1.4.2 Pa$\bar{3}$ A₃C₆₀ Superconductors

When the smaller Na⁺ ion is intercalated into C₆₀, there are two main structural differences with the previous class of A₃ structures[43]. First, the cubic lattice constants, a, are smaller, e.g. the largest of this class is Na₂Cs, $a \approx 14.1$Å compared to the ambient pressure K₃ $a \approx 14.2$Å. Second, again because of the small Na⁺ ionic radius, the C₆₀ can rotate easily to adopt energetically optimal orientations, and the structure at low temperature is orientationally ordered (space group Pa$\bar{3}$), i.e. the rocksalt structure similar to fullerite. The Pa$\bar{3}$ materials have structural phase transitions, from this oriented phase to a high temperature FCC phase where the molecules are completely orientationally disordered. These first-order structural phase transitions occur close to room temperature[44] ($T_s \approx 300$K for Na₂Cs and Na₂Rb). Recently, it has also been found that the C₆₀^-3 molecules in these structures polymerize (at ambient pressure for Na₂Rb [45] and under modest pressure $P \le 3$kbar for Na₂Cs [46]). More recent studies of the pressure dependence are reported in [47] Thus the rocksalt structure below T_s is only metastable, but the polymerization is incomplete probably because it is limited kinetically. In close analogy with the polymeric A₁ structure, polymerization on Pa$\bar{3}$ A₃ involves an orthorhombic distortion of the cubic lattice, and the formation of chains of closely spaced covalently bonded C₆₀^-3 ions.

The superconducting transition temperatures in the Pa$\bar{3}$ systems are low, the highest known is Na₂Cs with a T_c = 12K. T_c is even more strongly dependent on the cubic lattice constant. It was initially thought that this may have been the result of the higher degree of order, but with the new discovery of the polymeric phases has complicated this interpretation. Zhu has suggested that the polymer chains may in fact be the superconducting phase, but recent evidence from the case of Na₂Rb suggests that the polymer chains are not superconducting. If this is correct the strong correlation between T_c and a may be explained by a strong supression of T_c caused by partial polymerization in nominally Pa$\bar{3}$ samples.

In contrast to Rb₃ and K₃, the superconducting properties of the Pa$\bar{3}$ systems have not been well characterized. This may be partially because of the difficulty in making samples with reproducible values of T_c, which could also be a consequence of the metastability of the superconducting Pa$\bar{3}$ structure. The role of orientational disorder has, however, been studied theoretically[6,48]. The possibility that the electronic properties would be significantly different for the ordered Pa$\bar{3}$ structure (as predicted for instance by Mele and Erwin[48] was the original motivation for our study of Na₂Cs. However, the influence of polymerization, discovered after the experiments presented here, has turned out to be more significant, see section 4.3.2.