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...

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.

Tunneling measurements are reported for break junctions on Bi 2 Sr 2 CaCu 2 O 82d single crystals with various oxygen concentrations. Superconducting energy gaps D are observed in the underdoped samples which are considerably larger ͑ϳ30%͒ than found in optimal doped crystals. The trend of decreasing D and 2D͞kT c with increasing hole doping is continued into the overdoped region. Thus the superconducting gap and strong-coupling ratio change monotonically and dramatically over a narrow doping region where T c exhibits a maximum. [S0031-9007(97)04904-1] PACS numbers: 74.50. + r, 74.25.Dw, 74.62.Dh, 74.72.Hs Tunneling spectroscopy and angle-resolved photoemission spectroscopy (ARPES) have emerged as powerful, complementary probes of the superconducting gap D in high-T c superconductors (HTS). ARPES has made important contributions in Bi 2 Sr 2 CaCu 2 O 82d (Bi2212), including strong support for d-wave symmetry of the gap and the evolution of the superconducting gap into a pseudogap which persists well above T c for underdoped samples [1][2][3]. At present there is no generally accepted model for the ARPES spectral function A͑k, E͒ in HTS, and this leads to uncertainty in the magnitudes of energy gaps, but also limits the ability to distinguish superconducting gaps from those arising from other electronic correlations such as charge density waves. It is therefore crucial to establish a correspondence to other traditional probes of superconductivity such as tunneling spectroscopy. We report here tunneling measurements in Bi2212 crystals using superconductor-insulator-superconductor (SIS) break junctions for which the peak in tunneling conductance is a direct measure of 2D. The Bi2212 crystals each have a T c 95 K at optimal doping and by changing the oxygen concentration they span a range from overdoped to moderately underdoped. We find a surprisingly strong, monotonic dependence of the superconducting energy gap and strong coupling ratio 2D͞kT c on doping concentration. Furthermore, we find that the magnitude of D measured by tunneling agrees with the low-temperature peak position of A͑k, E͒ measured in ARPES along the ͑p, 0͒ momentum direction [1-3] and that the temperature and doping dependence of the tunneling spectra display the same trends as found in ARPES. Thus we confirm the superconducting origin of the gap in ARPES below T c .This work builds upon previous tunneling studies of Bi2212 in both the SIS and SIN (N: normal metal) configurations [4-10], but here we present a detailed, sys-tematic examination of the doping dependence. The reproducibility of the SIS spectra indicates that the crystals have a homogeneous oxygen composition. In SIN tunneling the conductance at T 0 K is proportional to SA͑k, E͒jT k j 2 where the summation is over quasiparticle momentum k. Assuming that the tunneling matrix element T k varies only weakly with k, it follows that tunneling probes the quasiparticle density of states (DOS), r͑E͒ SA͑k, E͒ and this leads to a natural connection to ARPES [11]. A significant advantage of S...

New tunneling data are reported in Bi 2 Sr 2 CaCu 2 O 81d which show quasiparticle excitation gaps, D, reaching values as high as 60 meV for underdoped crystals with T c 70 K. These energy gaps are nearly 3 times larger than those of overdoped crystals with similar T c . Despite the large differences in gap magnitude, the tunneling spectra display qualitatively similar characteristics over the entire doping range. Detailed examination of the spectra, including the Josephson I c R n product measured in break junctions, indicates that these energy gaps are predominantly of superconducting origin. , and thus if the gap has a superconducting origin it strongly suggests that the pseudogap state is due to some type of precursor superconductivity [1,4,5]. However, the smooth dependence on doping may also originate from a quasiparticle gap that evolves from superconducting character in the overdoped phase to another type (e.g., charge density wave) in the underdoped phase [6]. In support of this picture are some measurements that suggest a superconducting order parameter (or coherence gap) that scales with T c [7][8][9]. Thus, a critical question is whether the large energy gap found in tunneling originates entirely from superconducting pairing or has a contribution from some other electronic effect. Here we address the nature of the gap measured by tunneling and report new data in more heavily underdoped Bi2212. Energy gaps, D, of 51 6 2, 54 6 2, and 58 6 2 meV are observed for three underdoped crystals with T c 77, 74, and 70 K, respectively, extending the previously reported trend [2] further into the underdoped regime. Detailed examination of the tunneling spectra over a wide doping range, including the Josephson I c R n product, show that these energy gaps are predominantly of superconducting origin.Superconductor-insulator-superconductor (SIS) junctions provide an accurate measure of the gap from the peaks in tunneling conductance (at a bias voltage jeV p j 2D) which are only weakly affected by thermal smearing or quasiparticle scattering [2,10]. However, the large magnitudes of energy gaps observed here lead to such extraordinarily large values of 2D͞kT c (as high as 20) that it is necessary to examine carefully the entire tunneling spectrum to clarify their physical origin. Most theoretical models of HTS stress the importance of electronic correlations which lead to spin density waves [11,12], or charge density waves in the underdoped phase [6,13]. These correlations give rise to gaps (or pseudogaps) in the electronic excitation spectrum, D c ͑k͒, that are distinct from those arising from superconductivity, D s ͑k͒. Since these other correlation gaps are used to explain pseudogap phenomena above T c , our investigation here has a direct bearing on this issue. The experimental goal is to determine whether the single-particle excitation gap as measured in tunneling has contributions from both D s and D c . We argue that if two distinct gaps exist, (i) they should have different magnitudes as well as different dopi...