Introduction

Over 30 years of research on the cuprates has led to a “unified” form of the phase diagram, supposed to be applicable to various cuprates1. According to it, the Mott insulator with the antiferromagnetic (AF) order persists up to about 5% of carrier doping (p ~ 0.05), followed by a dome-shaped superconducting (SC) phase; these two phases are clearly separated without the slightest overlap. In the underdoped region, the pseudogap2,3 and charge-density-wave (CDW)4 states compete with superconductivity5,6,7,8,9. These states develop most significantly around the antinode [or (π, 0) region], leaving only arc-like segments of the Fermi surface (FS) even above Tc10. As the hole doping decreases, the Fermi arc shrinks and eventually becomes point nodes (or nodal liquid state) at the edge of the Mott insulating phase11,12,13,14,15. In this state, the quasiparticle peak is tiny and accompanied by polaron-like broad spectra. In addition, this peak disappears with leaving off the node since very broad spectra severely damped by the pseudogap prevail everywhere in momentum space. At doping levels further less, a gap is opened even in the (0,0)-(π, π) direction13,14,16, turning the nodal liquid state into a full gap state consisting only of polaronic broad spectra all around the Brillouin zone (BZ).

Notably, the above phase diagram is based on the data of single- and double-layered cuprates; it is different from the phase diagrams with a significant overlap of the AF and SC phases in multilayer systems with three or more CuO2 planes per unit cell17,18. In the single- and double-layered cuprates, the CuO2 plane is affected by the random potential induced by the adjacent dopant layers, leading to an inhomogeneous electronic state as revealed by scanning tunneling microscopy (STM)19,20. It is, therefore, possible that the phase diagram is relevant only for disordered CuO2 planes, especially in the lightly-doped region sensitive to disorder. This circumstance may have hindered a fair comparison of the data with the theory describing the doped Mott state, which usually supposes an ideal CuO2 plane without disorder21,22. It could, however, be solved by focusing as a research target on the inner planes of the multilayer cuprates, which are protected by the outer CuO2 planes screening the disorder effect from the dopant layers. According to nuclear magnetic resonance (NMR) studies17,18, the carrier doping in the inner planes is much more homogeneous than that in the CuO2 planes of other compounds, including the single-layered HgBa2CuO4+δ (Hg1201) and double-layered YBa2Cu3O6.5 (Y123) thought as to be clean systems. With this advantage, the small Fermi Pocket, which had been elusive while predicted in the doped Mott state, was recently observed in the inner plane of a 5-layer compound23. The multilayer cuprates, therefore, provide an excellent platform to unveil the genuine electronic properties of the lightly-doped region, which is key to elucidating the pairing mechanism in cuprates. Above all, since the highest achievable Tc among the existing substances is obtained in one of the multilayer cuprates (the trilayer HgBa2Ca2Cu3O8+δ24,25,26), the current subject is crucial for the development of condensed matter physics.

In this article, we have selected the six-layer Ba2Ca5Cu6O12(F,O)2 (Tc = 69 K; Supplementary Fig. S1) for a study, where the effective carrier doping of the inner planes should be very low. The electronic properties of the clean CuO2 planes are revealed over a wide range of hole doping which is controlled by varying the number of inner planes and the in situ potassium deposition on the sample surface. The spectra with well-defined quasiparticle peaks lacking the polaronic features are detected all over the closed Fermi surface (or a tiny Fermi pocket), even at the doping level extremely close to the half-filling; it is distinct from the nodal liquid state and the polaronic state established in the heavily underdoped cuprates with the inevitable disorder. Furthermore, we find that the superconducting pairing occurs at ~4% doping, almost the same critical doping as in single-layered cuprates with CuO2 planes severely disordered. This doping level (~4%), therefore, is not the consequence of an increase by the disorder but should be the critical amount of carriers essential for the pair formation even in the ideally clean CuO2 plane.

