Phonons in Lattice and Structural Dynamics

Abstract

The critical temperature () of superconductivity in compounds is generally lower smaller with alkali atoms (A). Furthermore decreases with applied pressure. In the BCS model, these trends are explained by the lower density of states at the Fermi level for a decreased lattice constant (R). There is more than one counterexample, however, suggesting that BCS does not give the whole truth. The most important one is that the compound with the largest lattice constant, , is not superconducting at all at ambient pressure. In this paper we derive a novel model where a negative lattice contribution to HubbardU, proportional to1/R, is taken into account. It is possible to explain why compounds with A = Li, and Na have a low or are not superconducting at all, and why is superconducting only at applied pressure and then with the highest of all alkali fullerides. It is concluded that the density of states mechanism derived in the BCS model is in doubt. Nevertheless superconductivity in depends on electron-phonon coupling. The dominating phonon is the bond stretching phonon, a breathing phonon for the whole fullerene molecular ion.