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High-temperature superconductivity in the cuprates occurs by doping a Mott insulator for which the antiferromagnetic ground state and low-energy excitations are well understood1. By adding carriers, the parent insulator turns into a superconductor for dopings that exceed 0.05 holes per CuO2 plane. The d-wave nature of the superconducting ground state2 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.

Figure 1: Data for insulating samples.
figure 1

a, Phase diagram of Bi2Sr2CaCu2O8+δ in the hole-doping (δ), temperature (T) plane (the arrow indicates δ for the insulator) AFM: antiferromagnet. b, Resistance versus T. c, ARPES intensity versus k at T=16 K (averaged over a 0 to 10 meV window). The high-intensity points map out the underlying Fermi surface (kF) versus angle θ. d, EDCs at kF with θ increasing from 0∘ (top) to 45∘ (bottom). e, MDCs along the cuts marked in c (same colour coding in c–e). The top two MDCs are at E=18 and 22 meV respectively; the rest are at E=0 meV. f, Nodal dispersion for a δ=0.04 sample different from that in c–e.

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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 angle-resolved photoemission spectroscopy (ARPES) data on single crystals and thin films3 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 Tc 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 Bi2Sr2CaCu2O8+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 diffraction spectra3.

Once sufficient oxygen is removed, the samples have an insulating upturn in resistance R(T) with decreasing temperature, shown in Fig. 1b, that is well described by two-dimensional-variable range hopping4,5 (see Supplementary Information). We have measured the diamagnetic susceptibility down to 1.5 K, finding no trace of superconductivity (sensitivity: 1% of volume fraction).

Figure 1d shows the energy distribution curves (EDCs, spectra at constant momentum k versus binding energy). Despite the low temperature, no sharp, coherent features are discernible in the spectra. This is not surprising, because earlier work had found a strong suppression of coherent spectral weight in the superconducting state with underdoping6. In contrast, the momentum distribution curves (MDCs) in Fig. 1e at zero energy show clearly visible peaks. Thus, the excitations are much better defined in k-space than they are in energy, and are sharper near the zone diagonal than near its boundary (the Brillouin zone is shown in Fig. 1c). Remarkably, despite the insulating-like nature of the resistivity, the MDC peaks indicate a locus of minimum energy excitations similar to that of the superconductors, visible in the ARPES intensity map in Fig. 1c. These ‘Fermi momentum’ (kF) values were in fact used to generate the EDCs in Fig. 1d. Figure 1f shows the ARPES intensity as a function of energy and k for another sample at the same doping, which shows that there is a well-defined dispersion despite the incoherent nature of the EDCs.

To better understand the electronic excitations in the insulator, we plot in Fig. 2d its EDCs at kF, symmetrized to remove the effects of the Fermi function7, and compare them with superconducting state spectra (Fig. 2e–g) at various dopings indicated in Fig. 2a. In Fig. 2d–g, the top curve corresponds to kF on the zone boundary (θ=0∘), whereas the lowest curve corresponds to kF on the zone diagonal (θ=45∘), with the Fermi surface angle θ increasing from top to bottom.

Figure 2: Spectral function versus doping.
figure 2

a, Doping levels δ of four samples for which spectra are plotted in d–g. b, Insulator nodal spectrum and background (D in a) at T=16 K. c, Background-subtracted, symmetrized intensity for sample D, showing a gap at the antinode and zero gap at the node. d–g, Symmetrized EDCs for an insulating film at T=16 K (d), a Tc=33 K film at T=16 K (e), a Tc=69 K crystal at T=20 K (f) and a Tc=80 K film at T=40 K (g); the spectra are plotted from the antinode (top) to the node (bottom). The intersection of the red lines in d defines the gap in the insulator.

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In the insulator (Fig. 2d) we see a highly anisotropic energy gap that decreases monotonically from a maximal value at θ=0∘, to zero at θ=45∘. Even though there are no sharp coherence peaks at any angle, there is a clearly discernible low-energy gap. This is the pseudogap at low temperature (16 K) in the non-superconducting sample. With increasing doping, we move from the insulator (Fig. 2d) to the highly underdoped superconductor (Fig. 2e), for which the EDCs look qualitatively similar to those in Fig. 2d, except for the appearance of observable coherent quasiparticle peaks at the gap edge for all θ. These peaks grow in strength with increasing doping (Fig. 2f,g), as the energy gap evolves smoothly going from the insulator (Fig. 2d) to the optimally doped superconductor (Fig. 2e–g).

Much of the EDC intensities in Fig. 2d can be traced to a large ‘background’ that is present for all k-points in the zone. The origin of this background is not entirely clear, although it can be readily identified as the ARPES spectra for unoccupied states (k much beyond kF), or extracted from the ‘flat’ (k-independent) part of the MDCs (ref. 8), and is plotted in Fig. 2b. We note that following the signal, the intensity of the background also continuously decreases with decreasing doping (see Supplementary Information). If this background is subtracted from the data in Fig. 1d, we obtain the symmetrized results shown in Fig. 2c, which further emphasize the presence of a low-energy pseudogap (θ=0∘) and a node (θ=45∘).

