Main

Although the thermodynamic5 and magnetic properties6 of C6Ca infer the isotropic s-wave superconducting order parameter within the conventional Bardeen–Cooper–Schrieffer theory, substantial deviations and anomalies beyond the conventional framework have been reported by tunnelling spectroscopy7,8 and electron spin resonance experiments9, proposing the strong-coupling superconductivity, the anisotropic gap and/or the multi-component gaps. The discovery of ‘high-Tc’ graphite intercalation compounds has stimulated several theoretical proposals for the superconducting mechanism, ranging from the electronic pairing10 to the coupling to lattice vibrations (phonons)11,12,13,14,15. Recent first-principles calculations11,12,13,14,15 have suggested that the electron coupling to the out-of-plane carbon and intercalant phonons is responsible for achieving higher Tc values, although a clear demonstration to experimentally distinguish various models has not yet been made. This key issue as well as the discrepancy in the nature of the superconducting gap among experiments urgently requires further precise investigations on the momentum and Fermi-surface dependence of the superconducting gap. Although angle-resolved photoemission spectroscopy (ARPES) is most suitable for these investigations, few such experiments have been carried out because of the small superconducting gap as well as the lack of high-quality single crystals. We used a high-quality C6Ca single crystal grown from kish graphite (artificially grown single-crystalline graphite). We have succeeded for the first time in observing the interlayer band and the Fermi-surface-sheet-dependent superconducting gap and electron–phonon coupling.

Figure 1 shows the temperature dependence of the magnetic susceptibility of the C6Ca sample for zero field cooling and field cooling at 10 Oe. The sharp drop in the zero-field-cooling curve confirms that the crystal exhibits superconductivity with the onset Tc=11.5 K.

Figure 1: Characterization of C6Ca single crystal.
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Magnetic susceptibility of C6Ca as a function of temperature for zero field cooling (ZFC) and field cooling (FC) at 10 Oe. Inset: Photograph of a C6Ca single crystal used for ARPES measurements.

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Figure 2a,b shows the experimentally determined valence-band structure along two high-symmetry lines ΓK and ΓM. Although the overall band structure looks similar between graphite and C6Ca, the band dispersion of C6Ca is shifted as a whole towards high binding energy by 1.0–1.5 eV, indicating that electrons are certainly doped into pristine graphite by Ca intercalation. A small electron pocket that appears near the Fermi level (EF) at the K point in C6Ca is ascribed to the C 2pπ* band, which is above EF in pristine graphite and is shifted down below EF by electron doping16,17,18. It is noted that the overall valence-band dispersion basically follows the periodicity of the Brillouin zone for graphite rather than that for C6Ca, possibly owing to the relatively weaker periodic potential of C6Ca with the symmetry than the potential of bulk graphite. Figure 2c shows the Fermi surface of C6Ca determined by ARPES, compared with that of graphite (Fig. 2d). The Fermi-surface topology of C6Ca is drastically different from that of graphite. In C6Ca, we find two different Fermi surfaces, a circular Fermi surface at the Γ point and a triangular Fermi surface at the K point, whereas only one tiny Fermi surface is observed at the K(H) point in graphite19. The triangular Fermi surface at the K point originates in the π* band and is well explained in terms of the simple rigid shift of the chemical potential due to the electron doping20. In contrast, the small Fermi surface observed at the Γ point is not explained by the simple rigid shift of graphite bands or the folding of the π* band due to the superstructure of Ca intercalants, because the shape and size of the Fermi surface are distinctly different from those of the π* Fermi surface. On the other hand, the band-structure calculations10,11,12,13,14,15 have predicted an extra band at the Γ point in C6Ca named the interlayer band, which has a sizable contribution from the intercalant states and produces a small free-electron-like spherical Fermi surface at the Γ point. Considering a good agreement in the location and the shape as well as the superconducting-gap size (discussed later in detail), we assign the small Fermi surface observed at the Γ point to the interlayer band in C6Ca. To our best knowledge, this is the first direct observation of the interlayer band in graphite intercalation compounds.

