LAUSR

It has been a long-standing puzzle why electrons with repulsive interactions can form pairs in unconventional superconductors. Here we develop an analytic solution for renormalization group analysis in multiband superconductors, which agrees with the numerical results exceedingly well. The analytic solution allows us to construct soluble effective theory and answers the pairing puzzle: electrons form pairs resonating between different bands to compensate the energy penalty for bring them together, just like the resonating chemical bonds in benzene. The analytic solutions allow us to explain the peculiar features of critical temperatures, spin uctuations in unconventional superconductors and can be generalized to cuprates where the notion of multibands is replaced by multipatches in momentum space.