Results

Figure 1a plots the spectral intensities close to the Fermi level (EF) measured by laser-ARPES at the lowest temperature (T = 5 K). We found three sheets of FSs: One exhibits an arc-like structure typical for the underdoped cuprates, and the other two show small pockets around (π/2, π/2) corresponding to the doped Mott states with the AF order27. To further validate the ARPES results, we also observed the de Haas-van Alphen (dHvA) effect by the torque measurement, a bulk-sensitive probe. We detected quantum oscillations (Fig. 1c) consisting of mainly two frequencies (arrows in Fig. 1f), corresponding to the FS areas covering 1.2 and 4.8% of the Brillouin zone. These values almost perfectly agree with the ARPES results (1.0 and 4.3%). Since carriers are doped from the dopant layers (hatched by orange in Fig. 1f), the doping amount should become less toward the inner planes. It is, thus, expected that the small Fermi pocket, large Fermi pocket, and Fermi arc are each formed by the innermost layer (IP0), second-inner plane (IP1), and outer plane (OP), respectively, as noted in Fig. 1a, f. The validity of this one-to-one correspondence between FSs and CuO2 layers can be confirmed by comparing these results with those of the five-layer compound23, as demonstrated below.

Fig. 1: Fermi surfaces of six-layer cuprate and the comparison with those of 5-layer cuprate.
figure 1

a Fermi surface mapping obtained by integrating the intensities of ARPES spectra at 5K around the Fermi energy (EF). b Fermi surfaces zoomed inside the black dot square in a determined from the peak positions of MDCs at EF for six-layer (red) and five-layer (blue)23 compounds. c Quantum oscillations of the dHvA effect observed in magnetic torque signals at several temperatures. In the data, the smooth background is subtracted. The crystallographic c-axis was set to 2∘ from the magnetic field direction during the measurements. d Fast Fourier transform spectra of c. The arrows show the two main peaks (F0 and F1), which correspond to the two Fermi pockets observed by ARPES in a. e Comparison of the Fermi pocket areas between the five-layer and six-layer compounds determined by dHvA (top) and ARPES (bottom). The listed values are the area in percentage (%) covering the Brillouin zone for the small and large Fermi pockets labeled as IP0 and IP1, respectively. As noted with arrows, the area of the small Fermi pocket (IP0) decreases to almost half with increasing the number of layers from five to six, while that of the large Fermi pocket (IP1) is almost the same between the two. f The crystal structure of the five-layer and six-layer compounds. The number of the innermost CuO2 plane (IP0) gets doubled in the 6-layer compound, as represented by arrows.

Full size image

In Fig. 1b, we overlay the FSs of the five- and six-layer compounds determined from the laser-ARPES data. Here, note that the samples we observed have similar Tc values (Tc = 65 K and 69 K for five- and six-layer compounds, respectively), and thus these two should have similar doping levels. We found that the small Fermi pocket gets much smaller than that of the five-layer compound, while the other FSs (large Fermi pocket and Fermi arc) remain almost the same. We also obtained the results supporting this conclusion by synchrotron-ARPES (Supplementary Fig. S2) with higher photon energies more generally used in the cuprate research. As summarized in Fig. 1e, the area of the small Fermi pocket labeled as IP0 is changed by adding one more CuO2 plane in the unit cell from five to six, and importantly, the area of the 6-layer compound gets half that of the 5-layer compound (arrows in Fig. 1e). This indicates that the carriers in IP0 are simply split into two for IP0s doubled in the 6-layer compound (arrows in Fig. 1f) without affecting other planes (IP1 and OP); this means that the wave function of IP0 is independent of those of IP1 and OP. It is further justified by our experimental result that the superconducting gap is observed on the Fermi pocket of IP1 but not of IP0 (Supplementary Fig. S4). The mixing of layers should produce superconducting gaps of similar magnitudes, so our data against it indicate that the two pockets derive each from different layers (IP0 or IP1) that are essentially electronically decoupled.

