Superconductivity

The first observation of superconductivity in doped C60 attracted a great deal of attention because of the relatively high transition temperature Tc that was observed, the first observation being in the alkali metal-doped K3C60 with a Tc of 18 K [15.1]. Ever since, superconductivity of doped fullerenes has remained a very active research field, as new superconducting fullerene materials were discovered and attempts were made to understand the unusual aspects of superconductivity in these fascinating materials and the pairing mechanism for the electrons. At the present time, superconductivity has been reported only for C50-based solids, although transport properties down to ~1 K have been measured on alkali metal-doped C70 [15.2] and perhaps higher-mass fullerenes as well.

In this chapter the experimental observations of superconductivity in various fullerene-related compounds are reviewed, followed by a discussion of critical temperature determinations and how Tc relates to the electronic density of states at the Fermi level. Magnetic field phenomena are then summarized, followed by a discussion of the temperature dependence of the energy gap, the isotope effect, and pressure-dependent effects. The leading contenders for the pairing mechanism (the electron-phonon and electron-electron interactions) are then discussed, although it is by now generally agreed that the electron-phonon interaction is the dominant pairing mechanism, giving rise to a mostly conventional Bardeen-Cooper-Schrieffer (BCS) fullerene superconductor [15.3].

15.1. Experimental Observations of Superconductivity

The first observation of superconductivity in a carbon-based material goes back to 1965, when superconductivity was observed in the first-stage alkali metal graphite intercalation compound (GIC) C8K (see §2.14) [15.4]. Except for the novelty of observing superconductivity in a compound having no superconducting constituents, this observation did not attract a great deal of attention, since the superconducting transition temperature Tc in C8K was very low (~140 mK) [15.5]. Later, higher Tc values were observed in GICs using superconducting intercalants (e.g., second-stage KHgC8, for which Tc = 1.9 K [15.6,7]) and by subjecting the alkali metal GICs to pressure (e.g., first-stage C2Na, for which Tc ~ 5 K) [15.8],

As stated above, the early observation of superconductivity in a doped fullerene solid attracted interest because of its relatively high Tc (18 K in I^C^q) [15.1], This work was soon followed by observations of superconductivity at even higher temperatures: in Rb3C60 (Tc = 30 K) [15.9, 10], in RbCs2C60 {Tc = 33 K) [15.11,12], and in Cs3C60 under pressure (Tc = 40 K) [15.13], It is interesting to note that if superconductivity had been found in these alkali metal-doped C60 compounds prior to the discovery of superconductivity in the cuprates [15.14], the alkali metal-doped fullerenes would have been the highest- Tc superconductors studied up to that time. At present, the highest- Tc organic superconductor is an alkali metal-doped fullerene, namely Cs3C60 under pressure (~12 kbar) with Tc ~ 40 K [15.13], breaking a record previously held by the tetrathia-fulvalene derivative (BEDT-TTF)2CuN(CN)2Cl with Tc = 12.8 K under 0.3 kbar pressure [15.15]. Table 8.3 lists the transition temperatures for various fullerene-based superconductors.

For the alkali metal-doped fullerenes, a metallic state is achieved when the -derived level is approximately half-filled, corresponding to the stoi-chiometry M3C60 for a single metal (M) species or M^M^Qq for a binary alloy dopant, as discussed in §14.1. Increases in Tc relative to that of K3C60 have been achieved by synthesizing compounds of the type M^Mj^C«,, but with larger intercalate atoms, resulting in unit cells of larger size and with larger lattice constants as seen in Table 8.3 and in Fig. 15.1. As the lattice constant increases, the intermolecular C60-C60 coupling decreases, narrowing the width of the ilu-derived LUMO band and thereby increasing the corresponding density of states. Simple arguments based on BCS theory of superconductivity yield the simplest BCS estimate for Tc kBTc = 1.130JphexP(-^i-^), (15.1)

where ttJph is an average phonon frequency for mediating the electron pairing, N(Ef) is the density of electron states at the Fermi level, and V is the superconducting pairing interaction, where the product N{EF)V is equal to Aep, the electron-phonon coupling constant. The Debye temperature as measured from a specific heat experiment for the case of fullerenes refers

Fig. 15.1. (a) Early reports on the dependence of Tc for various M,M'3_ xCm compounds on the fee lattice constant a0 [15.16]. (b) More complete summary of the dependence of Tc on aa [15.12], including points provided by pressure-dependent studies of Tc [15.17],

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