EDCs [4] (see Supplementary Information) show a peak centered at the chemical potential -consistent with the metallic state of the sample. Upon cooling below T * , the low energy spectral weight decreases (within ∼20 meV), leading to a characteristic dip and very broad spectral peaks that signify the opening of an energy gap, as shown in Fig. 1(d). The loss...

Photoemission spectra of Bi2Sr2CaCu2O 8+δ reveal that the high energy feature near (π, 0), the "hump", scales with the superconducting gap and persists above Tc in the pseudogap phase. As the doping decreases, the dispersion of the hump increasingly reflects the wavevector (π, π) characteristic of the undoped insulator, despite the presence of a large Fermi surface. This can be understood from the interaction of the electrons with a collective mode, supported by our observation that the doping dependence of the resonance observed by neutron scattering is the same as that inferred from our data.

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Comparing ARPES measurements on Bi2212 with penetration depth data, we show that a description of the nodal excitations of the d-wave superconducting state in terms of non-interacting quasiparticles is inadequate, and we estimate the magnitude and doping dependence of the Landau interaction parameter which renormalizes the linear T contribution to the superfluid density. Furthermore, although consistent with d-wave symmetry, the gap with underdoping cannot be fit by the simple coskx-cosky form, which suggests an increasing importance of long range interactions as the insulator is approached.

An oxide single-crystalline whisker with high thermoelectric properties at temperatures (T) higher than 600 K in air has been discovered. This whisker is assigned to Ca2Co2O5 phase (abbreviated to Co-225 whiskers) and has a layered structure in which Co–O layers of two different kinds alternate in the direction of the c-axis. Seebeck coefficient of the whiskers is higher than 100 µV·K-1 at 100 K and increases with temperature up to 210 µV·K-1. Temperature dependence of electric resistivity shows a semiconducting-like behavior. These results indicate that the electric carriers are transported via hopping conduction. Using thermal conductivity of a Co-225 polycrystalline sample, figure of merit (Z T) of the Co-225 whiskers is estimated 1.2–2.7 at T≥873 K. This compound is characterized with regard to low mobility and high density of carriers, which contradicts the conventional materials with high thermoelectric properties.

The discovery of the pseudogap in the cuprates created significant excitement amongst physicists as it was believed to be a signature of pairing [3], in some cases well above the room temperature. In this "pre-formed pairs" scenario, the formation of pairs without quantum phase rigidity occurs below T * . These pairs condense and develop phase coherence only below T c [3]. In contrast, several recent experiments reported that the pseudogap and superconducting states are characterized by two different energy scales [4][5][6][7], pointing to a scenario, where the two compete [14][15][16]. However a number of transport, magnetic, thermodynamic and tunneling spectroscopy experiments consistently detect a signature of phase-fluctuating superconductivity above T c [17][18][19][20][21][22] leaving open the question of whether the pseudogap is caused by pair formation or not. Here we report the discovery of a spectroscopic signature of pair formation and demonstrate that in a region of the phase diagram commonly referred to as the "pseudogap", two distinct states coexist: one that persists to an intermediate temperature T pair and a second that extends up to T * . The first state is characterized by a doping independent scaling behavior and is due to pairing above T c , but significantly below T*. The second state is the "proper" pseudogap -characterized by a "checker board" pattern in STM images, the absence of pair formation, and is likely linked to Mott physics of pristine CuO 2 planes. T pair has a universal value around 130-150K even for materials with very different T c , likely setting limit on highest, attainable Tc in cuprates. The observed universal scaling behavior with respect to T pair indicates a breakdown of the classical picture of phase fluctuations in the cuprates.The traditional approach of exploring the paring origin above T c by tracking the energy scale of spectral features has not yielded convincing results so far, as these features are poorly defined above T c due to broad spectral peaks. The apparent smooth evolution of the spectral gap from the lowest temperatures up to T * [1,2,11,12] has previously been interpreted as key evidence for a common origin of the pseudgap and pairing gap. However, very detailed, high precision data (e. g. Fig. S3E in Supplementary Information), shows the gap size varies non-monotonically across T c . This behavior raises doubt about the above interpretation.A better approach is to investigate the spectral weights, which are easier to quantify and in many cases interpret. A key such measure is the density of states at the Fermi energy 2 D(E F ). In conventional, clean superconductors this weight is zero below T c , but can be finite if there are strong impurity scattering effects. In such cases D(E F ) reflects the pair breaking state. Another possibility is the case of an inhomogeneous superconductor such as cuprates [23,24], where superconducting and "normal" patches coexist in the sample, with the latter being likely due to pair breaking states states (generic de...