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...

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Compact solid-state sources of terahertz (THz) radiation are being sought for sensing, imaging, and spectroscopy applications across the physical and biological sciences. We demonstrate that coherent continuous-wave THz radiation of sizable power can be extracted from intrinsic Josephson junctions in the layered high-temperature superconductor Bi 2 Sr 2 CaCu 2 O 8 . In analogy to a laser cavity, the excitation of an electromagnetic cavity resonance inside the sample generates a macroscopic coherent state in which a large number of junctions are synchronized to oscillate in phase. The emission power is found to increase as the square of the number of junctions reaching values of 0.5 microwatt at frequencies up to 0.85 THz, and persists up to~50 kelvin. These results should stimulate the development of superconducting compact sources of THz radiation.

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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.

T he response of a material to external stimuli depends on its low-energy excitations. In conventional metals, these excitations are electrons on the Fermi surface-a contour in momentum (k) space that encloses all of the occupied states for non-interacting electrons. The pseudogap phase in the copper oxide superconductors, however, is a most unusual state of matter 1 . It is metallic, but part of its Fermi surface is 'gapped out' (refs 2,3); low-energy electronic excitations occupy disconnected segments known as Fermi arcs 4 . Two main interpretations of its origin have been proposed: either the pseudogap is a precursor to superconductivity 5 , or it arises from another order competing with superconductivity 6 . Using angle-resolved photoemission spectroscopy, we show that the anisotropy of the pseudogap in k-space and the resulting arcs depend only on the ratio T/ T * (x), where T * (x) is the temperature below which the pseudogap first develops at a given hole doping x. The arcs collapse linearly with T/ T * (x) and extrapolate to zero extent as T → 0. This suggests that the T = 0 pseudogap state is a nodal liquid-a strange metallic state whose gapless excitations exist only at points in k-space, just as in a d-wave superconducting state.In Fig. 1a,b we show data for a slightly underdoped sample of Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) with a transition temperature T c = 90 K, for the superconducting state at 40 K, and the pseudogap phase at 140 K. The energy distribution curves (EDCs) at the Fermi momentum k F , which have been symmetrized 4 to remove the effects of the Fermi function on the spectra. k F is determined by the minimum separation between the peaks in the symmetrized spectra along each momentum cut. Fifteen momentum cuts were measured, as shown in Fig. 1e. Details of the symmetrization procedure are explained in the Methods section. The difference between the spectra in the two states is apparent: sharp spectral peaks are present in the superconducting state, indicating longlived excitations, and the superconducting gap vanishes only at points in the Brillouin zone, known as nodes; on the other hand, the spectra in the pseudogap phase are much broader, indicating short-lived excitations. Although a pseudogap is seen in cuts 1-7, substantial parts of the Fermi surface, cuts 8-15, show spectra peaked at the Fermi energy, indicating a Fermi arc of gapless excitations.The gap size can be estimated as half the peak-to-peak separation in energy. A more quantitative estimate is obtained by using a simple phenomenological function to describe the spectral lineshapes 7

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.

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.