Fullerene-based materials have emerged as a significant class of superconductors since the discovery of superconductivity in alkali-doped C60 compounds. These materials exhibit unique electronic and structural properties that make them distinct from conventional superconductors. The interplay between molecular orbitals, crystal symmetry, and electron-phonon coupling in fullerene superconductors provides a rich framework for understanding high-temperature superconductivity in molecular systems.
The critical temperature (Tc) in fullerene superconductors varies significantly with doping and crystal structure. The highest reported Tc in alkali-doped C60 is 33 K in Cs3C60 under high pressure, while at ambient pressure, Rb3C60 and Cs3C60 exhibit Tc values of 29 K and 28 K, respectively. The trend in Tc correlates with the lattice parameter, where an expanded unit cell enhances electronic density of states at the Fermi level and strengthens electron-phonon coupling. Smaller alkali ions like K+ result in lower Tc (19 K in K3C60), demonstrating the importance of intermolecular spacing in optimizing superconducting properties.
Crystal structure plays a crucial role in determining the superconducting behavior of fullerene-based materials. Undoped C60 crystallizes in a face-centered cubic (fcc) structure, but upon alkali metal intercalation, it transforms into a body-centered cubic (bcc) or face-centered cubic (fcc) arrangement depending on the dopant concentration. The A3C60 stoichiometry (where A = alkali metal) is particularly significant, as it introduces three electrons into the t1u LUMO band of C60, creating a half-filled conduction band. The orientationally ordered or disordered states of C60 molecules also influence electronic properties, with the merohedral disorder in fcc structures affecting electron pairing mechanisms.
The superconducting mechanism in fullerene-based materials is primarily phonon-mediated, with strong coupling to intramolecular vibrational modes. The high-frequency C60 molecular vibrations, particularly the Hg modes around 1500 cm-1, contribute significantly to the pairing interaction. Electron-phonon coupling constants (λ) in A3C60 compounds range from 0.5 to 1.0, placing them in the strong-coupling regime. The Coulomb pseudopotential (μ*) is relatively small (0.1-0.2) due to the large molecular size and weak on-site Coulomb repulsion. This combination of strong electron-phonon coupling and reduced Coulomb repulsion enables relatively high Tc values compared to conventional BCS superconductors.
Pressure effects on fullerene superconductors reveal important insights into their electronic structure. Application of hydrostatic pressure initially increases Tc in A3C60 compounds by enhancing intermolecular hopping and electronic bandwidth. However, beyond an optimal pressure, Tc decreases due to band broadening that reduces the density of states. The pressure dependence of Tc follows a dome-shaped curve, similar to high-Tc cuprates, suggesting competing interactions in the superconducting state. The maximum Tc occurs at a balance between increased electron-phonon coupling and decreased electronic correlations.
The electronic structure of doped fullerenes exhibits several unique features. The t1u-derived conduction band has a width of approximately 0.5 eV, placing these materials in the intermediate coupling regime between narrow-band and wide-band limits. The Fermi surface consists of nearly spherical sheets centered at the Γ point, favoring isotropic superconducting gaps. Band structure calculations show that the degeneracy of the t1u orbital is crucial for maintaining high density of states at the Fermi level, while Jahn-Teller distortions could potentially compete with superconductivity.
Comparative studies of different fullerene derivatives provide additional insights into superconducting mechanisms. Endohedral doping, where metal atoms are encapsulated inside the C60 cage, produces distinct electronic properties compared to interstitial doping. Compounds like La@C60 exhibit modified electron-phonon coupling due to charge transfer between the encapsulated atom and the carbon cage. However, these systems generally show lower Tc values than alkali-doped C60, highlighting the importance of three-dimensional intermolecular interactions in achieving higher transition temperatures.
The isotope effect in fullerene superconductors provides direct evidence for phonon-mediated pairing. Studies with 13C-enriched C60 show an isotope exponent α ≈ 0.3, intermediate between the BCS value (0.5) and that observed in high-Tc cuprates. This suggests that while phonons dominate the pairing mechanism, other factors such as electronic correlations may play a secondary role. The relatively large isotope effect also confirms the importance of high-frequency intramolecular vibrations in the pairing interaction.
Recent developments in fullerene superconductivity include exploration of expanded cage structures and heteroatom-doped fullerenes. Larger fullerenes like C70 and C82 show modified superconducting properties due to their lower symmetry and altered electronic structure. However, their Tc values remain lower than C60-based compounds, reinforcing the importance of high molecular symmetry for optimal superconductivity. Nitrogen- or boron-doped fullerenes introduce additional carriers but often at the expense of reduced crystal quality and coherence length.
The superconducting coherence length in fullerene materials is typically 2-4 nm, much larger than in cuprates but smaller than in conventional superconductors. This places fullerene superconductors in the clean limit with relatively weak vortex pinning. The upper critical field Hc2 reaches 30-50 T, making these materials potentially useful for high-field applications. The anisotropy of superconducting properties is relatively small due to the cubic symmetry of the crystal lattice, though slight deviations occur in non-cubic phases.
Future research directions in fullerene superconductivity include precise control of molecular orientation, exploration of new doping strategies, and investigation of interface effects in thin films. The development of air-stable fullerene superconductors remains a challenge, as most alkali-doped compounds are highly sensitive to moisture and oxygen. Advances in encapsulation techniques and alternative doping methods may address these stability issues while potentially enhancing superconducting properties.
The study of fullerene-based superconductors continues to provide valuable insights into molecular superconductivity mechanisms. Their tunable electronic structure, strong electron-phonon coupling, and relatively high Tc values make them an important model system for understanding unconventional superconductivity. While challenges remain in materials processing and stability, the unique properties of these carbon-based superconductors offer potential for both fundamental research and practical applications in quantum technologies and energy transmission.