Figure 3 shows the angular anisotropy of the spectral gap (Δ) for all of our thin-film and single-crystal samples. The superconducting samples were measured at temperatures between 16 and 40 K, well below their Tc; the non-superconducting sample was measured at 16 K. The energy gap of the superconducting samples was determined from half the spacing between coherence peaks in symmetrized spectra at their corresponding kF. For the non-superconducting sample, we determine the low-energy gap from the raw data (as indicated by the intersection of red straight lines in Fig. 2d), from the background-subtracted data (Fig. 2c), and also from line-shape fits. All three methods lead to the same gap estimates within error bars.

Figure 3: The spectral gap as a function of doping and angle around the Fermi surface.
figure 3

a, The spectral gap Δ(θ), normalized by its value at the antinode, versus the Fermi surface angle θ. Δ(θ) at all doping levels is consistent with the d-wave form |cos(2θ)| (black curve). b, Maximum gap as a function of hole-doping. Gaps of the superconducting samples are denoted by filled symbols (blue for thin films and red for single crystals, and green for published data6), and open circles are used for the non-superconducting samples. Error bars are given by the uncertainty in EDC peak positions at kF.

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Normalizing the gaps to their maximal value at θ=0∘, we find (Fig. 3a) that they follow a simple |cos(2θ)| behaviour for all samples, superconducting and non-superconducting. This ‘d-wave’ gap is universal in nature, and does not distinguish between the d-wave superconductor and the low-temperature pseudogap phase. The maximal energy gap values, plotted in Fig. 3b, monotonically increase with underdoping as found earlier6, although they might decrease near the superconductor–insulator boundary.

Our results confirm an earlier extrapolation9, based on ARPES measurements above Tc for underdoped superconducting samples, that the low-temperature pseudogap phase should be characterized by a node along the zone diagonal. They are also consistent with thermal conductivity (κ) measurements10 in highly underdoped YBa2Cu3O6+δ, which show that the low-temperature κ/T of the insulating phase proximate to the superconducting dome is the same as that in the d-wave superconducting phase, where it is dominated by nodal excitations.

Many experiments report a node in the superconducting state but a gap that deviates from the simple |cos(2θ)| form with underdoping. This behaviour is attributed to two different order parameters (see ref. 11 and references therein), with an energy gap in the antinodal region (near θ=0∘) larger than what would be inferred by extrapolating the gap from the nodal region (θ=45∘). Our own work12 a decade ago found evidence for a flattening of the gap around the nodes, but at that time the detectors had at least an order of magnitude lower k-resolution and sparser angular sampling compared with the present study. Recent ARPES studies13,14,15 and scanning tunnelling microscopy16,17 have also reported ‘two gap’ behaviour.

The present results are not consistent with a two-gap picture. Several other experiments also find evidence for a simple d-wave gap. These include thermal transport data18, where the nodal-gap slope extrapolated to the antinode was consistent with the maximum gap, and ARPES data on underdoped La2−xSrxCuO4(ref. 19), 1/8-doped La2−xBaxCuO4 (ref. 20) and Bi2201 (refs 21, 22). Why some experiments and/or samples show ‘two-gap’ behaviour whereas others show a simple d-wave gap is not understood at present. We must emphasize here that we observe coherent quasiparticle peaks at the gap edge at all kF for all superconducting samples down to the lowest Tc values. If, however, quasiparticle peaks were absent near the antinodes, one would erroneously estimate much larger gap values in the vicinity of these k-points.

Another important question in highly underdoped samples is the possible existence of hole pockets, reported in a recent ARPES measurement23. We have not found any evidence for such pockets. Our MDCs always trace out a large underlying Fermi surface as in Fig. 1c.

This brings us to the implications of our main result, the observation of a d-wave-like gap that persists through the insulator-to-superconductor transition. One possibility is that our insulating sample is highly inhomogeneous and has a small fraction of superconducting regions that dominate the low-energy signal, whereas the less-doped insulating regions produce the large spectroscopic background and dominate the transport. This inhomogeneity should be intrinsic, and not a surface phenomenon, because we have found very similar results in the superconducting samples for thin films and single crystals of Bi2Sr2CaCu2O8+δ, as well as single crystals of La2−xSrxCuO4 (ref. 19) (which involved a completely different surface preparation). We emphasize that our diamagnetic susceptibility measurement puts a bound of 1% on the superconducting fraction, which seems too small to account for the signal-to-background ratio observed in Fig. 2b. The T=0 superconductor-to-insulator transition is driven by quantum fluctuations24 of the phase of the superconducting order parameter. The corresponding thermal fluctuations, which are vortex-like excitations in the pseudogap phase, have been probed by Nernst25 and diamagnetism26 experiments.

Our observations imply that the sharp quasiparticles of the superconducting state exist down to the lowest doping levels while rapidly losing spectral weight, but are no longer visible on the insulating side. Nonetheless, a low-energy d-wave-like gap survives the phase-disordering transition. Obviously, the node must disappear as the Mott insulator is approached27. We note that sample charging prevents us from making low-temperature measurements for δ<0.04, suggesting a fully gapped insulator.

We emphasize that our experiments probe the excitation spectrum, but not any possible broken symmetries of the nodal-liquid state. The simplest picture consistent with our data is that the nodal liquid is just a phase-incoherent version of the d-wave superconductor28,29,30, and adding charged carriers to this liquid establishes phase coherence, leading to high-Tc superconductivity.