Figure 2: Comparison of electronic structure and Fermi surface between C6Ca and graphite.
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a,b, Valence-band structure of C6Ca (a) and graphite (b), determined by plotting the ARPES spectral intensity as a function of wave vector and binding energy. Expansion near EF is also shown in the upper panel. c,d, Fermi surfaces for C6Ca (c) and graphite (d), determined by plotting the ARPES spectral intensity integrated within ±10 meV with respect to EF and folding with the hexagonal symmetry. Solid red and white lines in c are surface Brillouin zones of graphene and C6Ca, respectively.

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Figure 3a shows ARPES spectra near EF of C6Ca at 6 K measured at two representative Fermi vectors (kF) on the circular Fermi surface at the Γ point and the triangular Fermi surface at the K point, respectively. The spectral intensity shows a sudden drop at 80 meV on the circular Fermi surface (point A), whereas a small but clear dip is observed at 170 meV in the spectrum measured on the triangular Fermi surface (point B). The energy position of the 170 meV dip is similar to that of the dispersion kink observed in graphite21 and C6Ca (ref. 22). We find that the energy position of the dip does not vary in the momentum region around the kF point. This is not explained by the presence of another band located around the dip energy, but is reminiscent of the strong many-body effects observed in high-Tc copper oxides23,24 and Ba0.67K0.33BiO3 (ref. 25). In fact, as seen in Fig. 3a, the Eliashberg function α2F(ω) calculated for C6Ca (ref. 11) shows dominant peaks at 50–75 meV and 160–180 meV originating in the out-of-plane and the in-plane vibrations of carbon atoms, respectively, in good agreement with the anomalies in the ARPES spectra. This suggests that electrons on the circular Fermi surface at the Γ point are strongly coupled to the out-of-plane vibrations, whereas those on the triangular Fermi surface at the K point are coupled dominantly with the in-plane phonons. This experimentally demonstrates that the interlayer electrons strongly interact with the surrounding lattice unlike in the free-electron picture, as predicted from first-principles calculations13,14. The reason π* electrons at the K point are only weakly coupled to the out-of-plane phonons may be the antisymmetry of the wave function with respect to the graphene layer11. On the other hand, the interlayer band forming the circular Fermi surface at the Γ point is expected to be strongly coupled to the out-of-plane phonons owing to the symmetry14. A spectral dip related to the coupling with the Ca vibrations is not clearly observed in Fig. 3a, possibly because the dip is broad (20–30 meV) compared with the Ca phonon energy (15 meV).

Figure 3: Electron–phonon coupling and superconducting gap in C6Ca.
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a, ARPES spectra of C6Ca measured at 6 K on (A) the circular Fermi surface and (B) the triangular Fermi surface (points A and B in Fig. 2c, respectively), compared with the calculated Eliashberg function α2F(ω) as a function of binding energy11. Filled triangles denote the characteristic energy scales where the spectrum shows a distinct anomaly. b, ARPES spectra of C6Ca in the vicinity of EF at points A and B, measured at temperatures below/above Tc (6 K and 15 K). c, Top: Comparison of ARPES spectrum at 6 K among points A, A′, B and B′. Bottom: Numerical fit (black curve) to the 6 K spectrum at point A (red circles) with the Dynes function26 multiplied by the Fermi–Dirac function at T=6 K convoluted with a Gaussian taking into account the instrumental resolution.

