Strong-coupling superconductivity due to soft boson modes in MgB₂, cuprates, borocarbides and some heavy fermions

We report micro-Raman measurements that reveal a low-energy soft mode at 16-19 meV in MgB_2 which becomes sharper in the superconducting state. With a boson spectrum based on this mode we reproduce, within Eliashberg theory, the T_c, the T-shape of the NMR relaxation rate as well as unusual dip-hump features in available tunneling data. We compare MgB_2 to cuprates, borocarbides and UPd_2Al_3, where we identify soft bosonic modes at energies which scale with their T_c suggesting that all these materials are very strong coupling superconductors to soft bosonic modes, that are possibly precursors of quantum instabilities.