We perform a model calculation based on our ARPES results and demonstrate that the mixing of layers is, indeed, negligible (Supplementary Fig. S3). The hybridization among layers is prevented by a potential difference induced by the carrier distribution along the c-axis. The inclusion of an interlayer hopping parameter (V) in the calculations doubly splits the small Fermi pocket, similar to the bilayer splitting observed in double-layer cuprates28. This is attributed to double IP0s adjacent to each other and sensitive to the V parameter. In contrast, splitting does not appear in the large Fermi pocket even for a relatively large value of V since double IP1s are structurally separated. Notably, splitting of the small Fermi pocket (IP0) is not experimentally observed both in ARPES and dHvA. We also note that the peak of the fast Fourier transformation (FFT) spectrum of the dHvA effect for the small Fermi pocket is relatively sharp in width (at least, sharper than the spectra of Y12329 and Hg120130), and it is almost the same as that for the large Fermi pocket. It indicates that there is not even the slightest splitting in the small Fermi pocket, so the interlayer hopping should be negligibly small in our samples. This is a remarkable feature of a low doping state, and compatible with the observation in Bi2212 that the bilayer splitting energy gets smaller with decreasing carrier concentration31. Calculations with such a small V estimate the mixture of wave functions from different CuO2 planes to be negligible (less than 3%; Supplementary Fig. S3d). This leads us to conclude that the three FSs we observed are independently formed by three different CuO2 planes (IP0, IP1, and OP). We emphasize that this is a new aspect of multilayered cuprates that was clarified only through the measurement of the 6-layer compounds with double IP0s.

The above argument allows us to estimate the carrier concentration of each CuO2 plane directly from the area of each FS. Our data indicate that the innermost CuO2 plane (IP0) is doped by only 1% of hole carriers, which is extremely close to the half-filling. In Fig. 2b, c, we plot the energy distribution curves (EDCs) around the small Fermi pocket for IP0 (orange circles in Fig. 2a) and those symmetrized about EF to eliminate the Fermi cut-off effect, respectively. Surprisingly, we find very sharp peaks in the spectra even for a state with such low carrier density. Here, note that the superconducting gap is absent most likely because the state of 1% doping is situated outside the superconducting dome in the phase diagram. The spectral peak width is estimated to be about 7.1 meV (arrows in Fig. 2c), which is comparable to or even smaller than that (blue curve in Fig. 2c) of the optimally doped Bi2Sr2CaCu2O8+δ (Bi2212)32, the cuprate material most well-studied by ARPES. This means that quasiparticles as long-lived as those in the optimally doped state can develop with a tiny amount of carrier doping in an ideally clean CuO2 plane.

Fig. 2: Well-defined quasiparticle peaks without polaronic features all around the closed Fermi surface even in the slightest amount of carrier doping (p ~ 1 %).
figure 2

a The small Fermi pocket for IP0 zoomed around (π, π). b EDCs measured along the small Fermi pocket. The corresponding kF points are plotted by orange circles in a. For a fair comparison of the peak shapes, the EDCs are normalized to each peak intensity. The spectrum at the nodal point for the optimally doped Bi2212 (Tc = 92 K) is overlayed (blue curve) to demonstrate that spectra of IP0 in the six-layer compound are even sharper than it. c Same data as b, but symmetrized about the Fermi energy to eliminate the Fermi cut-off and clarify that there is no energy gap at EF along the entire Fermi pocket. d Angle ϕ (defined in b) dependence of the full width at half maximum (FWHM) of the symmetrized EDCs in c obtained by fitting to the Lorentz function. The dashed line is the guide to the eye to represent that the spectral width is constant with the value of 7.1 meV along the Fermi pocket. Error bars represent standard deviations of the spectral peak widths. e The Fermi surface mapping up to the second Brillouin zone, disentangling the Fermi arc (lower region of second BZ) and pockets (upper region of second BZ), by employing the matrix element effect in ARPES. f, g The band dispersions of the Fermi arc and pockets each crossing nodal kF points of Fermi arc (OP) and small Fermi pocket (IP0) along the white dotted lines in e. In upper panels, MCDs at EF are extracted to confirm that OP and IP0 are indeed separately observed. The Lorentzian functions (colored curves) are fit to the data (black curve). h The EDC at kF for IP0, indicating a well-defined quasiparticle peak accompanied by the spectral tail with relatively low intensities lacking polaronic features.

