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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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.

Photoemission spectra of Bi 2 Sr 2 CaCu 2 O 81d below T c show two features near the ͑p, 0͒ point of the zone: a sharp peak at low energy and a higher binding energy hump. We find that the sharp peak persists at low energy even as one moves towards ͑0, 0͒, while the broad hump shows significant dispersion which correlates well with the normal state dispersion. We argue that these features are naturally explained by the interaction of electrons with a sharp mode which appears only below T c , and speculate that the latter may be related to the resonance seen in recent neutron data.