Unconventional Superconductivity of Alkali-doped Fullerenes

The superconductivity of the alkali-doped fullerenes ($A_3$C$_{60}$, $A$ = alkali metal) has been so far discussed within the standard theory of superconductivity developed by Bardeen, Cooper and Shrieffer (BCS), even thought, they exhibit relatively high critical temperatures (up to $T_c = 32$ K). However, after our recent high-pressure measurements on Cs$_3$C$_{60}$ such description became questionable. We have shown that the superconducting phase of $A_3$C$_{60}$, in fact, borders the antiferromagnetic insulating phase (AFI), commonly observed for high-temperature superconductors like cuprates or pnictides. In addition, we also increased the maximal $T_c$ to 38 K. To investigate this peculiar superconductivity close to the border with AFI state we employed nuclear magnetic resonance technique on Cs$_{3-x}$Rb$_{x}$C$_{60}$ and on Cs$_3$C$_{60}$ at various high pressures. Our results could not be correctly explained either by the standard BCS or the extended BCS that includes electron-electron repulsion interaction - the Migdal-Eliashberg theory. Far better agreement is obtained by the Dynamical Mean Field Theory. Due to similarity with other unconventional superconductors these results could also be relevant to other unconventional high-temperature superconductors.