Full size image

Notably, the peak width is constant all around the Fermi pocket including hot spots at which the FS and the antiferromagnetic zone boundary (AFZB) cross33,34. This is very different from the anisotropic nature widely acknowledged for the underdoped cuprates3. We also emphasize that the electronic state unveiled here is distinct from the following features illustrated for the single- and double-layered cuprates: the nodal liquid state, where only the nodal direction is metallic and the other kF points are dominated by broad spectra with the pseudogap11,12,13,14, and the polaronic state, where quasiparticle peaks are tiny and largely buried by a hump-shaped incoherent part. In stark contrast, our data for inner planes exhibit surprisingly simple metallic features, forming a closed Fermi pocket (instead of the nodal liquid state) with well-defined quasiparticles (instead of the polaronic state). Here, note that the quasiparticle in IP0 is not a product of the superconducting proximity effect from the outer planes. This is evidenced by the fact that quantum oscillations (signals of well-defined quasiparticles) have been observed under conditions that the superconductivity is completely suppressed. ARPES also confirmed that the quasiparticle peak persists even above Tc although its width gets broadened due to the thermal broadening effect (Supplementary Fig. S10).

The bands of Fermi arc and pockets are mutually close in momentum space, so their ARPES signals could interfere at high binding energies. To examine single-particle spectra of IP0, we conducted band-selective measurements by utilizing the matrix element effect. In Fig. 2e, we map the FS by synchrotron-ARPES not only of the 1st BZ but also up to the 2nd BZ. The data in the 2nd BZ are enhanced in intensity, and moreover, separate the bands of Fermi arc (OP) and pockets (IP0 and IP1) in the upper and lower half of the 2nd BZ, respectively. This separation is further confirmed in Fig. 2f, g by plotting the ARPES dispersions each across nodal kF points of OP and IP0 (dashed lines in Fig. 2e). Only the latter exhibits the folded bands about AFZB, which are also revealed by MDCs at EF (the upper panels of Fig. 2f, g). We extract the EDC for IP0 at kF in Fig. 2h, and find a sharp peak accompanied by a tail with relatively low intensities up to the energy scale of the bandwidth. This validates that the Fermi pocket possesses well-defined quasiparticles lacking polaronic features, even though the doping level is extremely small.

In order to explore a wider doping range, we have performed the in situ potassium deposition on the samples. This technique is commonly used in ARPES35 including a study of cuprates36,37,38. Figure 3a–c displays the FS mapping before and after the potassium deposition for different times (0, 30, and 60 s, respectively). The Fermi pockets get smaller with deposition time. This variation is more clearly demonstrated in Fig. 3f by extracting the momentum distribution curves (MDCs) along the AFZB at EF. The momentum distance between each paired kFs becomes shorter in the two pockets, representing the reduction of hole carriers in both inner planes. In Fig. 3d, e, we plot the large and small Fermi pockets for IP1 and IP0, respectively, at three different deposition times, determined from the ARPES spectra. A systematic shrinkage of the pockets is confirmed, as estimated in Fig. 3g from their areas (or carrier concentrations ps). The p value decreases faster in the large pocket (IP1) than in the small pocket (IP0); this is expected since IP1 lies closer to the surface dopant layer where potassium is deposited, so it should be more efficiently doped. Our experiments could reduce the doping level of the innermost plane (IP0) down to 0.7% (p = 0.007), which is so small as to nearly reach the half-filled Mott state.

Fig. 3: Evolution of the Fermi pockets with in situ potassium deposition.
figure 3

a–c Fermi surface mapping zoomed around (π, π) to focus on the two Fermi pockets for three cases: before deposition (a) and after deposition for 30 s (b) and 1 min (c). The spectral intensities were integrated within an energy window of 10 meV around EF. d, e Fermi pockets determined from the peak positions of MDCs for IP1 (d) and IP0 (e), respectively. In each panel, the results of three different deposition times (0 s, 30 s, and 60 s) are plotted. f Comparison of MDCs at EF along the antiferromagnetic zone boundary (AFZB). Along this momentum cut, the Fermi velocity is fastest, thus the largest shift of kF with carrier doping is expected. g The deposition time dependence of the area of the Fermi pocket or the hole carrier concentration p. The dotted line remarks that IP0 reached the doping level as extremely low as 0.7 % (p = 0.007) after the deposition for 60 s.