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Figure 3b shows ultrahigh-resolution ARPES spectra near EF of C6Ca measured at the same two points as in Fig. 3a at temperatures below/above Tc. At point A, the midpoint of the leading edge in the spectrum at 6 K is shifted towards high binding energy by approximately 0.8 meV with respect to EF, whereas the spectrum at 15 K has the midpoint at EF. This clearly indicates the opening/closing of a superconducting gap as a function of temperature. On the other hand, at point B, the midpoint of the leading edge is located at around EF even at 6 K, and the spectrum shows a simple temperature dependence to obey the Fermi–Dirac function, suggesting the absence or the very small magnitude of the superconducting gap. This marked difference is better illustrated in Fig. 3c, where the spectra at 6 K at points A and B are directly compared. To clarify the possible anisotropy of the gap in each Fermi-surface sheet, we also plot the 6 K spectra measured at points A′ and B′ on the same Fermi surfaces but on different high symmetry lines (Fig. 2c), because the anisotropy, if it exists, should be largest between points A and A′ (B and B′). We note that the ARPES technique basically observes the gap averaged over kz (k perpendicular to the surface), so that it measures the anisotropy of the gap in the kx–ky plane. As seen from Fig. 3c, the leading edge at point A′ (B′) almost coincides with that of point A (B). This suggests that the anisotropy of the superconducting gap is very small in both circular and triangular Fermi surfaces, although the gap size is markedly different between these two Fermi surfaces. To estimate the size of the superconducting gap, we numerically fit the spectrum using the Dynes function26. The representative result for point A is shown in Fig. 3c. The estimated gap size Δ at 6 K is 1.8±0.2 and 2.0±0.2 meV at points A and A′, respectively. The reduced gap value of 2Δ(0)/kBTc determined by assuming the mean-field temperature dependence is 4.1±0.5, indicating intermediate- to strong-coupling character. The first-principles calculation13 has predicted a similar gap value. On the other hand, at points B and B′, the estimated superconducting-gap size is 0.2±0.2 meV. These results suggest that the deviation from the single isotropic s-wave gap function in the tunnelling density of states7, interpreted in terms of the anisotropic s-wave gap, is not explained by the anisotropy of the gap within the interlayer Fermi surface at the Γ point, but is actually influenced by a smaller superconducting gap of other Fermi surfaces, most likely the π* Fermi surface. The reported deviation of the specific heat27 from the single isotropic s-wave behaviour13,15 would also be explained by this Fermi-surface dependence of the superconducting gap.

The present results demonstrate that the coupling of electrons in the interlayer band with the out-of-plane phonons is essential to realize superconductivity in C6Ca, whereas simple electron doping into the π* band of graphene layers may not lead to superconductivity at such a high temperature. The next challenge is to clarify the role of intercalant (Ca) phonons, which have been theoretically proposed to enhance the Tc value11,12,13,14,15.

Methods

High-quality C6Ca single crystals were grown by heating kish graphite mixed with molten lithium–calcium alloy at around 350 ∘C for 6 days under high vacuum28. The typical size of the crystals was 3×3×0.5 mm3. ARPES measurements were carried out using an SES-2002 spectrometer with a high-flux discharge lamp and a toroidal grating monochromator at Tohoku University. As the sample is very unstable in the atmosphere, almost all of the steps such as sample mounting were done in a glove box filled with Ar gas. The superconducting volume fraction is estimated to be 90±10% at 5 K, higher than previous reports1,28. The X-ray diffraction measurement confirmed that inclusion of C6Li is at most 5%. The crystal was cleaved in situ along the (0001) plane in an ultrahigh vacuum better than 2×10−11 torr to obtain a clean surface for ARPES measurements. The He IIα (40.814 eV) resonance line was used to excite photoelectrons. The energy and angular (momentum) resolutions were set at 4.5 meV and 0.2∘(0.01 Å−1), except for in the measurement of the wide valence-band region (ΔE=16 meV). The temperature of the samples was controlled to remain stationary within ±0.1 K during measurements by monitoring with a silicon diode sensor embedded below the sample. The Fermi level of the sample was referenced to that of a gold film deposited onto the sample substrate. No degradation of the sample surface was observed during the measurements. We checked the reproducibility of the data by measuring several samples.