In order to understand the origin of high-temperature superconductivity in copper oxides, we must understand the normal state from which it emerges. Here, we examine the evolution of the normal state electronic excitations with temperature and carrier concentration in Bi 2 Sr 2 CaCu 2 O 8þδ using angle-resolved photoemission. In contrast to conventional superconductors, where there is a single temperature scale T c separating the normal from the superconducting state, the high-temperature superconductors exhibit two additional temperature scales. One is the pseudogap scale T Ã , below which electronic excitations exhibit an energy gap. The second is the coherence scale T coh , below which sharp spectral features appear due to increased lifetime of the excitations. We find that T Ã and T coh are strongly doping dependent and cross each other near optimal doping. Thus the highest superconducting T c emerges from an unusual normal state that is characterized by coherent excitations with an energy gap.cuprates | photoelectron spectroscopy G eneral features of the phase diagram of the copper oxide superconductors have been known for some time. The superconducting transition temperature T c has a dome-like shape in the doping-temperature plane with a maximum near a doping δ ∼ 0.167 electrons per Cu atom. Although in conventional metals the electronic excitations for T > T c are (i) gapless and (ii) sharply defined at the Fermi surface (1), the cuprates violate at least one of these conditions over much of their phase diagram. These deviations from conventional metallic behavior are most easily described in terms of two energy scales T Ã (2, 3) and T coh (4), which correspond to criteria (i) and (ii), respectively.To address the role of these energy scales in defining the phase diagram, we concentrate on spectra where the superconducting energy gap is largest, the antinode [ðπ;0Þ → ðππÞ Fermi crossing], where the spectral changes with doping and temperature are most pronounced (the SI Appendix has further details). Spectral changes at the node have been previously studied by Valla et al.(5) and such spectra remain gapless for all doping values (6). In Fig. 1, we show spectra at fixed temperature as a function of doping. Data points are indicated in Fig. 1A (See SI Appendix for experimental conditions and sample details). Initially, we show spectra at fixed momenta as a function of energy (energy distribution curves, or EDCs) that have been symmetrized (7) about the Fermi energy to remove the effects of the Fermi function. Later, we show that equivalent results are obtained from division of the EDCs by a resolution-broadened Fermi function. In the following figures, because two values of the doping can result in the same T c , samples are labeled as OP for optimally doped, OD for overdoped, and UD for underdoped.The spectra at the antinode at the highest temperature (approximately 300 K) in Fig. 1D show two remarkable features: They are extremely broad in energy, exceeding any expected thermal broadening, and their line...

A key question in condensed-matter physics is to understand how high-temperature superconductivity emerges on adding mobile charged carriers to an antiferromagnetic Mott insulator. We address this question using angle-resolved photoemission spectroscopy to probe the electronic excitations of the non-superconducting state that exists between the Mott insulator and the d-wave superconductor in Bi 2 Sr 2 CaCu 2 O 8+δ . Despite a temperature-dependent resistivity characteristic of an insulator, the excitations in this intermediate state have a highly anisotropic energy gap that vanishes at four points in momentum space. This nodal-liquid state has the same gap structure as that of the d-wave superconductor but no sharp quasiparticle peaks. We observe a smooth evolution of the excitation spectrum, along with the appearance of coherent quasiparticles, as one goes through the insulator-tosuperconductor transition as a function of doping. Our results suggest that high-temperature superconductivity emerges when quantum phase coherence is established in a nonsuperconducting nodal liquid.High-temperature superconductivity in the cuprates occurs by doping a Mott insulator for which the antiferromagnetic ground state and low-energy excitations are well understood 1 . By adding carriers, the parent insulator turns into a superconductor for dopings that exceed 0.05 holes per CuO 2 plane. The d-wave nature of the superconducting ground state 2 and its low-lying excitations are also well understood. Between these phases lies an electronic ground state that is poorly understood. As the temperature is raised, this intermediate 'pseudogap' state occupies a larger and larger region of the phase diagram (Fig. 1a). It is from this phase that superconductivity emerges for all but the most highly doped samples. Consequently, the nature of this phase holds the key to the origin of high-temperature superconductivity.Whereas the electronic excitations in the high-temperature pseudogap region have been studied extensively, there is little spectroscopic data at low temperatures, as there is only a very narrow window of dopings where neither superconducting nor antiferromagnetic order occurs. Here, we present angleresolved photoemission spectroscopy (ARPES) data on single crystals and thin films 3 with doping levels that range all the way from the insulator to the over-doped superconductor. We focus in particular on non-superconducting thin films, just to the left of the superconducting transition temperature T c dome (see Fig. 1a), with an estimated hole doping ∼0. 04 (ref. 3). It is normally quite difficult to span the insulator-superconductor transition in Bi 2 Sr 2 CaCu 2 O 8+δ single crystals. However, it is possible to obtain very underdoped thin films by removing oxygen without film decomposition, as their large surface/volume ratio allows much lower annealing temperatures than those required for crystals. The integrity of the insulating films was confirmed by re-oxygenating them and checking their resistivity R(T ) and X-ray diffracti...

The energy gap for electronic excitations is one of the most important characteristics of the superconducting state, as it directly reflects the pairing of electrons. In the copper-oxide hightemperature superconductors (HTSCs), a strongly anisotropic energy gap, which vanishes along high-symmetry directions, is a clear manifestation of the d-wave symmetry of the pairing. There is, however, a dramatic change in the form of the gap anisotropy with reduced carrier concentration (underdoping). Although the vanishing of the gap along the diagonal to the square Cu-O bond directions is robust, the doping dependence of the large gap along the Cu-O directions suggests that its origin might be different from pairing. It is thus tempting to associate the large gap with a second-order parameter distinct from superconductivity. We use angle-resolved photoemission spectroscopy to show that the twogap behavior and the destruction of well-defined electronic excitations are not universal features of HTSCs, and depend sensitively on how the underdoped materials are prepared. Depending on cation substitution, underdoped samples either show two-gap behavior or not. In contrast, many other characteristics of HTSCs, such as the dome-like dependence of T c on doping, long-lived excitations along the diagonals to the Cu-O bonds, and an energy gap at the Brillouin zone boundary that decreases monotonically with doping while persisting above T c (the pseudogap), are present in all samples, irrespective of whether they exhibit two-gap behavior or not. Our results imply that universal aspects of high-T c superconductivity are relatively insensitive to differences in the electronic states along the Cu-O bond directions.E lucidating the mechanism of high-temperature superconductivity in the copper-oxide materials remains one of the most challenging open problems in physics. It has attracted the attention of scientists working in fields as diverse as materials science, condensed matter physics, cold atoms, and string theory. To clearly define the problem of high-temperature superconductors (HTSCs), it is essential to establish which of the plethora of observed features are universal, namely, qualitatively unaffected by material-specific details.An important early result concerns the universality of the symmetry of the order parameter for superconductivity. The order parameter was found to change sign under a 90°rotation (1, 2), which implies that the energy gap must vanish along the diagonal to the Cu-O bonds, i.e., the Brillouin zone diagonal. This sign change is consistent with early spectroscopic studies of near-optimally-doped samples (those with the highest T c in a given family), where a jcos 2 ϕj energy gap (3, 4) was observed (ϕ being the angle from the Cu-O bond direction), the simplest functional form consistent with d-wave pairing. More recently, there is considerable evidence (5-8) that, with underdoping, the anisotropy of the energy gap deviates markedly from the simple jcos 2 ϕj form. Although the gap node at ϕ = 458 is observed...