Researchers investigate the competition between the electron-vibron interaction (interaction with the Jahn- Teller phonons) and the Coulomb repulsion in a system with local pairing of electrons on the triply degenerate lowest unoccupied molecular orbital (LUMO). The electron-vibron interaction radically changes conductivity and magnetic properties of alkali-doped fullerides AnC60, which should be antiferromagnetic Mott insulators: we have found that materials with n = 1, 2 and A = K, Rb are conductors but not superconductors; n = 3 and A = K, Rb are conductors (superconductors at low temperatures), but with A = Cr are Mott insulators; n = 2, 4 are nonmagnetic Mott insulators. We have shown that superconductivity, conductivity and insulation of these materials have common nature. Based on the alkali-doped fullerides they propose a hypothetical material with a significantly higher critical temperature using the model of superconductivity with the external pair potential formulated in another paper (Arxiv - BCS theory with the external pair potential)
Consideration of a hypothetical substance, where interaction between (within) structural elements of condensed matter (molecules, nanoparticles, clusters, layers, wires etc.) depends on state of Cooper pairs: an additional work must be made against this interaction to break a pair. Such a system can be described by BCS Hamiltonian with the external pair potential term. In this model the potential essentially renormalizes the order parameter: if the pairing lowers energy of the structure the energy gap is slightly enlarged at zero temperature and asymptotically tends to zero as temperature rises. Thus the critical temperature of such a superconductor is equal to infinity formally. For this case the effective Ginzburg-Landau theory is formulated, where the coherence length decreases as temperature rises, the GL parameter and the second critical field are increasing functions of temperature unlike the standard theory. If the pairing enlarges energy of the structure then suppression of superconductivity and the first order phase transition occur.
In this model the potential essentially renormalizes the order parameter so that if the pairing lowers the energy of the molecular structure, then the energy gap tends to zero asymptotically as 1/T with increasing of temperature - Eq.(31). Thus, formally, in this model the critical temperature is equal to infinity, however the energy gap remains finite quantity. For practical realization of this model we propose a hypothetical superconductor on the basis of alkali-doped fullerides using endohedral structures He@C60, where a helium atom is in the center of each fullerene molecule. In an endohedral fullerene the helium atom interacts with a carbon cage by Van der Waals force. The interaction depends on a state of excess electrons on surface of the molecule. They have shown that energy of the molecule if the excess electrons on its surface are in the paired state (7)(when two electrons are in a state with the same quantum numbers) is lower than the energy if the electrons are in the normal state (8)(when the electrons are in a state with different quantum numbers and maximal spin). Thus difference of the energies of the molecules plays a role of the external pair potential.