Full size image

Here we examine the doping evolution of the ARPES spectra. Figure 4a plots the EDCs at kF on the AFZB for IP0 (orange circle in the inset of Fig. 4a) in 1.0, 0.9, and 0.7% of doping levels. In the right panel, the symmetrized EDCs are also plotted. We found that sharp quasiparticle peaks persist down to the lowest carrier concentration of 0.7% (p = 0.007). Although the peak intensity was slightly suppressed due to the sample surface deterioration, the spectral peaks have almost the same width (Supplementary Fig. S8), indicating that the scattering rate (or lifetime) of quasiparticles is hardly changed going toward the half-filling. The results imply that a single hole doped into the Mott insulator can behave as a long-lived quasiparticle in a clean CuO2 plane (Fig 4b). It is in stark contrast to the property of the single- and double-layered cuprates, in which a quasiparticle peak rapidly dies out at doping levels lower than ~10%13,14,16,37, and even if there is some spectral weight at EF, it is rather broad and disappears immediately with going away of the nodal direction12,39.

Fig. 4: Doping evolution of ARPES spectra and phase diagram of the lightly-doped cuprates with disorder removed.
figure 4

a Doping evolution of the energy distribution curves (EDCs) and those symmetrized about EF, measured at kF on the antiferromagnetic zone boundary (AFZB) for the small Fermi pocket (orange circle at the inset). The spectra plotted are for three different doping levels (1, 0.9, and 0.7%) controlled by potassium deposition. b Schematic of electronic state in real space for the 1% doped CuO2 plane, illustrated based on our data suggesting that a single hole can behave as a long-lived quasiparticle in the antiferromagnetic background. c Schematic density of states for the 1% doped CuO2 plane corresponding to b. d–f Doping evolution of EDCs and those symmetrized about EF for three different kFs (purple circles in the inset of each panel) of the large Fermi pocket. The spectra plotted are for three different doping levels (4.3, 4.0, and 3.6%) controlled by potassium deposition. The arrows point to the spectral peaks, clarifying the gap opening or closing for each spectrum. g The phase diagram in lightly-doped region summarized from our data of clean inner CuO2 planes in 6-layered cuprates. AF, QP, and SC abbreviate “antiferromagnetic'', “quasiparticle'', and “superconductivity'', respectively.

Full size image

IP1 also realizes a very clean electronic system as confirmed by its low Dingle temperature (TD, proportional to the scattering rate) obtained by the dHvA quantum oscillations: TD of IP1 is estimated to be 12.3 K (Supplementary Fig. S5), which is between those of Y123 (TD = 6.2 K)29,40 and Hg1201 (TD = 18 K)30,40. Note that the carrier concentration of IP1 directly estimated from the Fermi pocket area is small, only to be 4.3%, which is less than half those (~10%) of Y123 and Hg1201 samples used for the quantum oscillation measurements. Hence, the TD of IP1 is rather small, considering that it is obtained in such a low carrier concentration with a poor screening effect.

The spectra of IP1 before the potassium deposition exhibit the superconducting gap consistent with the d-wave symmetry, being the largest at the tip of the Fermi pocket (see Supplemental Fig. S4 for more details). This data indicates the coexistence of superconductivity and AF magnetic order, similar to the observations in the five-layer compound by NMR17,18 and ARPES23. Figure 4f plots the spectra at the tip of the Fermi pocket for three different doping levels (4.3, 4.0, and 3.6%) controlled by the potassium deposition. The superconducting gap observed at the original doping level of 4.3% closes at 4.0% (This is further justified in Supplementary Note 9). This indicates that the electronic state in IP1 has got out of the superconducting dome and entered the metallic phase, i.e., the same as that of IP0, by decreasing the hole doping. Also, the relatively small superconducting gap observed for the pristine surface (magnitude of Δtip = 5 meV at the tip of the Fermi pocket and the order parameter Δ0 = 11 meV determined by extrapolating it to the antinode) is attributed to the carrier doping level (4.3%) located almost at the edge of the superconducting dome. The superconducting to metal transition we observed occurs by closing a gap along the entire Fermi surface (or pocket) while maintaining well-defined quasiparticles all over it. This is very different from the phase transition for the underdoped cuprates with disordered CuO2 planes, where the pseudogap accompanied by the damped broad spectra plays a significant role. Rather, our observation is quite similar to the doping-induced phase transition across the superconducting dome on the overdoped side with no indication of the pseudogap, although the Fermi surface size is apparently different, corresponding to p, not to 1+p.

