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

Angle resolved photoemission data in the pseudogap phase of underdoped cuprates have revealed the presence of a truncated Fermi surface consisting of Fermi arcs. We compare a number of proposed models for the arcs and find that the one that best models the data is a d-wave energy gap with a lifetime broadening whose temperature dependence is suggestive of fluctuating pairs.

Angle resolved photoemission on underdoped Bi 2 Sr 2 CaCu 2 O 8 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. DOI: 10.1103/PhysRevLett.99.157001 PACS numbers: 74.25.Jb, 74.72.Hs, 79.60.Bm We present in this Letter angle resolved photoemission spectroscopy (ARPES) data on the energy gap in the superconducting (SC) and pseudogap phases of the underdoped high T c superconductor Bi 2 Sr 2 CaCu 2 O 8 (Bi2212). Reduced T c samples which lie in between the optimally doped, highest T c material and the undoped Mott insulator are called ''underdoped.'' Such samples exhibit an unusual normal-state pseudogap, whose signature in ARPES [1,2] is a loss of spectral weight in parts of k space, leading to low-energy electronic excitations which live on disconnected ''Fermi arcs '' [3]. Both the SC gap below T c and the pseudogap above T c are anisotropic gaps in the singleparticle excitation spectrum, but their relationship is not well understood. Our goal is to gain insight into how the SC gap, with its d-wave anisotropy [1,2] at low T, changes as a function of temperature and evolves into the anisotropic pseudogap upon heating through T c .Our first result is that the magnitude and anisotropy of the d-wave SC energy gap is essentially T independent for all T T c . This behavior is completely different from a mean field description of a d-wave superconductor. Within mean field theory the anisotropy would be T independent, but the gap magnitude, proportional to the order parameter, would be suppressed with increasing T and vanish at T c . Remarkably, our data show that the k-dependent SC gap in underdoped cuprates does not even know about the scale of T c .Second, there are four point nodes at which the energy gap vanishes for all T < T c , but above T c each point node abruptly expands into a gapless Fermi arc of finite extent. We show that this remarkable change occurs within the width of the resistive transition at T c . The abrupt change from point nodes to gapless arcs is not just thermal smearing, but rather it is closely connected with the loss of superconducting order.We present ARPES data on two underdoped Bi2212 films, one near optimality (T c 80 K) and the other more underdoped (T c 67 K), both of which exhibit a significant pseudogap. The films, prepared by RF sputtering on a SrTiO 3 substrate [4], exhibit only very weak superstructure replicas which simplifies the data analysis. The measurements were carried out at the Synchrotron Radiation Center, Wisconsin, using a Scienta R4000 analyzer with 22 eV photons, and momentum cuts and polarization para...

We measured the electronic-structure of FeSexTe1−x above and below Tc. In the normal state we find multiple bands with remarkably small values for the Fermi energy εF . Yet,below Tc we find a superconducting gap ∆ that is comparable in size to εF , leading to a ratio ∆/εF ≈ 0.5 that is much larger than found in any previously studied superconductor. We also observe an anomalous dispersion of the coherence peak which is very similar to the dispersion found in cold Fermi-gas experiments and which is consistent with the predictions of the BCS-BEC crossover theory.PACS numbers: