Conclusions

One of the recurring themes in the GIC superconductivity literature has been the question of whether the graphite or alkali metal layers are superconducting in C₈K.[120,234] The origin of the notion that either the graphitic or alkali electrons must be responsible for the superconductivity is a bit hard to fathom. After all, no one ever discusses the superconductivity of the transition metal layers of the transition metal dichalcogenides. The case that both graphitic and intercalant electrons contribute to GIC superconductivity[4] would seem to be even clearer than the equivalent TMDC question since neither the alkali metal nor the graphite is separately superconducting. In the MHg-GIC's, the starting alloys are superconducting by themselves. However, the potassium and mercury planes cannot be solely responsible for the superconductivity of the compound, since otherwise T_c would be expected to decline monotonically with increasing stage. In fact, as discussed in Section , T_c of the KHg-GIC's has the opposite trend from that predicted by the proximity effect.

Frequent reference has been made to the properties of the superconducting transition metal dichalcogenides in this work, especially to NbSe₂. In Chapter , a progression in increasing anisotropy was proposed that began with bulk Nb, followed by NbSe₂, alkali-intercalated NbSe₂, and ended by organic-molecule intercalated TMDC's. When this project first began, there was a natural tendency to compare the alkali-intercalated GIC's with the alkali-intercalated TMDC's and the acceptor GIC's with the organic-intercalated GIC's. This comparison is a bit misleading, though. The point that has been overlooked in this juxataposition is the rather obvious fact that NbSe₂ is already superconducting. Because the properties of the TMDC's are not strongly modified by alkali intercalation,[266] in that case it is perhaps appropriate to speak of the superconductivity of the NbSe₂ sandwiches.

What is the superconducting sandwich in the case of the GIC's? The line of reasoning presented here suggests that perhaps the carbon-intercalant-carbon sandwich is superconducting; or perhaps even more carbon planes are involved. If superconductivity is a joint property of both carbon and intercalant planes, perhaps the higher T_c of C₈KHg than C₄KHg is not the great surprise that it is sometimes made out to be. There is no reason that adding more carbon layers between the KHg trilayers should depress T_c if the carbon layers are also superconducting. Those sceptics who insist that mercury must dominate superconductivity in the KHg-GIC's should reflect on the fact that the critical fields of C₆K[13] are quite similar to those of C₄KHg. C₆K also has a T_c of 1.5 K.[13]

Iye and Tanuma projected that a 3D-2D crossover might occur for the stage 3 KHg-GIC, where they estimated that xi_{|| ^c} I_c.[120] One can easily see that this estimate should not be appropriate if the carbon planes also participate in superconductivity. If the carbon planes that are adjacent to the intercalant layers are also superconducting, then it is their separation that should determine the coupling dimensionality. Presumably at a high enough stage the superconducting packages would be expected to decouple, but it is not clear what the correct length scale to describe this decoupling would be.

Will a 3D-2D coupling-dimensionality crossover ever be seen in GIC's? The analogy with the TMDC's helps to clarify this question. When one takes a superconducting TMDC and intercalates it with an organic molecule, the molecules act as electron donors.[243] Nonetheless, the organic molecules partially decouple the TMDC layers, raise the resistivity anisotropy,[243] and allow 2D superconductivity at low temperatures.[46] Molecular intercalants into GIC's act as electron acceptors, not donors.[67] As in the TMDCIC's, molecular intercalants in GIC's act to decouple the layers and raise the resistivity anisotropy.[166] The analogy with the TMDCIC's leads one to suppose that acceptor should be 2D superconductors at a sufficiently low temperature. However, GIC's with molecular intercalants appear not to be superconducting.[64]

The lack of superconductivity in the acceptor GIC's is not that surprising if one believes that the cooperation of carbon and intercalant electrons is required. The intercalant bands are usually the major contribution to the c-axis conductivity, so the high resistivity anisotropy in these materials implies a low carrier density at the Fermi level in the intercalant bands. In fact, recent work, both experimental[166] and theoretical,[229,230] suggests that hopping conduction is responsible for c-axis transport in acceptor GIC's, at least for stages greater than one. Perhaps band conduction along the c-axis is a necessary condition for superconductivity in GIC's. That band conduction is not a sufficient condition for superconductivity is shown by the case of C₆Li, which has the lowest resistivity anisotropy of any GIC,[166], and yet is not superconducting.[64] This problem deserves further investigation.

If one believes following Al-Jishi[4] that the presence of intercalant electrons at E_F is necessary for superconductivity, then one possible implication may the non-existence of 2D superconductivity in GIC's. In other words, when one decouples the metallic planes with insulating intercalants in the TMDC's, one gets 2D superconductivity because the individual TMDC planes are themselves superconducting. In contrast, when one decouples the metallic carbon planes with insulating intercalants in the GIC's, one destroys superconductivity along with three-dimensionality. The Al-Jishi model may imply that three-dimensionality is needed for superconductivity in GIC's. These ideas lead back to the fundamental question of the nature of superconductivity in GIC's.