In Fig. 4g, we illustrate a phase diagram of lightly-doped cuprates with extremely clean CuO2 planes unveiled via the direct observation of the electronic structure by ARPES. The Mott insulating state is realized only when the CuO2 plane is non-doped, and is strictly half-filled; only the slightest amount of hole doping changes it to a metallic state forming a Fermi pocket with well-defined quasiparticles on the top of the lower Hubbard band (or charge transfer band). We find that the effective mass in the innermost layer (IP0) and the second-inner layer (IP1) with different carrier concentrations (~1 and ~4%, respectively) are almost the same (~0.6 m0) by quantum oscillation measurements (Supplementary Fig. S7). This indicates a lack of a pronounced band narrowing when varying p toward the half-filled Mott state. The transition to a Mott insulator most likely occurs by completely removing hole carriers from the lower Hubbard band until the perfect half-filling, rather than by controlling the bandwidth. At 4%, the metal-to-superconductor transition occurs by opening the superconducting gap, and the system enters the phase where the AF order and superconductivity coexist. Intriguingly, this critical doping level is almost the same as that of some single- and double-layer compounds, such as La2−xSrxCuO4 which is known to be severely disordered according to the NMR studies41,42,43,44. This indicates that 4% is the intrinsic critical doping level necessary to form the superconducting pairs even in the CuO2 planes with the clean-limit condition. This scenario differs from theories that suggest that superconductivity occurs simultaneously with the appearance of metallicities by carrier doping to the ideal Mott insulator without disorder21,22. Our results will provide crucial insight into understanding the intrinsic relationship between the Mott physics and the pairing mechanism in the lightly-doped CuO2 planes, which has not been accessible for the single- and double-layered compounds mainly studied in the long history of cuprate research.

Methods

Samples

Single crystals of underdoped Ba2Ca5Cu6O12(F,O)2 (see crystal structure in Fig. 1f) with Tc = 69 K were grown at between 1100 and 1200 ∘C under a pressure of 4.5 GPa without an intentional flux. The starting composition for the crystal synthesis is Ba2Ca3Cu4O7.9F2.1, which is known to be almost the same in single crystals45. We have conducted X-ray diffraction measurements along the c-axis for all the sample pieces and confirmed that they are single crystals, not mixtures of crystal domains with different numbers of CuO2 layers per unit cell. Magnetic susceptibilities for these crystals (Fig. S1) show a sharp superconducting transition with ~4 K in width, indicative of high quality in our samples; the signal-to-noise ratio is not so high owing to the small volume in our crystals (~300 × 300 × 50 μm in crystal size). Laue image of the single crystal (Fig. S1b) shows a four-fold rotational symmetry with no indication of structural modulations.

ARPES measurements

Laser-based ARPES data were accumulated using a laboratory-based system consisting of a Scienta R4000 electron analyzer and a 6.994 eV laser (the sixth harmonic of Nd:YVO4 quasi-continuous wave). The data presented are measured at 5 K. The overall energy resolution in the ARPES experiment was set to 1.4 meV. Synchrotron-based ARPES measurements were performed at a high-resolution branch (HR-ARPES) of the beamline I05 in the Diamond Light Source, equipped with a ScientaOmicron R4000 analyzer. The data presented are measured at the photon energy of 55 eV and at the temperature of 10 K. The overall energy resolution was set to ~10 meV in our experiments. In both the laser- and synchrotron-ARPES measurements, a typical cleavage method was used to get a clean surface of the samples: a top post glued on the crystal is hit in situ to obtain a flat surface suitable for the ARPES measurements. The cleavage plane has been confirmed by STM to be along the F/O dopant layers45.

Quantum oscillation measurements

Torque magnetometry experiments were performed with a commercial piezoresistive cantilever (SEIKO PRC-120)46 in pulsed magnetic fields up to 60 T (36 ms pulse duration). The cantilever directly detects the magnetic torque (τ) as the result of the anisotropic magnetization of the sample, τ = M × H, and the magnetic quantum oscillation known as the de Haas-van Alphen (dHvA) oscillation was observed. Figure 1c in the main paper shows the data after subtracting background, which was obtained by fitting a quadratic function to each curve of the raw data in the range of magnetic field between 26 and 60 T.